- Email: [email protected]
Progress in nonlinear optical materials for high power lasers
Prog. CryStal Growth and Charact. 1990. Vol. 20. pp. 5,9-113
0146.-3535/90 $0-00 ÷ .50 13¢J0 Pergamon Press pie
Printed in Great Britain.
PROGRESS IN NONLINEAR OPTICAL MATERIALS FOR HIGH POWER LASERS* D. Eimerl, S. Velsko, L. Davis and F. Wang Lawrence Livermore National Laboratory, P.O. Box 5808. Livermore, California 94550, U.S.A.
ABSTRACT Over the last few years, substantial progress has been made at the Lawrence Livermore National Laboratory tn nonlinear materials for high power laser applications.
Specifically, we are developing materials for
frequency conversion of lasers used in laser drtven, thermonuclear fuston experiments and in high average power laser systems.
He have developed
new experimental procedures for f u l l y characterizing the linear and nonllnear optical properties of mtcrocrystals.
Using new theoretical
results we have developed a systematic method of selecting and optimizing nonlinear crystals for high-power and high-average-power laser applications.
Our molecular engineering strategy for developing new
materlals for the fusion application has resulted in the discovery of several new materials with more attractive parameters than KDP.
*Hork performed under the ausptces of the U.S. Department of Energy by the Lawrence Ltvermore Natlonal Laboratory under Contract No. H-7405-ENG-48.
59
60
D. Eimerl et al.
CONTENTS PBge
I
Introduction
60
2
Selectlon and Optimizatlon of Nonllnear Materials
62
3
ThresholdPower
69
4
Databaseon Nonllnear Optical Materials
80
5
Microcrystal Characterization Techniques
81
6
DoubleSplndle Stage Refractometer
83
7
The Nonllnear Optical Gonlometer
87
8
OrganicMaterlals for ICF Applications
97
g
Optlcal Properties of Chiral Acid Crystals
101
lO
L-Arginine Phosphate
103
II
High Average Power Materials
106
12
Future Directions
107
Appendix: 3acobl E11iptic Function Subroutines
I.
II0
Intro~vction Over the last few years, experiments in laser-driven inertially
confined fusion (ICF) have shown clearly that targets use the drive laser energy more efficiently when irradiated with short wavelength lasers. 1'2
However, the efficiency of the ICF laser driver tends to
decrease at shorter wavelengths. The optimum wavelength will be a compromise between target efficiency and laser technology, and will almost certainly be in the range 250 nm-500 nm.
The most effective laser
architecture to reach this range uses harmonic generation of an efficient near-lnfrared laser source. KDP (Potassium Dihydrogen Phosphate),3 the material currently used in Nd:glass lasers for ICF research, is not ideal for future ICF drivers because i t has a low threshold for optical damage and its conversion efficiency is compromised by a combination of its acceptance angle and nonlinear coefficient.
To be economically viable, future Nd:glass or
other near-IR ICF lasers (which are very large) will require harmonic generators which are both very efficient, and cost-effectlve.
He have
therefore organized an investigation of new nonlinear materials, with the goal of developlng, and eventually deploylng, a materlal which is more
61
Nonlinear optical materials ~ r high power las41rs
e f f i c i e n t and l e s s expensive than KDP. At least one such material has been i d e n t i f i e d (d-LAP, deuterated 1-argtntne phosphate) 4 and i s c u r r e n t l y under development.
Materials whtch improve on KDP can be used
In many other applications where htgh power lasers are Involved.
He
therefore expect that despite the r e l a t i v e l y narrow near-term focus, progress In the ICF application w t l l also bring inexpensive new materials for many other applications. For the ICF appltcatlon, crystals grown etther by aqueous solutton or by low temperature Brtdgman methods are l i k e l y to be the most economical, and tn thts category, we have i d e n t i f i e d several classes of molecular crystals with appropriate properties. In p a r t i c u l a r , we are Investigating molecular crystals based on amtno acids. These molecules include both a chtral center, and a r e l a t l v e l y strong harmonic-generating u n i t , and are t o n i c a l l y bonded.
Most are more nonlinear than KDP, and
they possess a wtde range of btrefrtngence (0.01 to 0.15). have the advantage of being o p t i c a l l y btaxtal.
They also
Using new experimental
methods, characterization of Individual crystals ts carried out on I r r e g u l a r l y shaped mtcrocrystals 0.05 to 0.25 mm tn size. From such samples we measure the r e f r a c t i v e indices from below 400 nm to 1100 nm, and carry out a d i r e c t determination of the phasematchtng locus, and the nonlinear coupltng and angular acceptance along that locus. He can also measure the temperature bandwidth, i f needed.
By using such eastly
obtainable samples, we avoid the need for time-consuming crystal growth of a large number of materlals, and are able to concentrate crystal growth activity on Just those materials which are promising. Using these methods, we have Identlfled several salts of amino acids which are better than KDP. These Include LAP, and other arginlne salts, such as the fluorlde, chlorlde, bromide, and acetate. There are in fact many crystals in this class, and many of them are efficient nonlinear materials for hlgh power lasers. In addition to the ICF appllcatlon,
we are also Interested In
developlng nonllnear materlals for hlgh average power applications. Under these conditions thermal distortions arise from the 11near optlcal absorption of the crystals, and In general the beam quality of the laser source degrades, albelt slowly, with increasing average power. Thus high average power calls for nonllnear materials with very low absorption, high resistance to thermal fracture, and a tolerance for thermooptlc effects and imperfect beam quality.
For the average power appllcation,
we have concentrated on characterlzlng the commonly avaliable materlals rather than developlng new ones. The level of characterization required
O. Eimerl et al.
62
Is quite extenslve, 5 and is exemplified In our work on barium borate. 6 This paper reviews the research results at the Lawrence Llvermore National Laboratory In new nonllnear materials and the strategy we have developed to Identify new nonllnear materials for ICF applications.
This
paper addresses both the required materials parameters and figures of merit, ? and discusses new microcrystal experimental techniques.
We
also review our recent work on new, inexpensive, frequency conversion materials for ICF such as the arginines.
Finally, we compare several
common nonlinear materlals for high average power applicatlons. 2.
Selectlon and ODtlmlzatlon of Nonlinear Materials I t is we11-known that the efficiency of frequency conversion is very
small unless the process Is phase-matched.8 Phasematching means that the output waves originating from all points within the nonlinear crystal are in phase wlth each other Just as they leave the crystal.
For (Type
I) second-harmonlc generation, phasematching requires that the f i r s t and second harmonic electromagnetlc waves have the same phase velocity; in other types of frequency conversion I t gives a more complex relationship between the interacting waves' velocities.
However, because of wavelength
dispersion, the refractive Indices of optically Isotroplc materials Increase as the wavelength decreases, and phasematchlng is not posslble. The most common way to achieve phasematching is then to use a blrefrlngent crystal, where the phase veloclty typically depends on the direction of propagation of the wave and on its polarlzatlon.
By
adjusting the polarizations and the direction of propagation I t is posslble to use the blrefringence to compensate for the natural wavelength dispersion.
In fact this is typlcally how nonlinear crystals
are configured for frequency conversion. For a partlcular direction of propagation, the Interaction Is exactly phasematched, but for neighboring directions the waves no longer have the same velocities and the conversion efficiency is reduced. The range of angles over which the conversion efficiency remains high is called the acceptance angle of the crystal, and i t is strongly anisotropic. Referring to Fig. l, we define the sensitive plane to be the horizontal plane, and the insensitive plane to be vertlcal.
The acceptance angle is
very large for beam divergence In the insensitive plane, but in the sensitive plane I t Is typlcally small, about I mrad for a crystal I cm in length.
Consequently, the direction and beam divergence of the laser in
the sensitive plane must be controlled precisely to obtain high conversion efficiency.
Moreover, the acceptance angle of the crystal
63
Nonlinear optical materials for high power lasers e
Di
.
Crystal dimensions for frequency conversion using collimated beams. The larger dimension, Ds, lies in the plane wtth the smallest angular sensitivity. The acceptance angle In the orthogonal plane, containing DI, is about 100 mrad or larger for both unlaxlal and blaxlal crystals.
decreases as the length of the crystal increases; i f I t is I mrad for a I cm crystal, I t Is 0.5 mrad for a 2 cm crystal.
The longer the crystal,
the smaller the beam divergence in the sensitive plane must be to maintain high conversion efficiency. This has profound consequences. Diffraction provides a minimum value for the beam divergence, which is typlcally l mrad for a beam of wavelength 1064 nm and diameter 1 mm. For the typlcal nonllnear crystal the acceptance angle is about I mrad for a 1 cm long crystal; a crystal longer than I cm w111 therefore be less efficient, in general.
To be
efficient, a crystal with this sensitivity to beam mlsorlentatlon or divergence must be sufficiently nonlinear to convert the laser beam in less than I cm. longer than this.
Crystals with less angular sensitivity can of course be In general, high efficiency requires that the
conversion process proceed to saturation well before the effects of phase-mlsmatch are evident.
D. Eimerl et al.
64
He have completed a thorough study of the conditions under which e s s e n t i a l l y collimated beams5 have a high conversion e f f i c i e n c y .
The
equations for the general three wave mixing experiment, where two waves of frequencies = and f2 = mix to generate a wave at frequency (l+f2)~ are as follows: df/dz dgldz -
- C g*h e-iakz
(1)
- f2.C f*h e-iakz
(2)
+i&kz e
(3)
dh/dz = (1+f2).C fg
where the complex f i e l d amplitudes are f,g and h for the three frequencies u, f2 u, and (I+f2)~.
Thus for third harmonic generation,
f2 " 2, whereas for second harmonic generation f2 = I.
I t is
convenient to normalize the fields so that the intensity of the waves are F - f ' f , etc., with no other factors.
With this f i e l d normalization, the
nonlinear coupling C Is C I 2x(2Z0)112.deff/Xf.[ nfngnh] I/2
(4)
where Z0 = 377 Ohms is the impedance of free space, and the n's are the refractive Indices of the three waves. The term Ak in the exponent is the wavevector mismatch between the three waves.
In general Ak
receives contributions from beam divergence, temporal bandwidth, crystal homogeneity and temperature Inhomogenelty. Its minimum value is determined by the d l f f r a c t l v e contribution to the beam divergence. Ak
=
k f + kg
kh
-
Beae + other terms
Thus (5)
(6)
where AO is a measure of the beam divergence. The conversion efficiency n, is a function of only two parameters, in general.
These are the drive, ,10, and the dephaslng 6, defined
as follows. no =
f2.C2.12.(F+G)
(7)
6
(I12).Ak.I
(B)
=
Nonlinear optical materials for high power lasers
where 1 is the crystal length.
65
He have
(9)
n = nma x sn2 ([nolnmax ]I12, n~ax ) where sn Is a Jacobl e111ptlc functlon. (An algorlthm for the Oacobl e111ptlc functions which Is sultable for small desk-top computers Is Included In the Appendix.) As the argument of the 3acobl sn function increases, the efflclency peaks, and then falls, followlng Its perlodlclty. The maximum efficiency Is
112 nmax = 1 + 1/2x - [1Ix + 1/4x 2]
,
(10)
where
X - f2(F + G) C2/Ak 2.
(11)
The crystal length, at whtch the maximum efficiency ts achieved ts obtained from the value of no at the peak of the Jacob| function, namely at 2 2 nolnma x = K(nma x)
(12)
Thus the optimum crystal length lop t is given by •
f2.C 2 l~pt.(F+G)
2
m
nmax K(nmax)
2
(13)
These equatlons show how to optimize the crystal length, for a beam of glven Input Intenslty I = (F+G), and effectlve mismatch, &k.
There
are several slmple scallng laws contained in these results for nma x and lop t. Referring to Fig. I, let the beam or crystal aperture be D s |n the sensltlve d|rectlon, and D I In the Insens|tlve dlrectlon, and let the crystal length be I. The Intens|ty I = P/DsD I, where P is the total power in the laser beams (Intenslty.area product), and the relevant beam divergence Is &e = Q.X/D s. where 0 Is roughly the ratio of the beam divergence to that of a dlffractlon-11m|ted beam of the same aperture. In terms of the total power P and the beam quallty O, the drlve and dephaslng are
no = 8 =
f2.C2.[ 12/Ds0 i ] P (ll2).6e.Xf.CllDs).O
(14) (15)
D. Eimerl et al.
66
An immediate consequence of these equations is the important observation that both the drive and the dephaslng depend only on the crystal shade, and not on its absolute size.
I t is clear that Increaslng all the
crystal dimensions (I,D s, and DI) in the same ratio leaves no and unchanged. Thus, changing the beam intensity using telescopes for down-colllmatlon leaves both P and Q unchanged and merely results in a shorter optimum crystal length.
The optimum conversion efficiency and
the shape of the crystal which achieves this optimum are both unchanged. From Eqs. (10) and (11), the optlmum efficiency nmaX is a universal function of X, which is a measure of the laser brightness and a materlal figure of merit, the threshold power. That is X
,
P I PthQ2. [4Os/Di ]
(16)
and the threshold power Pth is Pth "
I / f 2 . [BSXf/C]2
(17)
Thus the maximum efficiency is independent of the absolute size of the beam, but is a unlversal function of the ratio p/Q2 and the threshold power, a material figure of merit. Figure 2 plots the maximum efficiency nmaX against the (dlmensionless) laser brightness, X, and Fig. 3 plots the optimum drive no at which the maximum efficiency is reached. Thus, given the task of optimizing the crystal dimensions for a general three-wave process, the procedure is as follows. (1)
Calculate the threshold power Pth for the three-wave process from the materials constants, C and ~e"
(2)
Calculate the dimensionless laser brightness, X, from the laser parameters P,Q, and Ds/Di , and the threshold power.
(3)
Read off the maximum efficiency from Fig. 2 (Eq. (]5))
(4)
Read off the drive no at which this efficiency occurs from Fig. 3, and use equation (]3) to calculate the crystal shade
[12/DsDi].
From this procedure, i t w i l l be apparent whether the material can be efficient for the given laser source, and i f so, what the crystal shape
67
Nonlinear optical materials for high power lasers 1.0
I
0.9 0.8
0.7 0.6
"6 O.5 '~ 0.4
8 "S
0.3
0.2
o.1
o .0100
.
I
I
I
[
I
.1000
1
10
100
1000
1000
The peak conversion efficiency for s p a t i a l l y and temporally f l a t pulses.
X ts the (dlmenstonless brightness, or power per untt solid
angle in the beam.
required w111 be.
He reemohasize that nothtna tn t h i s orocedure fixes
the absolute size of the crystal. I f the beam aperture is doubled using telescopes, then the optimum efficiency w i l l be reached wtth a crystal twice as long, and w i l l be exactly the same. The maximum conversion efficiency ts independent of the beam size. In contrast to arguments often made in the l | t e r a t u r e , the efficiency is not optimized by down-collimating to achieve high i n t e n s i t y ; down-collimation necessarily Increases the beam divergence and forces a shorter crystal length. The net r e s u l t ts that the maximum efficiency is unaltered by
D. Eimerl et a/.
68 12
10
._e .u
8 c
8
,J¢
o ._>= c~
o
~
.0100
.1000
I
I
l
i
1
10
100
1000
P
3.
10000
(4Ds
The drive no at which the peak efficiency given in Flg. 2 is reached.
X is the (dimensionless brightness, or power per unit solid
angle in the beam.
down-co]Iimation. considerations.
The crystal size is determined by other For example, i t is posslb]e to make the crystal as large
as is desired to avoid optical damage problems, or as small as desired to avoid problems associated wlth optical absorption and thermal gradients. This freedom to choose the size of the crystal without affecting the eFFiciency is extremely important in the design and optimization oF nonlinear devices. Thus the flnal step in choosing the crystal dimensions is (5)
Choose the beam aperture.
Nonlinear optical materials for high power lasers
This can be chosen on to s a t i s f y any number of requirements, not a l l of which are coa~)atible.
For example, the aperture is minimized to
reduce the undesirable effects of absorption or made large to design around optical damage issues. I t may also be determined simply by the size of available crystals. In t h i s connection, i t is important to note that the damage threshold of a nonlinear crystal is not so much a function of the crystal i t s e l f , as i t is a function of the imperfections, impurities and stresses introduced during crystal growth. Thus there may be a s i g n i f i c a n t sample-to-sample variation in the damage threshold of an optical c r y s t a l , depending on that p a r t i c u l a r sample's individual chemical h i s t o r y . Table 1 l i s t s the optical damage thresholds for some common nonlinear materials, as supplied. Specific individual crystals grown with fewer impurities and imperfections w i l l e x h i b i t a higher damage threshold than indicated in t h i s table. On the other hand, less perfect examples w i l l be less resistant to damage. 3.
The Threshold Power I t is apparent that the threshold power appearing tn the brightness X (Eq. 16 and 17, and Figs. 2 and 3), ts the fundamental figure of merit which determines whether a material can be e f f i c i e n t with a given laser source. Physically, t t is approximately the peak total laser power required in a c i r c u l a r , d i f f r a c t i o n - l i m i t e d beam in order to reach about 40~ conversion efficiency. Thus, in selecting materlals for a p a r t i c u l a r process, i t is necessary (but not always s u f f i c i e n t ) that the threshold power of the materlal be s t g n l f l c a n t l y less than p/Q2 for the laser source. Clearly, the threshold power is a useful figure of merit for ranking nonlinear opttcal materials; the material with the lower threshold power is considered superior, because i t can reach a higher efficiency at i t s optimized shape. Because I t represents the opttmum balance between i n t e n s i t y and beam divergence effects, the threshold power is q u a n t i t a t i v e l y useful only to the extent that beam divergence is the primary source of dephastng. For example, in short pulse applications the laser bandwidth is the primary source of dephastng, and therefore requiring that the threshold power be low enough is a necessary, but i n s u f f i c i e n t condition for high efficiency. The importance of the threshold power is that d i f f r a c t i v e contributions to the beam divergence are always present, and therefore i t is always a relevant parameter. The threshold power for doubling a 1.064 pm laser using a Type I I process in KDP is about 80 MH. Thus, for a twice dlffraction-llmited
69
70
O. Eimerl et al.
Table I.
Material
DamaaeThresholds of Nonlinear Materlals
Damage Fluence
Remarks"
(31cm2)
LAP
g.8
LAP
13.4
d-LAP
9.2
d-LAP
13.0
KDP
5.0
KDP
15.0
KD*P
5.0
KTP
g.o
KTP
13.0
KTP
> 20.0
LtNbO3:MgO
Recrysta111zed twice
Recrysta111zed twice
Improved growth process
Hydrothermal Flux (BeJjing) Phosphate flux (PhJllps)
10.0
LIfO3
- 2.0
BaB204
13.0
SrxBal_xNbO3
6.0
KNbO3
7.0
Fujian x = .60, room temperature data
Data for I n s Gausslan pulses at 1064 nm. "Damage threshold depends on sample history and growth parameters. The threshold for other samples may therefore vary considerably from the data presented here.
beam containing about 500 m3 in 6 ns, the conversion efficiency optimizes at about 50%. The threshold powers for frequency doubllng in other materials are presented in Fig. 4 for some common uniaxial crystals, and the associated angular sensitivities and coupllngs, Be and C are
Nonlinear optical materiels for high power lasers
1000
I
71
I BzO4 (U)
KDP(11) ~ " "
i
.oP(,)
10 0.4
0.6
0.8
1.0
1.2
1.4
1.6
Wavelength (microns)
4.
The threshold power for second harmonic generation for some common unlaxlal crystals.
presented tn Figs. 5 and 6. Calculations for some btaxial crystals are given tn Figs. 7, 8 and g. The data used tn these calculations ts ltsted tn Tables 2 and 3. Htth the knowledge that Pth represents the mtntmal peak power needed to obtain roughly 50~ conversion e f f i c i e n c y , the uttllty
of a matertal for doubltng can be tmmedlately tnferred from these
graphs. The threshold power, of course, varies from materlal to materlal, but it ~Iso varies along the phasematchlng curve for each materlal.
For
example, In KOP Type II doubllng the phasematchlng curve Is a circle , e . constant, encloslng the polar, or z-axls.
Thls clrcle lies
paralle1 to the xy plane , and posltlon along the phasematchlng curve Is specified by ~, the angle between the radlus vector at a given polnt on the clrcle, and the x-axls.
Thus, ¢ - 0 where the phasematchlng curve
intersects the xz plane, and ~ - =/2 where It Intersects the yz plane.
Along the phasematchlng curve, the nonllnear coefficient for KOP,
dell, varles as cos(Z~), but the angular senslt|vlty BB - 8(Ak)/ae Is a
72
D. E i m e r l et al.
100
I
1
103 (I)
s=O4 (i)
10 r
KDP (I)
_> LJrea(11) 1 p-
o,II III I, 0.4
5.
0.6
J,
0.8
, IIL'N°°,~''l
1.0 Wavelength (l.U11)
1.2
1 1.4
1.6
The angular sensltlvlty, ~klBe, for the materials Included In Fig. 4.
10
I~
)J
I
J
I
8
A
6
-
,
\\--..~o,
(,)
4
>~ ,,=, 2
0 0.4
6.
,,,KDP (
0.6
1
0.8
1
1.0 Wavelength (pro)
~
1.2
1.4
1.6
The coupling C, (units: GH-I12) for the materials included in Fig. 4
73
Nonlinear optical materials for high power lasers Table 2.
OotJcal Constants for Selected UntaxJal Nonlinear Materials
(a) n2
1 + S1 + S2X2 + S3Z4 + S4X2/(X2-S~) + S6/(X2-S ~)
I
sI (DP
Jrea
LtIO 3
BBO
CD*A
LiNbO3
Sellmeter Parameters (~ tn um)
s2
s3
s4 12.99707
s5 20.0
s6
1.260476
0
0
1.133831
0
0
1.1823
0
0
0
0
0.01250
0.173205
1.51527
0
0
0
0
0.0240
0.173205
2.39503
0
0
0.696664
6.5703223 0.059542
0.052416
1.92106
0
0
2.261063
24.46665
0.003362
0.178943
1.7405
-0.0155
0
0
0
0.0184
0.1338
1.3730
-0.0044
0
0
0
0.0128
0.1249
3.227935 20.0
0.01011279
s7 0.1137646
0.008653247 0.110875
0.6278496 -0.018220 0.0002813 0.780817
0.1407699 0
0.6236063 -0.009339 0.0019654 0.724959
0.141485
1.392928
-0.026301 -0.000087 2.520353
0.2170176 0
0
1.313283
-0.020484 -0.000237 2.266851
0.2097321 0
0
(b) d36 KDP
0.39
Urea
1.17
LtNbO3
Nonllnear Oottcal Constants (om/V) d15
dll
d22
4.43
LI IO3
B~ CO*A
0
0.2
1.40
0.60 4.64
2.45
74
O. Eimerl et al.
Table 3.
Ootlcal Constants for Selected Biaxlal Nonlinear Materlals (a)
n2 l
I + SI + s2X2 + s3~4 + s4~2/(X2-s~) + s6/(X2-S~)
s1
KTP
d-LAP
LFa
(a)
Sellmeler Parameters (X in um)
s2
s3
s4
s5
s6
s7
2.0129
-0.01664 0
0
0
0.03807
0.2070
2.0333
-0.01695 0
0
0
0.04106
0.2224
2.3209
-0.01763 0
0
0
0.05305
0.2441
2.2352
-0.00683 0
0
0
0.0118
0.1208
2.4313
-0.0143
0
0
0
0.0151
0.1463
2.4484
-0.0115
0
0
0
0.0172
0.1513
-1.606
-0.00131 -0.00083 2.44644 0.056364 0
0
-2.449
-0.00610 -0.00149 3.600]6
0.063803 0
0
-0.230344 0.00580 -0.07841 1.47954 0.111192 0
0
These Sellmeler parameters give accurate indices only in the region of
transparency, 0.19 - 1.2 ~m (b)
Nonlinear Ootlcal Constants (Dm/V)
KTP
0 0 5.4
0 0 4.15
0 0 11.4
0 6.3 0
5.1 0 0
0 0 0
LAP
0 0.4 0
0 0.92 0
0 -0.84 0
-0.58 0 -0.84
0 -0.58 0
0.4 0 -0.58
LF
0 0 0.95
0 0 -I.08
0 0 1.58
0 -I.08 0
0.95 0 0
0 0 0
constant.
Therefore the threshold power is a minimum where the coupling
def f is a maximum, namely at ~ = O.
In general, the optimum
operating point for a nonlinear materlal
is that point along the
phasematchtng curve where the threshold power is a mtnimum, but this is
75
Nonlinear optical materialsfor high lower lasers not necessarily the potnt at which def f ts a maximum. For the example of KDP, t t ts true that the threshold power ts a mtntmum where def f Is a maximum, because Be ts a constant along the phasematchtng curve. In general, for untaxtal materials, the angular s e n s i t i v i t y ts always a constant along the curve, and so tn general, for untaxtal materials, the optimum operating point ts that which maximizes deff. On the other hand, the angular s e n s i t i v i t y for btaxial materials varies in a nontrtvtal manner along the phase matchtng curve, and the optimum operating point ts not tn general gtven by the maximum of deff. The maxtmum efficiency obtainable wtth a particular mater|a1 ts obta|ned for that crystal orientation along the phasematchtng curve where the threshold power ts a mtntmum. There are some circumstances where t t may be desirable to operate at some other potnt, but I t wtll seldom be advantageous to do thts. Posstble motivations for choosing a non-optimal operating potnt tnclude: (a) avoiding or reductng orientation-dependent effects such as stimulated Raman scattering, photorefracttvtty, nonlinear self-focussing, thermal expansion and thermal stresses, and ltnear optical absorption, (b) avotdtng poss|ble complications tn the cutttng, 104
lOa
LAP(l)-
Z,,o!
/ /
F- lo-'
E
10"3 0.4
[ 0.6
0.8
1.0
1.2
1.4
1.6
Wavelength(microns) 7.
The threshold power for second harmonic generation for the btaxtal crystals, lithium formate monohydrate (LF), KTP, and d-LAP.
D. Eimerl et al.
76
100 (
I
l
i
I
I
E
> C Q
=
~
I
C
o.i 0.4
KTP (im)
I
I
I
I
I
0.6
0.8
1.0
1.2
1.4
1.6
W~elength(~m)
8.
The angular sensitivity, a~klee, for the materlals included in Fig. 7 I 14
-
12
-
f
J
I
]
ee
o =
8
0 4
-
L
I
I KTP
)
0 0,4
9.
0.6
0.8
1,0 Wavelength (~ m)
1.2
1.4
1.6
The coupling C, (untts: GH-112) for the materials included in Fig. 7
Nonlinear o~ical mate~all ~r high powerla~m polishing and coating of the crystals, and (c) tn the case of very large crystals, Increasing the yield of useful crystals from freshly grown crystal boules.
In many circumstances, these are not Important
considerations whereas htgh conversion efficiency ts desirable. Therefore, the threshold powers quoted here are the mtntmum along the phase~tchtng locus, and therefore they represent the htghest efficiency configurations for the material. Occasionally, another ftgure of mertt Is quoted for nonlinear materials, namely, deff/2 n3. This figure of mertt ts essentially the square of the coupling, C2, and Is Insufficient on tts own to determine whether a material wtll be e f f i c i e n t tn a particular application. For this reason, C alone Is not the appropriate parameter to rank nonlinear materials for applications, although I t may be useful to bastc research on new materials. Thls emphasizes that, In appllcattons, the 11near opttcal properties play as Important a role as the nonlinearity; research atmed at developing new materials for spectftc applications must address the linear opttcal properties equally wtth the nonlinear opttcal properties. Near noncritical wavelengths, the angular s e n s i t i v i t y ts very small. and the behavtor of the threshold power ts determined by the effective coupling. For untaxtal crystals, the coupllng goes to zero for both Type I and Type I I coupllng for crystals tn the classes ~m2, "[, 622. 32. and 422. For the remalntng classes, the coupllng C rematns f t n t t e only for Interactions Involving two o-rays, and one e-ray. Thus, the coupllng goes to zero for Type I coupllng tn positively btrefrtngent crystals, and for Type I I coupltng In negatively btrefrtngent crystals. Thus. for KDP ~2m), the threshold power goes to zero for Type I coupling at the noncritical wavelength of 514 nm, but for the Type I I process, both G6 and def f go to zero, and the threshold power rematns f t n t t e at the noncritical wavelength, near 700 nm. Table 4 11sts the noncritical wavelengths for the ~ t e r t a l s In Ftgs. 4 and 7. along wtth thetr transparency range. The data presented tn the ftgures terminates at the noncritical wavelength tn the u l t r a v i o l e t , and Just beyond the absovpt|on edge tn the Infrared. The Importance of the 11near opttcal properties ts clearly Illustrated by the calculations for KTP (Ftgs. 7, 8, and 9). For Type I doubling the coupllng ts r e l a t i v e l y small, and the angular s e n s i t i v i t y ts qutte large, and the threshold power ts large, around 10 GH. However, for Type I I doubllng the coupllng C ts large, and In the regton between
77
78
D. Eimerl et al.
T a b l e 4.
Havelength
N o n c r l t l c a l Havelenath f o r Second H~rmgnJ~ Generatlon Material
(nm)
Propagation
Type
Axis a
Coupling (pmlV)
327
LF
8
II
0.95
378
LIIO 3
y
I
4.43
386
LF
y
II
--
400
LIIO 3
y
I
--
409
BBO
y
I
0.2
464
d-LAP
8
I
--
480
Urea
--
I
--
488
d-LAP
y
I
--
519
KDP
(x÷y)/42
I
527
BBO
--
II
589
Urea
(x+y)/42
II
626
d-LAP
8
II
0.39 -1.17 --
658
d-LAP
y
II
718
LF
=
I
--
736
KTP
8
I
--
737
KDP
--
I
--
801
KTP
=
I
--
990
KTP
8
II
5.1
I045
CD*A
(x+y)142
I
0,6
1062
LINbO3
y
I
4.6
I081
KTP
=
II
6,3
(a) For b l a x l a l c r y s t a l s ny > nB > n .
0.4
For u n i a x l a l c r y s t a l s
(xyz) are c r y s t a l l o g r a p h i c coordinate systems.
about I ~m and 1.1 ~m the phasematching curve intersects the low bJrefrlngence (xy - ab) plane where the angular s e n s i t i v i t y is small. KTP has two n o n c r i t i c a l wavelengths, one at each end of t h i s spectral region.
The threshold power goes to zero at these n o n c r i t i c a l
wavelengths and because the angular s e n s i t i v i t y is small between them, the threshold power remains low throughout the e n t i r e 1 - 1.1 l~m band. S i m i l a r l y f o r l i t h i u m formate monohydrate, there is a n o n c r l t i c a l wavelength close to 900 nm, but l i t h i u m formate does not have a low
N~limNIr optical mamnals~r highpowerleINl~
79
btrefrtngence plane, and therefore the threshold power dips to zero near 900 nm, but quickly rises to large values on either stde of t h i s n o n c r i t i c a l wavelength.
On the other hand, LAP does have a low
btrefr|ngence plane, and t h i s gives rise to a low threshold power band ~ust below 500 nm, where the Type I coupltng ts large and the angular s e n s i t i v i t y ts small. Thts band ts very narrow, about 20 nm wtde, and ts qutte far tnto the UV, where the absorption at the second harmonic near 240 nm may be s i g n i f i c a n t . LAP also has Type I I n o n c r i t i c a l wavelengths, but the coupltng vanlshes for these configurations. There ts no wavelength at which t t s threshold power dtps to zero. Graphs such as Ftgs. 4 and 7 tn effect summarize the technology of nonlinear opttcs. I d e a l l y , t t would be desirable to have a sutte of materials such that for whatever process ts being considered, a low threshold power matertal would be available. However, from Ftgs. 4 and 7 t t t s clear that over most of the W - v i s i b l e spectrum low threshold power materials are lacking. These graphs also show that untaxtal materials are not, tn general, as wavelength-flexible as btaxial materials. Each new uniaxtal material brtngs one noncritical wavelength where the threshold power can be low, and a small band of wavelengths to the red from t h i s wavelength where the threshold power is small.
On the other
hand, a btaxtal crystal has the potential for two r e l a t i v e l y close n o n c r i t i c a l wavelengths. Thts ts I l l u s t r a t e d by the KTP curves in Fig. 7. Such a crystal exhtbtts a band of low threshold power behavior, bounded by the two n o n c r i t i c a l wavelengths.
Between the two noncritical
wavelengths, the phasematchtng curve Intersects a low btrefrtngence plane, where the angular s e n s i t i v i t y is small.
To have two n o n c r i t i c a l
wavelengths close together, a btaxtal crystal must have two indices of r e f r a c t i o n close together, and both must be s t g n t f l c a n t l y d i f f e r e n t from the t h i r d . In other words, the crystal must be close to untaxtal. signature of a low btrefrtngence plane (and therefore of two close
The
n o n c r i t i c a l wavelengths) in a btaxtal matertal ts that i t s opttc angle be small but not zero, perhaps not larger than about 45 deg. The smaller the optic angle, the closer the crystal is to untaxtal, and the narrower the band of low threshold power. On the other hand, for larger opttc angles the separation between the noncritical wavelength becomes large (as in ltthtum formate) and the low threshold power band does not r e a l l y e x t s t . In any case, the potential for two n o n c r i t i c a l wavelengths tn btaxtal crystals makes them more a t t r a c t i v e than untaxtal materials as candidates for the desired suite of nonlinear materials. Other thtngs betng equal, the technology of nonlinear opttcs benefits more from a new
D. Eimerl et
80
al.
btaxtal crystal whose linear optical properties are close to, but d i s t i n c t from, unlaxlal behavior, than from a new unlaxlal material.
4.
Database on Non!lnear Ootlcal Matertal~ He have seen above that the threshold power is the c r i t i c a l
figure of
merit in ranking nonlinear materials for applications, and that graphs of the threshold power as a function of wavelength are a very useful aid in summarizing the technology of frequency doubling from a materials standpoint.
Of course, similar sun~rtes can be generated for any
three-wave interaction; for example third harmonic generation by mixing the f i r s t and second harmonics has been studied for the KDP famtly of tsomorphs 3 and the results published.
Hhtle t t is useful to summarize
the threshold powers of commonly available materials, i t would be much more useful to summarize the capability of all known nonlinear materials.
Also, i t would be useful to generate a summary for frequency
mixing and optical parametric oscillators as well as for frequency doubling.
Only with thts information, can an informed choice be made
regarding which known materials should be developed.
Also, from such
graphs, i t will be evident which spectral regions are under-represented by nonlinear opttcal materials. To this end, a database has been constructed which contains the nonllnear coefficients and Sellmeter data for every known nonllnear material for which such data is available in the l i t e r a t u r e . 7 About one hundred materials are s u f f i c i e n t l y well-characterized for inclusion in this database, and some materials are represented more than once to reflect conflicting data in the l i t e r a t u r e ,
This database in accessed by
a btaxtal phasematchtng code which calculates the phasematchtng curve for each matertal and phasematchtng type requested, and determines the minimum threshold power along the phasematchtng curve.
Note that for
btaxtal crystals the coupling tn more than one octant of the index ellipsoid must be calculated.
The code is completely general, and treats
the general three-wave interaction and all phasematching types.
The code
calculates the threshold power for each material, and prints out a l i s t of those materials for which phasematchtng is possible, ordered by their threshold power. The data represented in Figs. 7, 8, and 9 was generated using this expert system.
A f u l l e r description of this expert system
will be published elsewhere. In establishing this database, a thorough review of the l l t e r a t u r e was necessary, and'many of the Sellmeter parameters were calculated from the l i t e r a t u r e data for the f i r s t time.
A surprising discovery was made
Nonlinearo~ical materials~r high powerlasers that there ts a coefficient d~ ~ o 1n - values . . . . . Is tables II report
81
s i g n i f i c a n t disagreement regarding the nonlinear of KDP t t s e l f , where the spread tn reported 0.39 pmlV to 0.78 pm/V, whereas the standard reference 0.63 pmlV. There are relatlvely few absolute
determinations of the nonllnear coefficients of KDP and I t s tsomorphs, and most were made tn the 1960's. The early experiments used a focussed beam geometry, and t h e i r i n t e r p r e t a t i o n ts complicated by the effects of beam walk-off, and the nonuniform laser proflle near the focus. The most tellable measurements are more recent and use dlffractlon-llmtted or stngle mode, hlgh energy, pulsed lasers to measure the conversion e f f i c i e n c y of hlghly collimated beams. The advantages of a large aperture and collimated geometry are: (1) beam walk-off Is n e g l i g i b l e , (2) there is no d i f f r a c t i o n as the beam propagates through the sample, and (3) the beam divergence can be made much less than the acceptance angle of the sample. The plane-wave experiments a l l agree to within 2% on the nonlinear coupling of KDP. For Type I I doubltng the coupling is C =
o.g5
GW-1/2
(18)
which corresponds to d36
-
0.39
pm/V
(19)
The large aperture results for C tn the 11terature also agree exactly wlth our (unpubllshed) experience wlth frequency conversion of the NOVA laser. Unfortunately, d i f f e r e n t authors use d i f f e r e n t deftnlttons of the d - c o e f f i c i e n t ; the d e f i n i t i o n used here ts the same as that in Zerntke and Midwinter. 8 The d e f i n i t i o n s used the other collimated beam experlmentsg'10 differ from thls by a factor of two, and quote 0.78 pm/V. The discrepancy between the co111mated beam, hlgh intensity experiments and the other determinations of d36 remains unexplained. 5.
Hlcrocrvstal Characterization Technlaues Characterization Is an essentlal element In the development of new
nonllnear optlcal materlals.
The minimum data requlred are the angular
s e n s l t l v l t y and the nonlinear coupllng throughout the transmlsslon range of the material. From these data the threshold power can be computed, and the material can be ranked against other, known nonlinear materials. Until recently, this characterization was posstble only wtth crystals about 10 mm tn size, s u f f i c i e n t to permit a precise determination of the
D. Eimerl et al.
82
Individual components o f t h e d-tensor, and also of the refractive indices throughout the transparency range of the crystal.
I t was necessary to
grow crystals of htgh opttcal quality at about the 1 cm3 size in order to compute the threshold power and thereby to rank the material against other materials.
However, we22 have recently developed new techniques
of mtcrocrystal characterization which can determine the necessary parameters ustng I r r e g u l a r l y shaped crystals just 50 - 250 microns tn size.
Using these new techniques, i t is posstble to measure the relevant
matertal parameters without the costly and time-consuming step of crystal growth to the 10 m scale.
Often, crystals of sufficient size are
obtained as a routine result of chemical synthesis.
By avoiding the
Intermediate crystal growth step, these techniques provide a rapid and cost-effective way to evaluate a new nonlinear matertal at an early stage of study.
Subsequent crystal growth efforts can then be directed towards
materials whtch have been already characterized at the mtcrocrystal scale, and are therefore known to possess attractive properties. He have developed two new microcrystal devices and characterization techniques which apply Fully to all crystal symmetries Including blaxtal crystals, and indeed, their power lies in the ease with which they handle such o p t i c a l l y complex materials.
The f t r s t instrument determines the
ltnear opttcal properties using the double splndle stage refractometer, 14 a modification of a polarizing microscope used in opttcal mineralogy to characterize minerals.
The double sptndle stage
refractometer determines the refractive indices throughout the visible and near infrared with an accuracy of about 0.0001.
The sample must be a
stngle crystal, but i t s shape can be nonsphertcal, and its slze can be as small as 25 microns.
Crystallttes of 50 to 100 micron dimensions are
preferred, depending on their btrefrtngence.
The same instrument is also
capable of determining thern~optlc coefficients in the range 0.0001 "K-1.
The second new devlce is a nonlinear optlcal
gontometer,22 which measures the nonlinear opttcal properties and phasematchtng characteristics d i r e c t l y on small mlcrocrystals (slze). Hlth thts instrument, the phasematchlng locus for any three-wave process can be dtrectly measured.
I t also determlnes the nonlinear coupling and
the angular s e n s i t i v i t y along that locus.
An extension of the instrument
allows i t to determine the temperature and wavelength s e n s | t l v t t y of the crystal as well.
The sample for this instrument must also be a stngle
crystal, which may be asphertcal.
The sample stze can be as small as
100 microns, but the accuracy of the data is highest for crystals 250 - 500 microns tn size.
83
Nonlinear optical materials ~ r high power lasem
6.
The DQuble $otndle Stage Refractometer
The double sptndle stage refractometer ts a modification of the (stngle) sptndle stage mlcroscope developed by Bloss. 12'13 I t ts e s s e n t i a l l y a polarizing transmission microscope wtth coil|mated i l l u m i n a t i o n of the sample. The sample ts held tn a small temperature controlled cell along wtth another small reference c r y s t a l . As the orientation of the crystal ts changed, the transmission through the crossed microscope polarizers varies. By determining the mtcrocrystal orientations for complete e x t i n c t i o n , the optic axes of the crystal can be found, and the mtcrocrystal can therefore be oriented o p t i c a l l y .
In
p a r t i c u l a r , t t can be oriented so that any one of the three principal optical directions l i e s tn the plane of the microscope stage ( h o r i z o n t a l ) , and perpendicular to the direction of l i g h t propagation { v e r t i c a l ) . Once the principal opttcal directions of the sample have been determined, the sample can be oriented so that the relevant index of refraction for l i g h t parallel to the ( v e r t i c a l ) axis of the microscope ts any one of the three principal lndtces. otl immersion methods.
These can then be determined by
Typically otl immersion methods are, however, subject to systematic errors associated wtth the degradation of the otl over time. The r e f r a c t i v e index of an otl ts affected by the loss of v o l a t t l e components, contamination, and other unavoidable aging processes. Accurate work therefore requires that the Immersion o t l s be calibrated regularly. I f thts c a l i b r a t i o n ts not carried out with every experiment on a mtcrocrystal, systematic errors can occur. Thts c a l i b r a t i o n error is eliminated t f the r e f r a c t i v e index of the otl ts determined tn s t t u , at the same ttme and temperature as the sample is measured.
To thts
purpose, a reference crystal ts tncluded wtth the sample tn the immersion o t l , and is used to determine the refractive index of the o11.
In
essence, the double sptndle stage compares the r e f r a c t i v e index of the sample d i r e c t l y wtth the r e f r a c t i v e index of the reference c r y s t a l . Thus the systematic error associated wtth the use of an immersion otl ts v i r t u a l l y eliminated. Figure 10 shows how a untaxtal crystal on a sptndle axis serves as a mlcrorefractometer to obtaln the ol1's refractive index for a particular wavelength of light. The reference crystal is precisely mounted with its unique (optic) axls perpendicular to the spindle axls and aligned in a plane parallel to the microscope's polarizer. As the reference crystal Is rotated on the spindle, the full range of indices are observed - from light vibrating parallel to the optic axis, n e. to light vibrating
O. Eimerl et al.
84
S
z
III
.....
~
// I
I !
//
I ip
S
$
fs
~
,•
jl
| I I
//
#S 4¢
! st
10. The ordinary (o), and extraordinary (e) polarlzatlons for a plane wave In a unlaxlal crystal wlth wave normal s.
perpendicular, no .
Once an otl ts found which matches the desired
r e f r a c t i v e index of the unknown crystal at the wavelength of i n t e r e s t , the reference crystal Is rotated by angle e unttl tndex n(e) matches the o t l .
I t s extraordinary
The mutual r e f r a c t i v e indices of the
standard, oii and unknown are then determined from Eq. (20).
n(e) -
n~n0 2 stn2B)i/2 (n e 2 cos2e + no
(20)
Here, e Is the angle between the direction of index matching and the optic axls of the reference crystal and ne and no are the prlnclpal refractive indices of the reference crystal at the wavelengths of Interest.
The procedure may be repeated for addltional wavelengths untll
a s u f f i c i e n t number of data points to characterize the dispersion curve are determined.
At least four data points are required, and preferably
about eight evenly separated wavelengths should be used. Because a
Nonlinearoptical materials~r high powerlase~
85
reference crystal has a 11mtted range of r e f r a c t i v e tndtces, several posstble reference c r y s t a l s , spanntng the range from 1.335 to 1.908 are 11sted tn Table S. A schemttc drawtng of a sptndle stage microscope configured for thts type of refractoeetry ts shown tn Ftg. 11. The most elegant prevtous r e a l i z a t i o n of the "double sptndle stage refractometer" constructed to date ts described by Nedanbach. 14 However, thts and prevtous devtces have been 11mired to v l s t b l e 11ght. 15'16 To assess frequency conversion characteristics for near tnfrared and u l t r a v i o l e t 11ght, accurate values of r e f r a c t i v e tndlces tn those spectral regtons are necessary. Stmple extrapolations of dispersion data measured tn the v t s t b l e are usually Inadequate for thts purpose. Therefore, a feature of our sptndle stage refractometer destgn was a CCD camera coupled to one port of the microscope that permitted tmagtng of the reference and unknown crystal from 0.38 to 1.10 pm on a t e l e v i s i o n monttor. The tndtces of refraction for the reference crystals were also measured through thts spectral regton on larger samples cut for prlsm spectrometry. Refractive tndtces collected at a sertes of wavelengths are least-squares f t t to the Sellmeler equation: n2 - A + _ L _ + X2+C
DX2
(21)
where X ts the wavelength in I~m and n is the principal r e f r a c t i v e index of i n t e r e s t . To assess the accuracy of our apparatus over the f u l l range of wavelengths, we measured the r e f r a c t i v e tndlces of several known materials. Including deuterated 1-argintne phosphate (d-LAP). 4 Accurate dispersion data for the three principal indices of LA*P have been determined previously by prlsm spectrometry. 4 The Individual
Table ~,
Compound
Reference Crystals for Solndle Staae Refractometrv
ne
no
NaNO3
1.335
1.585
CaCO3
1.486
1.658
BaB204
1.553
1.670
ZnCO3
1.621
1.849
Lt103
1.754
1.908
86
D. Eimerl et al.
FP
~ )
FP
[ Camera Reference spindle
,~
Sample spindle
Graded interference...........!......... !
filter
..........
Lamp i ~
I I . Schematic of splndle stage refractometer (oll cell not shown).
Pl
and P2 - polarizers; F.P. - focal plane.
refractive index values determined by sptndle stage refractometry deviate from the more accurate prism values by as much as 0.002. However, these deviations appear to be random, and are due in part to the uncertainty in determining the precise match of standard, unknown and o i l . The Sellmeter formula (Z]) and values of the refractive indices were obtained at each wavelength by use of b e s t - f l t curves. The data are shown in Fig. 12. Table 6 shoes that these values, reported for the Nd:YAG fundamental and second harmonic wavelength, compare more favorably to the prism data, with a standard deviation of 5 x 10-4 . The main source of errors are related to sample quality.
Strain,
poor surface quality and the shape of the grain all affect the quality of the conoscoplc 13 figure used to orient the crystal.
In addition, an
unambiguous match between oll and crystal is dependent on the graln's boundaries, with sharp and clean surfaces at the edges providing the most sensitive conditions.
87
Nonlinear optical materials for high power lasers 1.680
1.490 3,000
S,O00
8,000 Wavelength (A)
11,000
12. D1sperslon of d-LAP. The curves are a Sellmeler f i t to the data.
Table 6.
Refractive Indices for LA*P Determined bv Minimum Deviation
(M.D.) and Solndle Staae Refractometrv (S.S.) for Selected Havelenqths
Principal Index n
nB
n
7.
Y
X(vm)
nM.D.
ns.s.
1.064
1.4960
1.4941
0.532
1.50go
1.5089
1.064
1.5579
1.5577
0.532
1.5759
1.5754
1.064
1.5655
1.5651
0.532
1.5846
1.5845
The Nonllnear Ootlcal Gonlometer Untll recently, the most common approach to new nonlinear optlcal
materlals has relied on powder SHG methods to identify new phasematchable second harmonic generators. 17 Large crystals of attractive candidates are then grown for careful evaluation of refractive index dlsperslon 18 and nonllnear coefflclents. Ig
From this "global" Informatlon, the
theoretlcal efficiency for mlxlng any pair of incident wavelengths can be
88
D. Eimerlet al. computed. 20 To date, over one hundred materta]s have been characterized at this level of detatl.11'21 However, this characterization method is quite slow because SHG powder tests on t h e i r own give i n s u f f i c i e n t , and often q u a n t i t a t i v e l y unreliable data, and progress is made at the rate that r e l a t i v e l y large crystals can be grown. The nonlinear optical gonlometer in contrast permits accurate characterization of a new matertal s u f f i c i e n t to rank i t against other nonlinear materials without requiring r e l a t i v e l y large crystals. The nonlinear optical gontometer determines the phasematchtng curve for any frequency conversion process of i n t e r e s t , and measures the coupling and angular s e n s i t i v i t y along that curve. I t requires only one high q u a l i t y , single crystal several hundred microns in size. Such crystals are often available at the t n t t t a l stages of synthesis without spectal e f f o r t , and e x h i b i t the same phase matching properties as larger c r y s t a l s . This level of material characterization is intermediate between powder SHG measurements on the one hand, and detatled ltnear and nonlinear s u s c e p t i b i l i t y determinations on the other. In a d i r e c t phasematchtng measurement, a laser beam (or beams) is passed through a c r y s t a l , and the angular orientation of the crystal is adjusted u n t t l a sharp increase in harmonic l t g h t i n t e n s i t y c h a r a c t e r i s t i c of phasematchtng is found. 23 For a given incident wavelength, and a given set of polarizations, the continuous set of such orientations comprises the phasematchtng locus. 24 Three basic kinds of information about phase-matched harmonic generation can be obtained from crystals by direct measurements, as I l l u s t r a t e d in Figs. 13-16. The slmplest is the position of the phase matching locus for a given process, i . e . Type I , I I or I I I mtxfng 6 of the wavelengths of i n t e r e s t . Figure 13 shows a set of phasematchtng loci for doubllng, t r i p l i n g and quadrupling of the Nd:YAG fundamental in a 1 nln diameter crystal of a new blaxtal harmonic generator, L-argtntne f l u o r i d e (I.AF). In a classic paper, 25 Hobden obtained loci such as this in ( r e l a t i v e l y ) large crystals of some other compounds by direct measurement, but only to confirm the accuracy of loct computed from r e f r a c t i v e index data. The data in Fig. 13 represent the d i r e c t determination of the phasematchtng locus of a microcrystal of LAF in the ~b~ence of r e f r a c t i v e index data. In LAP, the phasematchtng 1oct for doubling 1064 nm are almost c f r c u l a r e l l i p s e s enclosing the low index axis (¢), as shown in Fig. 14. The effective coupling varies along these l o c l , and in Fig. 14
Nonlinearopticelmaterialsforhighpowerlasers
~
3
0
)
TypeI
13. Phasen~tchlng Iocl for doubling, tripling and quadrupling 1.06 l~n obtained In a l nvn diameter crystal of L arglnlne fluoride.
The 3~
Type I locus Is not shown since It nearly overlaps 2= Type II. Asterisks mark the optic axis positions.
the maxima of def f are represented by dark circles, whereas the zeros are represented by open ctrcles. The low symmetry of UkP allows four Independent relevant d-tensor components, and the complexity in the variation of def f ts shown in Ftg. 15 and is a consequence of the interference and cancellations of the contributions from these four components. These data were used in Ref. 4 to determine the relattve signs of the d-tensor components, and to locate the optimum phasematchtng direction (marked IIA tn Ftg. 14). By monitoring the Intensity of SHG along the locus, the variation of def f can be obtained. By careful comparison with a standard, the approximate value of def f ts obtained. Flnally, by dlrectly scanning the crystal orientation In a dlrectlon orthogonal to the locus, the angular sensitivity can be determined from the phasematchlng "signature" as shown In Fig. 16. The direct measurement technique makes the characterization of unlaxlal materials nearly trivial because the phase matching Iocl are simple cones about the unique axis, the effective coupling varies slnusoldally along the locus, and the angular sensitivity is a constant. The real power of the technique Is realized in the characterization of blaxlal crystals, which exhibit nontrlvlal variations of coupling and
90
O. Eimerl et al.
=o
14. The phasematchlng loci for second harmonic generation in LAP are e11Ipses encloslng the low index axls (~).
The closed circles
represent local maxima in def f, and open circles represent zeros of def f •
angular acceptance along a locus, and whose loci can have complicated topologles.25
This data, along with the location of one or two
crystallographic planes determined by x-ray diffraction on the same sample, is sufficient to determine the orientation of cuts to produce desired doublers or mixers from large crystals once they become available. In certain cases, i t is possible to determine the signs and magnitudes of individual d coefficients by combining x-ray data and the positions of maximum or vanishing nonlinear coupling when the crystallographic point group is known.26 Of course, this level of characterization gives information only about the processes directly studied, and thus is less general than prism and wedge measurements. On the other hand, from a series of direct
91
Nonlinear optical materials for high power lasers 1
~2~1
I
I
I
I
IA
m
J e,o
A
z x
=
,s
0°
60°
120•
180~
240~
300~
I
I
I
I
I
LAP 20} II
lid
IIC
|
I,,
o 0
II
liB
0°
15. V a r i a t i o n for
60"
180°
o f second harmonic I n t e n s i t y
Type I I
calculated
120°
doubltng of curve.
o f the d - t e n s o r
240°
300°
360°
along the phasematching locus
1.064 ida t n d-LAP. The s o l i d
ltne
is the
These d a t a were used t o d e t e r m i n e t h e r e l a t i v e
components f o r
d-LAP.
sign
D. Eirnerl eta/.
92 LAP: Type U A
-10
0
10
Angle to plate normal (degrees)
16. Angular acceptance data for d-LAP Type I I at the point IIA of Fig. 14, where the coupllng C Is a maximum. Solld line Is least squares f i t to the function sJnc2 (I/2I~BL).
measurements at discrete wavelengths, the behavior of the materlal for other processes can often be assessed by Interpolation. I t is important to note the smallest crystal slze for which i t is theoretlcally posslble to make direct phase matching measurements. The sole criterion which must be satisfied is that the true phasematching positions be distinguishable from subsidiary intensity maxima where the coherence length is locally maximum, but not infinite.
For this to be
true, the slze of the particle must exceed the inverse of the angular sensitivity: >> 2~/~e
(22)
For example, for Type II doubllng of 1.06 ~m in potassium dihydrogen phosphate (KDP) which has an angular sensitivity of 2500 cm-I/rad , a particle size of 100 microns is sufficient to resolve the phase matching locus.
I t is, perhaps, surprising to note that this criterion is exactly
the same as the one derived by Kurtz and Perry17 to determine when phasematched SHG dominates the powder signal of a material.
Thus, I f
materials are synthesized with crystallite sizes large enough to determine whether or not they are phasematchable by a powder test, then i t is possible to obtain much more precise information about their
93
Nonlinear optical materials ~ r high power laserz
properties by direct measurements.
The sample handling methods we
currently employ allow us to study particles as small as 300 l~m in diameter, but improvements which w t l l permit the study of 100 I~n sized samples appear feasible. Samples for d i r e c t phasematchtng measurements can be produced by a variety of methods. I n l t l a l attempts at crystal synthesis, either by high temperature melt growth or by evaporation or cooling of solutions, often result in polycrystalline masses with single crystal domains a few hundred microns in size. In addition, submllllmeter sized samples produced by fast fiber pulling technlques 27 or by growth in caplllarles 2B are ideal for these studies. Hhile i t is possible to make measurements on c r y s t a l l l t e s in t he i r natural habits or on cleavage plates, we have found i t convenient to grind samples into a spherical or elllpsoldal shape, in part because i t is much simpler to estimate the optical path length as a function of orientation in a spheroidal sample. In addition, a well rounded sample presents an entrance surface which is nearly normal to the laser beam for all orientations, making refraction corrections less serious. Finally, manipulation of the crystal orientation for mounting (see below) is much easier for rounded samples. Figure 17 shows the morphology of a typical sample after rough grinding in a commercially available sphere former. Subsequentpolishing by tumbling with fine g r l t or solvent etching is often possible.
In any
case, scattering due to poor surface quality is greatly reduced by immersing the sample in an index matching f l u i d when measurements are made. This also reduces the lensing effect of the spherical sample since the focal length of a sphere of radius r and index nA immersed in a f l u i d of index nBls given by F - rnA/2(nA - n B ) . The refractive indices of the f l u i d and sample can usually be matched to better than 0.Ol. although for very birefringent samples this may necessitate changing the matching f l u i d for different phase matching types. Samples are permanently bonded to the glass fibers in particular orientations with respect to the principal di el ect ri c axes. Figure 18 shows a crystal mounted on a glass fiber and suspended in immersion f l u i d and shows that the transparency of even a roughly ground sample is reasonable when immersed in a f l u i d with a near index match. The positions of the principal axes of the refractive index ellipsoid of the small c r y s t a l l i t e are located by principal and optic axis interference figures, using the same techniques as the spindle stage microscope. 12'13 These principal axes are labelled ~, ~ and y with the convention that
94
D. Eirnerl eta/.
17. Spheroldal sample of barlum metaborate produced by a i r tumbling.
n
< nB < n .
Typically, two orientations are s u f f i c i e n t to
obtain the entire locus for any frequency mixing or doubling process in a biaxial crystal.
In the f i r s t , the crystal is mounted with the glass
fiber parallel to the 8 axis (perpendicular to the optic plane, using the convention n
< nB < ny ). In the second, the fiber is parallel to the highest index direction (y). For uniaxial crystals, a single orientation, either with the optic axis parallel or perpendicular to the f i b e r , is usually s u f f i c i e n t to obtain a particular locus. The apparatus for measuring SHG in small crystals is shown
Nonlinear optical materials for high power lasers
95
18. Crystal immersed in refractive index matching fluid.
schematically In Fig. 19.
Part of the laser beam is s p l l t off and
doubled (with low efficiency) in a separate nonlinear crystal.
The
doubled light intensity serves as a normaIizatlon slgnal to account for laser power fluctuations.
The second harmonic signal from the sample is
detected in a photomultipller, using a ground fused s i l l c a plate to diffuse and depolarize the detected light and calibrated neutral density f i l t e r s to attenuate the signal into the linear range of the detector. The second harmonic and normalization signals are collected, averaged and digitized for analysls.
As the phasematchlng curve is traced out, the
96
D. E i m e r l
et al. r. . . . . . .
A
A
;.2
I ,
2
~ i,
I F1
/
F2 PMT
T,~®.
;
w21
.
1
Boxcar trigger
I Normalization
signal
19. Schematic of apparatus for phasematchlng measurements. A:
aperture; PD: photodiode; KTPI and 2: doubling crystals;
HI,W2: waveplates; Fl, F2: f i l t e r s ; L: 20 cm focal length lens; P: polarizer.
The segment enclosed by the dashed line is inserted for
3~ and 4~ experiments.
azimuthal (¢) and polar (8) angles of the crystal in the iaboratory frame are recorded. The coupling C is determined from the signal for points exactly along the phasematching curve, Ip
=
[Cp.I p . l l n c]
2
(23)
Here lin c is the incident intensity, and the point P(e,¢) lies on the curve.
The optical thickness of the sample Ip is calculated by
modeling the sample as an ellipsoid.
The accuracy of this calculation
for typical samples is about 5%, although very occasionally, an oddly shaped sample results from the grinding process, and the e11ipsoidal f i t is less accurate.
Phase mismatch and walK-off are negligible because the
confocal parameter of the focused beam greatly exceeds the crystal size, as does the walkoff length due to double refraction.
The absolute
magnitude of the coup]ing is obtained by careful comparison with a suitable standard.
The angular sensitivity at the point P is measured by
scanning along the arc at P perpendicular to the phasematchlng curve.
If
is the angle describing location along this arc then
Ip(~) ~ sinc2(~p~)
(24)
Nonlinear optical materials ~ r high power l a i r s
where slnc(x) . s l n ( x ) / x , and ~p Is the angular s e n s i t i v i t y at the point P. The qualtty of the f i t to the phase matching signature (24) is a criterion for Judging crystal qualtty and the r e l i a b i l i t y of the angular s e n s i t i v i t y and intensity data. HJth the methods described above, phase matching angles can be determined to = 25 mrad, angular s e n s i t i v i t i e s to better than 20"I. and def f values in good qualtty samples to 25% for second harmontc generation at 1.064 microns. The major sources of error for the angular acceptance and intensity measurements are the sample surface qualtty, and the uncertainty tn opttcal path length. For work in the u l t r a v i o l e t , the relattve dispersion of available transparent immersion otls exacerbates the tndex mismatch problem. The accuracy of Cp is reduced to z 50%, but this is stt11 accurate enough to evaluate and rank the material. I f very accurate values of JCpI2 are obtained, i t is sometimes possible to deduce values of the Individual d-coefficients by f i t t i n g the observed varlatlon of Cp along the phasematchlng curve. Of course, one must know the crystal class of the sample must to reduce the number of independent d-coefficlents. The accuracy of the magnitude of Cp Is often marginal for this purpose, but much can be deduced from the 1ocatlon of i t s maxima, and of those zeros not required by crystal symmetry. Relatlve, signed values for individual d-coefflclents were obtained using this method for two materlals, d-LAP,4 and NaLaF4.26 K1elnmansymmetry8 reduces the number of unknowns, and is usually well within the uncertainty of these measurements. For blaxlal crystals in point groups I, 2, m, and mm2, some convention must be chosen for the positive direction of the polar axls to uniquely define the relative signs.
For unlaxial crystals in 3, 3m, 6 and 4 i t is
necessary to find the 1ocatlon of the maximum def f relative to the (lO0) or (010) directions. Nlth the optlcally oriented crystal mounted on a gonlometer head, i t is straightforward to determine the complete relatlonshlp between the optical and crystallographlc axes by x-ray dlffraction. 12 8.
Oraanlc Nonllnear Materials for ICF Aoolications The laser required for an economlcally vlable power station using ICF is large. Energyof I - 10 MJ in a nomlnally lOns pulse, with a beam divergence not greater than 0.1 mrad, at a wavelength in the near u l t r a v i o l e t and posslbly large frequency bandwidth are currently thought to be requlred. I'2 This wavelength range can be reached by frequency
97
D. Eimerl et al.
98
conversion of an e f f i c i e n t infrared laser. For the overall laser system to be cost-effective, the frequency conversion must be very e f f i c i e n t .
That is, the nonlinear materlal must
have a low threshold power, and must not have significant absorptions at any of the relevant wavelengths.
However, all materials which satisfy a
particular threshold power criterion are not equally suitable in practice.
In the f i r s t place, detalled calculatlons show that a very
nonllnear material would necessarily be configured as a thin plate to avoid back-converslon. 2g Thin plates are mechanlcally weak and cannot be fabricated Into large area plates, 11mltlng the Indlvldual aperture size.
In the second place, the cost of the laser driver increases
significantly with the the sum of the areas of a11 the output apertures. There is a minimum value (and therefore a minimum cost) for the total aperture which is determlned by materials limlts on the intensity or fluence.
Thus, the total area w111 be affected by damage thresholds of
optlcal elements, and by any other Intenslty-llmltlng effects such as two-photon absorption, st|mulated Raman or Br111ouln scattering and self-focusslng and/or phase-modulatlon.
The last three processes are
determined by the chemical composition and structure of the material, while the damage threshold is determined by the presence of inclusions, defects, or impurities incorporated during crystal growth. Thus, ICF applications call for a hlgh damage threshold (20 - 40 J/cm2 at 10 ns, a11 wavelengths), 1'2 an effective coupllng about 2 - 4 times as large as that of KDP, and a low absorption.
The
angular sensitivity, stimulated Raman gain, and nonlinear refractive index must be comparable to or smaller than those of KDP. The material must be inexpensive to grow, fabricate and pollsh, would preferably be posslble to antl-reflection coat.
We believe that a11 of these
conditions can be met by certain molecular crystals of slmple organic compounds. Many organic crystals with second harmonic generatlng properties are known, II'21'30 and are of interest prlmarily due to their large nonllnearlty, the SHG moiety is a conjugated ring or its derivative. However, the conjugated ring is not sultable for ICF because i t exhibits photochemical processes in the near ultravlolet, as well as losses due to 11near and nonlinear absorption losses.
However, since the nonlinearity
required is not much larger than that of KDP, other SHG molties can be used, such as the conjugate C02 group. Indeed, using the expert system described earlier, we calculated the threshold power of all (suffIclently well characterized) known materials ? for doubling or
Nonlinearoptical materials~r high powerlasers
99
t r l p l l n g 1.064 I~m. He found that h a l f the known materials with threshold powers less than 40 HH (recall KDP = 80 HH) were ~ l e c u l a r , organic crystals containing small, conjugated, ionic groups attached to chtral carbon centers.7 Hhen these groups are i n t r i n s i c a l l y acentric, they have much larger hyperpolarJzabtltttes than nonconJugated u n i t s , such as the phosphate ion. The nonlinear coupling in such crystals is therefore l i k e l y to be adequate. Holecular c h i r a l l t y guarantees that the crystals w t l l be acentrtc, and most crystals f a l l into point groups 2 or 222. Examples of t h i s kind of moiety are shown in Fig. 20. Crystals containing these molecules can be grown easily from aqueous solution as salts with various metallic or organic countertons or as zwttteriontc crystals. Horeover, such crystals are mechanically harder and more stable in a i r than KDP. On the other hand, structural differences among these compounds lead to a range of btrefrtngence and optic angles. This is i l l u s t r a t e d in Tables 7 and 8, which describe the linear and nonlinear optical properties of various l-Argtntne compounds.31 In the molecular "gas" model, the antsotroptc components of the optical properties of the crystal are given by summing the contributions of Individual molecules fixed in space. The v a r i a t i o n In the btrefrtngence and optic angle r e f l e c t s the d i f f e r i n g relattve orientations of the individual molecules. In general, chtral organic molecular crystals e x h i b i t a wtde v a r i e t y of phase-matching properties, such as angular s e n s i t i v i t y and n o n c r i t i c a l phase-matching wavelengths, but these properties depend on the structural details of the crystals and cannot be eastly engineered. Thus, the angular s e n s i t i v i t y , and the noncritical wavelengths are the major unknowns in thts class. However, because the chemical moieties in
H NH2
R'--
R'--.
--
I NH~,
R"/C ~
+..)c
--R
N
H Carboxyl
Guanadyl
Hlstadyl
20. A t t r a c t i v e chemical moieties for generation of 355 nm l i g h t in our molecular engineering approach to new nonlinear materials for laser fusion experiments.
D. Eimerl et al.
100
these crystals are similar and they are all lonlcally bonded, many other properties which rely less c r l t l c a l l y on structural details w111 show marked regularlties. In partlcuIar, their mechanlcal strength, and the linear and two-photon absorption properties, which arise from slmllar spectroscopic transltlons, are not expected to vary strongly from crystal to crystal. Of course, these properties may well have an orlentatlonal dependence which varles with structure. Thus, In following this strategy, the focus of ICF research is on the 11near optlcal properties: adequate nonllnearlty is more common than s u f f i c l e n t l y low angular sensitivity. In fact, most of the compounds we have examined have adequate blrefrlngence for second- and thlrd-harmonlc generation of 1.064 ~m, but most have a larger angular s e n s l t l v l t y than KDP because the blrefrlngence Is slgnlflcantly larger. He have found several crystals with nonlinearitles 2 - 4 tlmes greater than the d36(KDP). Table 7 gives the phase matching parameters for several crystals we have characterized recently using the mlcrocrysta111ne techniques. These Include L-arglnlne phosphate (LAP), L-arglnine fluorlde (LAF), and dlammonlum tartrate (DAT). Crystals of DAT and ~F T~ble 7.
ProDertles of some ionic oraanlc crystals for doubllna 1.064 um
Material
Type
LAP
I
0.99
6900
63
II
0.93
4]00
26
I
1.24
4900
21
II
0.93
4100
26
I
0.53
5700
154
II
0.37
2150
47
LAF
DAT
.
.
.
.
KDP
(a)
.
.
.
.
.
.
.
.
.
.
.
deff(pm/V)(a)
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
(cm-I/rad)
.
.
.
.
.
.
.
.
.
.
.
.
.
.
Pth(MW)
.
.
.
.
.
.
.
.
.
.
.
.
I
0.25
4900
500
II
0.35
2500
70
Maximumdef f for the given type.
Based on d36 - 0.93 pm/V.
.
.
.
.
.
.
.
.
.
.
.
.
Nonlinear optical materials for high pOwer lasers
101
and other compounds have been grown by slmple evaporatlon or coollng technlques to volumes between I and 10 cm3, and crystals of LAP to about 100 cm3 and larger. 9.
Oottcal prooert1~s of Chtral Actd Crvstals
The u l t r a v i o l e t edge ts determined by strong ~ - ~* t r a n s i t i o n s associated wtth the small conjugated groups. Thts edge ts generally at wavelengths lower than 250 nm for carboxylate or guanadyl groups, and may be somewhat redshtfted for tm|dazolyl (Ftg. ZO). However, LAP exhtbJts a s i g n i f i c a n t absorption feature 4 (1-3 ~/cm) in the region between 250 and 300 nm. Thts Js probably due to n - ~* t r a n s l t t o n s . The wavelength of these t r a n s i t i o n s Jn carboxyllc actds has been shown to depend s i g n i f i c a n t l y on the molecular structure, 3Z but very l t t t l e Information ts known about thetr behavtor tn other kinds of organic salts. In the near infrared, (0.9-1.5 Fm) overtone absorptions of N-H, O-H, and C-H stretching vibrations can be qutte strong. These crystals are extensively hydrogen and consequently have overtone absorptions whtch lead to losses of 10-20~/cm at the Nd:YAG fundamental wavelength. 33 DeuteratJon can reduce thts absorption s i g n i f i c a n t l y . 4
C-H stretching
overtones are s i g n i f i c a n t at 0.910 and 1.2 t~m. These covalently bonded protons are not as easily replaced by deuterium, however. L i t t l e information is available concerning two photon absorption tn organ|c s a l t s . Stmple symmetry arguments suggest that the same v - v* t r a n s i t i o n s which determine the 1 photon UV edge are also s i g n i f i c a n t l y two photon active. (In fact, they must be Jf these t r a n s i t i o n s are to flgure strongly in the x (Z) response.) Thus, the two photon edge Is expected to begin around 400 nm, making the strength of such transltJons an Important tssue for generating harmonics tn the near u l t r a v i o l e t . The nonllnear tndex determines the threshold | n t e n s i t t e s for catastrophic s e l f focusing. I t correlates strongly wtth the size of the l i n e a r Index and tts dispersion.
Heasurements on LAP at LLNL tndtcate
that nZ ts not s i g n i f i c a n t l y d i f f e r e n t than what would be predicted by r e f r a c t i v e index scaling. 34 Table 8 contatns data on the nonlinear refract|ve index nZ for LAP, KDP and potassium t t t a n y l phosphate (KTP) for comparison. High frequency, narrow Raman resonances can lead to low thresholds for stimulated Raman scattert~q (SRS).
Intense transverse SRS can cause
D. Eimerl et al.
102
Table 8,
Nonlinear refractive index (n 2) values for some freauency
doublinq crystals. (a)
~rvstal
~
Dz(X1013cm3/era)
KDP
1.49
1.0 - 3.6
LAP
1.55
1.87 - 3.04
KTP
1.77
2.5 - 5.7
(a) taken from Ref. 40. significant energy loss or even physlcal damage to the nonllnear crystals. 35 Of primary concern in organic crystals are aliphatic C-H vibrations in the 2900 cm-I region. These can have spontaneous Raman scattering intensities 2-3 times larger than other Raman active vibrations in these crystals, e.g. the carboxylate symmetric stretch at 1460 cm-l. 36 However, typlcal magnitudes of the a11phatlc C-H mode scattering cross sections in these crystals are not known, nor have the linewldths been quantltatlvely documented.
He may estimate the potential
SRS gain by noting that the C-H modes (2858 cm- I ) in the allphatic hydrocarbon decalln have an SRS gain coefficient of 0.7 cm/GH.35 (By comparison, the gain coefficient of the phosphate symmetric stretching mode in KDP is approxlmately 0.2 cmlGH.)35 The relevance of this estimate is uncertain because the linewldths of such vibrations in crystals may be much smaller than those of liquld deca]in. Nonetheless, i t demonstrates the potentlal impact of these modes on SRS thresholds. In summary, the group of chlral, ionic, organic crystals contains a significant number of materlals which have moderately large nonllnearlties (I-2 pm/V), favorable phase-matching properties for vislble or near ultravlolet, and which grow easily into large, high optlcaI quallty crystals.
The simple engineering approach of attaching
103
Nonlinearopti~l mmteHals~r high powerlase~ Small, conjugated 1onto groups to chtral carbon centers to produce new crystals of thts type ts far from exhausted. There ts evidently no i n t r i n s i c constraint imposed by optical damage, and the nonlinear r e f r a c t i v e tndex, the two-photon absorption and the stimulated R~uMn scattering strength are expected to be similar to those tn materials wtth similar l i n e a r refractive indices, UV edges and chemical moieties. The promise of thts class ts that t t may provide a set of nonlinear materials, al1 more nonlinear than KDP. and wtth a range of phasematchtng properties and noncritical wavelengths. A suite of such materials spanning the v i s i b l e and UV spectrum would represent a s i g n i f i c a n t advance tn the technology of frequency conversion of htgh power lasers. A summary of a study of crystals of other salts of L-argtntne has been published. 31 10. L-Aratntne Phosohate L-Argtnlne phosphate ts an example of the chtral organtc materials we have been studylng for laser fuston applications. Both LAP and tts deuterated analog, O-LAP, grow eastly from aqueous solution, are monocltntc, space group P21, and also they are phasematchable for a l l processes where KDP is phasematchable. Hith the posstble exception of harmontc generation to wavelengths shorter than about 270 nm, thetr threshold powers are smaller than those of KDP or barium borate by a factor of 2 or 3. In the absence of opttcal absorption, then, these materials are considerably more e f f i c i e n t , for a given laser source, than KDP. They are r e l a t i v e l y Inexpensive, posses a htgh damage threshold, and achieve higher efficiency than KDP using a smaller crystal volume. Table 3 sumartzes t t s linear and nonlinear opttcal properties, and Fig. 21 shows phasematchtng curves. The undeuterated crystal has substantial absorption at 1064 nm, between 5 and 20 ¢/cm, depending on the polarization.
Thts absorption ts
due primarily to overtones of OH and NH vibrational excitations, yet not to CH vibrations. The absorption can be removed by deuteratton, and for deuteratton levels above 95~ the absorption is less than 1 ¢/cm, which ts s u f f l c t e n t l y low for many applications Including ICF. I t ts not necessary to deuterate the CH sites, but only the NH and OH sttes, which ts eastly accomplished by r e c r y s t a l l t z a t t o n from aqueous solution. The deuteratton of the OH and NH sttes can be brought a r b i t r a r i l y close to 100¢ by thts procedure. A thorough study of the crystal growth and scaltng of D-LAP Is betng carrled out by Cleveland Crystals, Inc. Htgh opttcal q u a l l t y crystals suttable for harmonic generation have been grown as large as 7 x 8 x 4 cm.
104
D. Eimerl et a/.
Y
0 2~,4~ 10
20' 30 0 40: 50 60
70: 80 90 CZ
0
10
]L t
20 30 40
50
6"0
70
80
90
0
0
10
20 30 0 40 50 60 70 80 9O O~
10
20 30
40 ~ 50
60
70
80
90
21. Empirically determined phasematching loci for LAP. The solid lines are the same loci calculated from the Se]Imeier Formula. (a) 2~ Type I, (b) 2~ Type I I , (c) 4~ Type I, (d) 3~ Type I, (e) 3~ Type I f .
Nonlinear optical materials~r high power lairs TWO interesting features of D-LAP have emerged recently.
The f i r s t
ts that as currently grown, I t exhibits a weak blue fluorescence under Irradiation with 355 nm ltght, but extensive tests at thts wavelength indicate that they do not experience damage or solartzatton.
On the
other hand, under shorter wavelength 11ght they darken, apparently undergoing a photochemical process.
The wavelength where thts
photochemistry sets in Is not yet known, but t t ts certainly below 300 nm and we belteve that t t is near 270 nm.
He believe that the UV-tnduced
photochemistry below 270 nm may be intrinsic to the crystal, In which case the crystal would be generally unsuitable for UV applications below thls wavelength. On the other hand, the blue fluorescence seen In 355 nm experiments Is observed to have a strong dependence on position In the crystal, and Is certainly associated wlth inclusions. There Is no correlation between the sources of fluorescence and damage.
The chemical
nature of the fluorescing inclusions has not yet been identified, but It is likely that they are other organic molecules, such as aldehydes, or perhaps benzene rlng compounds and their derivatives, such as tryptophan. The fluorescence spectrum matches closely that of guanadyl, suggesting that energy Is transferred from absorbing inclusions to the guanadyl Ion, which then fluoresces. It may be possible to reduce the fluorescence by purifying the starting materials for crystal growth. Note that thls fluorescence Is not necessarily a disadvantage. For example, the output of a third harmonic generator wlll cause fluorescence, which will be monotonic In the 355-nm output energy. The fluorescence can therefore be used to sake an In sltu measurement of the conversion efficiency without the need for calorimetry In the target chamber. In fusion experiments, this would be of considerable value. The second interesting attribute of d-LAP concerns Its temperature bandwidth. The temperature bandwidth Is very large where the linear temperature sensitivity BT ts zero.
a&k/aT
(25)
In contrast to untaxtal crystals, in btaxtal crystals such as
LAP the temperature s e n s i t i v i t y varies along the phasematchtng curve. For LAP, t t actually has a zero, for both second and third harmonic generation of 1064 nm, and for both Type ! and Type I I processes.
At
these points on the phasematchtng curve, the temperature bandwidth ts very large. direction.
These points are close to the optimum phasemtchtng The threshold power at this zero ts about an order of
D. Eimerl et al.
106
magnitude larger than the minimum threshold power quoted earller, but is nonetheless low enough to provide efficient conversion.
For example, for
Type I I second harmonic generation, the minimum threshold power is about 30 MH, whereas at the zero of the temperature s e n s i t i v i t y , I t is about ]70 MH. Thus LAP and d-LAP are capable of temperature-insensitlve operation, at some cost in the threshold power, or efficiency. The posslbl]ity of large temperature bandwidth makes d-LAP a candidate for medium average power devices. However, under thermal load, the crystals w i l l also generate stress, and the presence of a cleavage plane makes i t vulnerab|e to thermal-stress-induced fracture. The eIastlc constants and thermal expansion of LAP have been measured recent]y, 37 and used to ca|cu|ate i t s resistance to therma] fracture. 5 Again, this varies along the phasematchlng curve, but at the location of the zero of the temperature s e n s i t i v i t y , i t Is about as resistant as KDP to thermal fracture. Therefore, we have concluded that d-LAP, whose absorption and thermal fracture properties are similar to KDP, does not derive any slgnlf|cant advantage over KDP In average power appIicatlons, despite its potentla]ly high temperature bandwidth. d-LAP Is currently under development for fusion applications.
In
addition to favorable optical properties, I t Is amenable to cutting, poItshlng, dlamond-turnlng and sol-gel anti-reflectlon coating. I t is currently our leading harmonic generation material for future laser fusion experiments. 11. Hioh Averaoe Power Material@ Under average power conditions, the optical absorptlon of the nonlinear material causes thermal gradients which disturb phasematching and can cause thermal fracture. 5 Thermal effects are described by two figures of merit, the thermal dephaslng parameter, and the fracture temperature. The thermal dephaslng parameter, Hm, relates the thermal dephaslng (In radlans) to the average power and the dimensions of the crystal. Hm
-
8K / =I~T
(26)
where K is the thermal conductivity, and ¢I Is the optlca] absorption.
The fracture temperature is a material figure of merit whIch
ranks materlals by their reslstance to thermal fracture. mechanlcally isotroplc material,
For a
Nonlinear optical materials ~ r high power l a i r s
&TF -
3SF(1-v)I2E¢T
107
(27)
where SF ts the surface fracture stress, v Is r a t i o . E Is Young's modulus, and ~T Is the thermal expansion c o e f f i c i e n t . Because fracture stress depends on the defects In the surface, the fracture temperature figure of merit ts defined for a p a r t i c u l a r d i s t r i b u t i o n of surface defects. Physically, the fracture temperature describes the fracture point of a thtn plate of i n f i n i t e area. whose surface has a p a r t i c u l a r d i s t r i b u t i o n of defects, tn which a quadratic temperature p r o f i l e has been established between the mtdplane and the surface. As the height of the quadratic temperature p r o f i l e ts increased, the surface stress increases, and at some point exceeds the surface strength. The fracture temperature describes that point. I t ts a materlal figure of merit describing an idealized s i t u a t i o n , and t t does not necessarily descrtbe the fracture point of real plates. In antsotroptc materlals the fracture temperature and the thermal dephastng parameter depend on the orientation of the plate. 5'3g For example, the fracture temperature of KDP ts shown tn Ftg. 22 as a function of o r i e n t a t i o n . Most nonlinear materials dtsplay the same large anlsotropy In t h e i r a b i l i t y to withstand thermal gradients; a summary of the results for some common materials ts given tn Table 9. 12. Future Directions Thts paper has reviewed progress In new, p o t e n t i a l l y inexpensive materials for nonlinear optics tn the wavelength range 300 - 1200 nm. The theoretical analysis has shown that the threshold power ts the essential parameter tn the frequency conversion of collimated laser beams, and thts single parameter serves to rank ~ t e r t a l s . Using the database and expert system, two points became clear.
F i r s t , that t t ts
not posstble for a materlal wtth a t y p t c a l wavelength dependence to t t s r e f r a c t i v e indices to be Ideal for a11, or even most, nonlinear opttcal processes. Second, that there ts a lower l t m t t on nonlinear opttcal technology represented by the fact that the smallest threshold powers for processes tn the v t s t b l e part of the spectrum are tn the tangle of i0 100 1414. Achieving htgh conversion efficiency wtth a matertal wtth a threshold power tn thts range, requires either a very htgh peak power laser, 1 - 10 GH, or a laser which ts close to d i f f r a c t i o n 11mtted, and which also has f l a t temporal and spattal p r o f i l e s . The technology of nonlinear optics w t l l beneftt most from a suite of nonlinear materials
D. Eimerl et al.
108 20
18
t
i
I
I
I
I
I
i
i
I
I
r
50
60
70
80
= 45 ° 16
o
14
¢ = 30
12
°
0 D
10 E O= 15 ° ,.,=
LL
(~= 0 °
0
I
o
lO
I
J
I.
20
30
40
90
Polar angle, 9
22. The fracture temperature of KDP as a function of orientation. nonllnear materials display a similar anisotropy.
Table 9.
Fracture Temoerature of Nonlinear Materials
Material
Range
epm (deg.)
KD*P
4-20
36 (I)
17
54 ( I I )
5 7
ATF ('C)
LiNbO3
4-11
- 90 (I)
LilO 3
5-19
31 (I)
10
BBO
20-285
23 (I)
200
32 ( I I )
90
Most
Nonlinear optical materials ~ r high power l a i r s
such that for any p a r t i c u l a r combination of wavelengths, a low-threshold-power ~ t e r J a l is available. Blaxtai ~ t e r t a l s have a greater potential than untaxlal materials for providing a range of low threshold power. The opttmal bJaxtal material, from t h i s perspective, has a low optic angle, so that t t possesses a low btrefrtngence plane. Ustng the molecular engineering strategy to develop new blaxlal materials, we found that I t ts r e l a t i v e l y straightforward tn organic materials to engineer materlals which are transparent from below 300 nm to 1200 nm, and which posses nonlinear couplings of 1 - 3 pm/V. The more d t f f l c u l t parameter to engineer ts the btrefrlngence. In thts sense, developing materials for high power applications ts more a program tn ltnear opttcal properties than In nonlinear opttcal properties. Unttl a deeper understanding of crystal structure of molecular crystals ts developed, we would expect that the ltnear opttcal properties w i l l conttnue to be the most important parameter of new nonlinear opttcal materials. Hlgh average power materlals must not only meet the threshold power requirement, but they must also withstand thermal gradients. The most important parameter for this application is therefore the 11near optlcal
absorption. In organ|c materlaIs the hydrogen vibrational overtones will necessarily lead to significant (about O.OOl/cm) absorption In the near infrared, because I t Is not posslble to remove all the protons from the crystal. He have consldered the possib111ty of organic materials without hydrogen, such as perfluorlnated materials, but very few of these are known, and I t Is not known whether they form acentrlc crystals. The lowest absorption w111 probably be found In the inorganic materlals, but as yet no slmple synthetic strategy exists for acentrlc Inorganic crystals. Eventually, I t w111 be necessary to address the problem of crystal structure of both organic and inorganic materials, together with the optical structure-property relations necessary for guidance. Unfortunately, crystal structure continues to be an impenetrable subject, and progress in nonllnear materlals wlll langulsh whlle an understanding of structure is lacklng. On the other hand, In the foreseeable future the most frultful area for ICF and other hlgh power appllcatlons w111 continue to be the organic molecular crystaIs of the type already under study. It Is entirely posslble that within thls class, low threshold power materlals w111 be found for most Interestlng appllcatlons.
109
110
D. Eimerl et al.
Acknowledqements I t Is a pleasure to acknowledge the c o n t r i b u t i o n s of D. Mllam and R. Gonzales, who carrled out the measurements of the damage thresholds.
AoDendIx:
Jacobl Function Routines
The f o l l o w l n g routines f o r the Jacobl e111ptlc functions are based on the i n f i n i t e product representations given in Ref. 40.
Although not
optimized for speed, they are e a s i l y f a s t enough f o r most applications in nonllnear optics.
The number of loops required f o r convergence diverges
as the laser brightness, X, becomes large.
For m < 10-4 , double
precision Is suggested, and f o r m < 10-7 , the a n a l y t i c s o l u t l o n f o r the conversion e f f l c i e n c y should be used i f posslble. ( I ) Comolete E111otlc Integral K(m) def fnkm(m)
'
Assumes that 0 < m < 1
qkn - sqr(m) : qkm- 2 " a t n ( l ) qkmloop: qkp - sqr(l-qkn'qkn) : qkn - (1-qkp)/(1+qkp) : qkm - qkm*(l+qkn) i f qkn > Ie-14 then go to qkmloop fnkm , qkm end def (2) Jacobi Functlons sn.cn.dn(u.m) '
Subroutine f o r sn cn dn Jacobl functions
pl - 4*atn(1) : mpr - 1-m : km - fnkm(m) : kmpr - fnkm(mpr) q - exp(-pl*kmpr/km) : x - u*pl/km : cp - cos(x) sn - 2 * s t n ( x / 2 ) * s q r ( s q r ( q / m ) ) cn -
2*cos(xl2)*sqr(sqr(q*mprlm))
dn -
sqr(sqr(mpr))
Jacloop:
qJ-q*qn
da -
l+qj*qJ
sn -
sn*(dl-d2)/dd
if
abs(d2)
: qn -
1
: qn-q*qj
: db - 2 * q J * c p
> le-14
: cn -
:dd - da-db
cn*(dl+d2)/dd
: dl
-
l+qn*qn
: d2 -
2*qn*cp
: dn - d n * ( d a + d b ) / d d
then goto Jacloop
end sub
Disclaimer This Document was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor the U n i v e r s i t y of C a l i f o r n i a nor any of t h e i r employees, makes any warranty, express or implied, or assumes any legal l i a b i l i t y or r e s p o n s i b i l i t y f o r the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents
111
Nonlinearo~ical matenals ~rhighpowMlase~
that its use would not infringe privately owned rights.
Reference
herein to any specific commercial products, process, or service by trade name, trademark, manufacturer, or otherwise, does not necessarily constitute or imply i t s endorsement, recommendation, or favoring by the United States Government or the University of California. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government hereof, and shall not be used for advertising or product endorsement purposes. References 1.
J. Holzrichter, E. M. Campbell, J. O. Ltndl, and E. Storm, "Research with High-Power Short-Navelength Lasers", Science 229, 1045 (1985).
2.
J. F. Holzrtchter, D. Etmerl, E. V. George, J. 8. Trenholme, N. N. Simmons, and J. T. Hunt, "Htgh Power Pulsed Lasers", J. Fuston Energy 2, S (1982) D. Elmerl, "E1ectro-optlc, Linear, and Nonllnear Optlcal Properties of KDP and I t s Isomorphs", Ferroelectrlcs 72, 95 (1987)
3. 4.
5.
D. E1merl, S. Velsko, L. Davis, F. Nang, G. LoJacono and G. Kennedy, "Deuterated L-Arglnine Phosphate: A New Efflclent Nonllnear Crystal", submitted to J Qu. El. D. Elmerl, "High Average Power Harmonic Generation", I . E . E . E . J . Quant. Electron. 0E-23, 575, (1987)
6.
O. Elmerl, L. Davis, S. Velsko, E. K. Graham and A. Zalkln, "Optlcal, Mechanlcal, and Thermal Properties of Barium Borate", O. App1. Phys. 62, 1968 (1987)
7.
D. Etmerl, "Frequency Conversion Materials From A Device Perspective", Proc. SPIE 681, 2 (1986) F. Zerntke and E. Midwinter, Aoolted Nonlipear Oottc}, (NIley, New York, 1973)
.
9.
R. S. Craxton, S. D. Jacobs, O. E. Rtzzo, and R. Boni, "Basic
Properties of KDP Related to the Frequency Conversion of ll~m Laser Radiation", I . E . E . E . J . Quant. Electron. OE-17, 1782 (1981) 10. D. Bruneau, R. M. Tournade, and E. Fabre, "Fourth Harmonic Generation of a Large-Aperture Nd:Glass Laser", Applied Opttcs 24, 3740 (1985) 11. S. K. Kurtz, J. ~erphagnon, and M. M. Choy, "Nonl|near D i e l e c t r i c S u s c e p t i b i l i t i e s " , tn Landolt-Bornstein New Series Vol. 11, p. 671 (Springer Verlag, N.Y., 1978); J. Jerphagnon, S. K. Kurtz, and J. L. Oudar, Landolt-Bornstetn new Series Vol. 18, p. 456 (1984).
112
D. Eimerlet al. 12. F. Donald Bioss, The Sptndle Stage:
Prlnciples and Practice,
Cambridge Unlv. Press, N.Y. (1981). 13. F. Donald Bloss, An Introduction to the Methods of Opttcal Crystallography, Holt, Rhtnehart and Hlnston, N.Y. (1961). 14. O. Medanbach, "A New Mtcrorefractometer Spindle-Stage and i t s Application", Fortsch. Miner., 63, 111 (1985). 15. J.-L. Crovtster, "Methode de Measure Rapide des t r o i s Indices de Refraction Principaux des Mineraux en Grains", Bull. Miner. 103, 40 (1980). 16. V. G. Fekllchev and N. V. Flortnsky, "A Universal Set to Determine Refractive Indexes by the Theodoltte-lmmerston Method", Isv. Akad. Nauk, CCCP, Ser Geol. 12, 106 (1965). 17. S. K. Kurtz and T. T. Perry, "A Powder Technique for the Evaluation of Nonlinear Optlcal Materials", ~. ADo], phvs. 39, 3798-3813 (1968). 18. M. L, Bond, "Measurement of the Refractive Indtces of Several Crystals", J. Apol. Phys. 36 (5), 1674-1677 (1965). 19. S. K. Kurtz, "Measurement of Nonlinear Optical S u s c e p t l b t l t t i e s " , Ouantum Electronics, Vol. IA, H. Rabin and C. L. Tang, eds. (Academic Press, New York, 1975). 20. J. Q. Yao and T. S. Fahlen, "Calculatlons of Optimum Phasematch Parameters for the Blaxial Crystal KTiOP04", J. App1. Phys. 55(I), 65-68, 1984. 21, S. Slngh, "Nonllnear Optical Materlals", In The Handbook of Laser Science and Technology, Vo1. I I I , M. J. Heber, editor (CRC Press, Boca Raton, FL., 1986) pp. 3-248. 22. S. Velsko, "Direct Assessment of the Phasematching Properties of New Nonlinear Materials", in Laser and Nonllne~r Ootlcal Ma~erl~1~, L. DeShazer, ed., Proc. SPIE 681, 25-29 (1986). 23. J. A. Giordomalne, "Mixing of Light Beams In Crystals", Phys. Rev. Lett. ~ ( I ) , 19-20 (1962). 24. P. D. Maker, R. H. Terhune, M. Nisenoff, and C. M. Savage, "Effects of Dispersion and Focusing on the Production of Optical Harmonics", Phys. Rev. Lett. ~(1), 21-22 (1962). 25. M. V. Hobden, "Phasematched Second Harmonic Generation in Biaxlal Crystals", J. Aopl. Phvs, 38, 4365-4372 (1967). 26. S. Velsko and D. Eimer], "Phasematched Second harmonic Generation in Sodium Lanthanum Fluoride", 3. Appl. Phys., 62(6), 2461-2465 (1987). 27. R. S. Feigeison, H. L. Kway, and R. K. Route, "Single Crystal Fibers by the Laser-Heated Pedestal Growth Method", In Infrared Ootlcal Materials and Fibers I l l , Proc. SPIE, Vol. 484, P. Klocek, ed.
Nonlinear opti~l materials for high power lasers
28. J. 8adan, R. Hterle, A. Pertgaud and P. Vtdakovtc, "Growth and Characterization of Holecular Crystals", in Nonlinear Oottcal Pronerttes of Oraantc Molecules and Crystals, Vol. 1, D. S. Chemla and 3. Zyss, eds. (Academic press, Orlando, FL, 1987). 29. D. Elmerl, unpublished 30. R. T. Twelg and K. Jaln, "Organic Materlals for Optlcal Second Harmonic Generation", in Nonlinear Ootlcal Prooertles of Oroanlc and Polvmerlc Materlals, David T. Hllllams, ed. (American Chem. Soc., Hashlngton, DC, 1982). 31. S. B. Monaco, L. E. Davis, S. P. Velsko, F. T. Hang, D. Elmerl, and A. Zalkln, "Synthesis and Characterization of Chemical Analogs of L-Arglnlne Phosphate', J. Cryst. Growth 85, 252 (1987) 32. H. Szyper and P. Zuman, "Electronic Absorption of Carboxylic Acids and their Anions", Anal. Chlm. Acta85, 357 (1976). 33. S. Velsko and D. Elmerl "New SHG Materlals for High Power Lasers" Proc. SPIE 622, 171 (1986). 34. R. Adair and L. Chase, private communication. 35. H. L. Smith, M. A. Heneslan, and F. P. Mllanovlch, "Spontaneous and Stimulated Raman Scattering in KDP and Index-Matchlng Fluids", in The Laser prooram Annual Reoort, UCRL-50021-8S, (1986). 36. DMS RamanlIR Atlas of Oroanlc Comoounds, B.Schrader and H. Meier, eds. (Verlag Chemle, GmBH, 1974). 37. H. Haussuhl and D. Elmerl, to be published 38. C. Chen and G. Llu, "Recent Advances in Nonlinear Optical and Electrooptlcal Haterlals", Ann. Rev. Mat. Sct. 16, 203 (1986). 39. D. Elmer1, "Thermal Aspects of High Average Power Electroopttc Switches", Z.E.E.E. 3. Quant. Electron. 0E-23, 2238 (1987) 40. I. S. Gradshteyn and I. H. Rhyzlk, "Tables of Integrals, Series and Products', Academic Press, New York and London, 1965 Ed., Equations 8.119 and 8.146 (22, 23, and 24).
113
0146.-3535/90 $0-00 ÷ .50 13¢J0 Pergamon Press pie
Printed in Great Britain.
PROGRESS IN NONLINEAR OPTICAL MATERIALS FOR HIGH POWER LASERS* D. Eimerl, S. Velsko, L. Davis and F. Wang Lawrence Livermore National Laboratory, P.O. Box 5808. Livermore, California 94550, U.S.A.
ABSTRACT Over the last few years, substantial progress has been made at the Lawrence Livermore National Laboratory tn nonlinear materials for high power laser applications.
Specifically, we are developing materials for
frequency conversion of lasers used in laser drtven, thermonuclear fuston experiments and in high average power laser systems.
He have developed
new experimental procedures for f u l l y characterizing the linear and nonllnear optical properties of mtcrocrystals.
Using new theoretical
results we have developed a systematic method of selecting and optimizing nonlinear crystals for high-power and high-average-power laser applications.
Our molecular engineering strategy for developing new
materlals for the fusion application has resulted in the discovery of several new materials with more attractive parameters than KDP.
*Hork performed under the ausptces of the U.S. Department of Energy by the Lawrence Ltvermore Natlonal Laboratory under Contract No. H-7405-ENG-48.
59
60
D. Eimerl et al.
CONTENTS PBge
I
Introduction
60
2
Selectlon and Optimizatlon of Nonllnear Materials
62
3
ThresholdPower
69
4
Databaseon Nonllnear Optical Materials
80
5
Microcrystal Characterization Techniques
81
6
DoubleSplndle Stage Refractometer
83
7
The Nonllnear Optical Gonlometer
87
8
OrganicMaterlals for ICF Applications
97
g
Optlcal Properties of Chiral Acid Crystals
101
lO
L-Arginine Phosphate
103
II
High Average Power Materials
106
12
Future Directions
107
Appendix: 3acobl E11iptic Function Subroutines
I.
II0
Intro~vction Over the last few years, experiments in laser-driven inertially
confined fusion (ICF) have shown clearly that targets use the drive laser energy more efficiently when irradiated with short wavelength lasers. 1'2
However, the efficiency of the ICF laser driver tends to
decrease at shorter wavelengths. The optimum wavelength will be a compromise between target efficiency and laser technology, and will almost certainly be in the range 250 nm-500 nm.
The most effective laser
architecture to reach this range uses harmonic generation of an efficient near-lnfrared laser source. KDP (Potassium Dihydrogen Phosphate),3 the material currently used in Nd:glass lasers for ICF research, is not ideal for future ICF drivers because i t has a low threshold for optical damage and its conversion efficiency is compromised by a combination of its acceptance angle and nonlinear coefficient.
To be economically viable, future Nd:glass or
other near-IR ICF lasers (which are very large) will require harmonic generators which are both very efficient, and cost-effectlve.
He have
therefore organized an investigation of new nonlinear materials, with the goal of developlng, and eventually deploylng, a materlal which is more
61
Nonlinear optical materials ~ r high power las41rs
e f f i c i e n t and l e s s expensive than KDP. At least one such material has been i d e n t i f i e d (d-LAP, deuterated 1-argtntne phosphate) 4 and i s c u r r e n t l y under development.
Materials whtch improve on KDP can be used
In many other applications where htgh power lasers are Involved.
He
therefore expect that despite the r e l a t i v e l y narrow near-term focus, progress In the ICF application w t l l also bring inexpensive new materials for many other applications. For the ICF appltcatlon, crystals grown etther by aqueous solutton or by low temperature Brtdgman methods are l i k e l y to be the most economical, and tn thts category, we have i d e n t i f i e d several classes of molecular crystals with appropriate properties. In p a r t i c u l a r , we are Investigating molecular crystals based on amtno acids. These molecules include both a chtral center, and a r e l a t l v e l y strong harmonic-generating u n i t , and are t o n i c a l l y bonded.
Most are more nonlinear than KDP, and
they possess a wtde range of btrefrtngence (0.01 to 0.15). have the advantage of being o p t i c a l l y btaxtal.
They also
Using new experimental
methods, characterization of Individual crystals ts carried out on I r r e g u l a r l y shaped mtcrocrystals 0.05 to 0.25 mm tn size. From such samples we measure the r e f r a c t i v e indices from below 400 nm to 1100 nm, and carry out a d i r e c t determination of the phasematchtng locus, and the nonlinear coupltng and angular acceptance along that locus. He can also measure the temperature bandwidth, i f needed.
By using such eastly
obtainable samples, we avoid the need for time-consuming crystal growth of a large number of materlals, and are able to concentrate crystal growth activity on Just those materials which are promising. Using these methods, we have Identlfled several salts of amino acids which are better than KDP. These Include LAP, and other arginlne salts, such as the fluorlde, chlorlde, bromide, and acetate. There are in fact many crystals in this class, and many of them are efficient nonlinear materials for hlgh power lasers. In addition to the ICF appllcatlon,
we are also Interested In
developlng nonllnear materlals for hlgh average power applications. Under these conditions thermal distortions arise from the 11near optlcal absorption of the crystals, and In general the beam quality of the laser source degrades, albelt slowly, with increasing average power. Thus high average power calls for nonllnear materials with very low absorption, high resistance to thermal fracture, and a tolerance for thermooptlc effects and imperfect beam quality.
For the average power appllcation,
we have concentrated on characterlzlng the commonly avaliable materlals rather than developlng new ones. The level of characterization required
O. Eimerl et al.
62
Is quite extenslve, 5 and is exemplified In our work on barium borate. 6 This paper reviews the research results at the Lawrence Llvermore National Laboratory In new nonllnear materials and the strategy we have developed to Identify new nonllnear materials for ICF applications.
This
paper addresses both the required materials parameters and figures of merit, ? and discusses new microcrystal experimental techniques.
We
also review our recent work on new, inexpensive, frequency conversion materials for ICF such as the arginines.
Finally, we compare several
common nonlinear materlals for high average power applicatlons. 2.
Selectlon and ODtlmlzatlon of Nonlinear Materials I t is we11-known that the efficiency of frequency conversion is very
small unless the process Is phase-matched.8 Phasematching means that the output waves originating from all points within the nonlinear crystal are in phase wlth each other Just as they leave the crystal.
For (Type
I) second-harmonlc generation, phasematching requires that the f i r s t and second harmonic electromagnetlc waves have the same phase velocity; in other types of frequency conversion I t gives a more complex relationship between the interacting waves' velocities.
However, because of wavelength
dispersion, the refractive Indices of optically Isotroplc materials Increase as the wavelength decreases, and phasematchlng is not posslble. The most common way to achieve phasematching is then to use a blrefrlngent crystal, where the phase veloclty typically depends on the direction of propagation of the wave and on its polarlzatlon.
By
adjusting the polarizations and the direction of propagation I t is posslble to use the blrefringence to compensate for the natural wavelength dispersion.
In fact this is typlcally how nonlinear crystals
are configured for frequency conversion. For a partlcular direction of propagation, the Interaction Is exactly phasematched, but for neighboring directions the waves no longer have the same velocities and the conversion efficiency is reduced. The range of angles over which the conversion efficiency remains high is called the acceptance angle of the crystal, and i t is strongly anisotropic. Referring to Fig. l, we define the sensitive plane to be the horizontal plane, and the insensitive plane to be vertlcal.
The acceptance angle is
very large for beam divergence In the insensitive plane, but in the sensitive plane I t Is typlcally small, about I mrad for a crystal I cm in length.
Consequently, the direction and beam divergence of the laser in
the sensitive plane must be controlled precisely to obtain high conversion efficiency.
Moreover, the acceptance angle of the crystal
63
Nonlinear optical materials for high power lasers e
Di
.
Crystal dimensions for frequency conversion using collimated beams. The larger dimension, Ds, lies in the plane wtth the smallest angular sensitivity. The acceptance angle In the orthogonal plane, containing DI, is about 100 mrad or larger for both unlaxlal and blaxlal crystals.
decreases as the length of the crystal increases; i f I t is I mrad for a I cm crystal, I t Is 0.5 mrad for a 2 cm crystal.
The longer the crystal,
the smaller the beam divergence in the sensitive plane must be to maintain high conversion efficiency. This has profound consequences. Diffraction provides a minimum value for the beam divergence, which is typlcally l mrad for a beam of wavelength 1064 nm and diameter 1 mm. For the typlcal nonllnear crystal the acceptance angle is about I mrad for a 1 cm long crystal; a crystal longer than I cm w111 therefore be less efficient, in general.
To be
efficient, a crystal with this sensitivity to beam mlsorlentatlon or divergence must be sufficiently nonlinear to convert the laser beam in less than I cm. longer than this.
Crystals with less angular sensitivity can of course be In general, high efficiency requires that the
conversion process proceed to saturation well before the effects of phase-mlsmatch are evident.
D. Eimerl et al.
64
He have completed a thorough study of the conditions under which e s s e n t i a l l y collimated beams5 have a high conversion e f f i c i e n c y .
The
equations for the general three wave mixing experiment, where two waves of frequencies = and f2 = mix to generate a wave at frequency (l+f2)~ are as follows: df/dz dgldz -
- C g*h e-iakz
(1)
- f2.C f*h e-iakz
(2)
+i&kz e
(3)
dh/dz = (1+f2).C fg
where the complex f i e l d amplitudes are f,g and h for the three frequencies u, f2 u, and (I+f2)~.
Thus for third harmonic generation,
f2 " 2, whereas for second harmonic generation f2 = I.
I t is
convenient to normalize the fields so that the intensity of the waves are F - f ' f , etc., with no other factors.
With this f i e l d normalization, the
nonlinear coupling C Is C I 2x(2Z0)112.deff/Xf.[ nfngnh] I/2
(4)
where Z0 = 377 Ohms is the impedance of free space, and the n's are the refractive Indices of the three waves. The term Ak in the exponent is the wavevector mismatch between the three waves.
In general Ak
receives contributions from beam divergence, temporal bandwidth, crystal homogeneity and temperature Inhomogenelty. Its minimum value is determined by the d l f f r a c t l v e contribution to the beam divergence. Ak
=
k f + kg
kh
-
Beae + other terms
Thus (5)
(6)
where AO is a measure of the beam divergence. The conversion efficiency n, is a function of only two parameters, in general.
These are the drive, ,10, and the dephaslng 6, defined
as follows. no =
f2.C2.12.(F+G)
(7)
6
(I12).Ak.I
(B)
=
Nonlinear optical materials for high power lasers
where 1 is the crystal length.
65
He have
(9)
n = nma x sn2 ([nolnmax ]I12, n~ax ) where sn Is a Jacobl e111ptlc functlon. (An algorlthm for the Oacobl e111ptlc functions which Is sultable for small desk-top computers Is Included In the Appendix.) As the argument of the 3acobl sn function increases, the efflclency peaks, and then falls, followlng Its perlodlclty. The maximum efficiency Is
112 nmax = 1 + 1/2x - [1Ix + 1/4x 2]
,
(10)
where
X - f2(F + G) C2/Ak 2.
(11)
The crystal length, at whtch the maximum efficiency ts achieved ts obtained from the value of no at the peak of the Jacob| function, namely at 2 2 nolnma x = K(nma x)
(12)
Thus the optimum crystal length lop t is given by •
f2.C 2 l~pt.(F+G)
2
m
nmax K(nmax)
2
(13)
These equatlons show how to optimize the crystal length, for a beam of glven Input Intenslty I = (F+G), and effectlve mismatch, &k.
There
are several slmple scallng laws contained in these results for nma x and lop t. Referring to Fig. I, let the beam or crystal aperture be D s |n the sensltlve d|rectlon, and D I In the Insens|tlve dlrectlon, and let the crystal length be I. The Intens|ty I = P/DsD I, where P is the total power in the laser beams (Intenslty.area product), and the relevant beam divergence Is &e = Q.X/D s. where 0 Is roughly the ratio of the beam divergence to that of a dlffractlon-11m|ted beam of the same aperture. In terms of the total power P and the beam quallty O, the drlve and dephaslng are
no = 8 =
f2.C2.[ 12/Ds0 i ] P (ll2).6e.Xf.CllDs).O
(14) (15)
D. Eimerl et al.
66
An immediate consequence of these equations is the important observation that both the drive and the dephaslng depend only on the crystal shade, and not on its absolute size.
I t is clear that Increaslng all the
crystal dimensions (I,D s, and DI) in the same ratio leaves no and unchanged. Thus, changing the beam intensity using telescopes for down-colllmatlon leaves both P and Q unchanged and merely results in a shorter optimum crystal length.
The optimum conversion efficiency and
the shape of the crystal which achieves this optimum are both unchanged. From Eqs. (10) and (11), the optlmum efficiency nmaX is a universal function of X, which is a measure of the laser brightness and a materlal figure of merit, the threshold power. That is X
,
P I PthQ2. [4Os/Di ]
(16)
and the threshold power Pth is Pth "
I / f 2 . [BSXf/C]2
(17)
Thus the maximum efficiency is independent of the absolute size of the beam, but is a unlversal function of the ratio p/Q2 and the threshold power, a material figure of merit. Figure 2 plots the maximum efficiency nmaX against the (dlmensionless) laser brightness, X, and Fig. 3 plots the optimum drive no at which the maximum efficiency is reached. Thus, given the task of optimizing the crystal dimensions for a general three-wave process, the procedure is as follows. (1)
Calculate the threshold power Pth for the three-wave process from the materials constants, C and ~e"
(2)
Calculate the dimensionless laser brightness, X, from the laser parameters P,Q, and Ds/Di , and the threshold power.
(3)
Read off the maximum efficiency from Fig. 2 (Eq. (]5))
(4)
Read off the drive no at which this efficiency occurs from Fig. 3, and use equation (]3) to calculate the crystal shade
[12/DsDi].
From this procedure, i t w i l l be apparent whether the material can be efficient for the given laser source, and i f so, what the crystal shape
67
Nonlinear optical materials for high power lasers 1.0
I
0.9 0.8
0.7 0.6
"6 O.5 '~ 0.4
8 "S
0.3
0.2
o.1
o .0100
.
I
I
I
[
I
.1000
1
10
100
1000
1000
The peak conversion efficiency for s p a t i a l l y and temporally f l a t pulses.
X ts the (dlmenstonless brightness, or power per untt solid
angle in the beam.
required w111 be.
He reemohasize that nothtna tn t h i s orocedure fixes
the absolute size of the crystal. I f the beam aperture is doubled using telescopes, then the optimum efficiency w i l l be reached wtth a crystal twice as long, and w i l l be exactly the same. The maximum conversion efficiency ts independent of the beam size. In contrast to arguments often made in the l | t e r a t u r e , the efficiency is not optimized by down-collimating to achieve high i n t e n s i t y ; down-collimation necessarily Increases the beam divergence and forces a shorter crystal length. The net r e s u l t ts that the maximum efficiency is unaltered by
D. Eimerl et a/.
68 12
10
._e .u
8 c
8
,J¢
o ._>= c~
o
~
.0100
.1000
I
I
l
i
1
10
100
1000
P
3.
10000
(4Ds
The drive no at which the peak efficiency given in Flg. 2 is reached.
X is the (dimensionless brightness, or power per unit solid
angle in the beam.
down-co]Iimation. considerations.
The crystal size is determined by other For example, i t is posslb]e to make the crystal as large
as is desired to avoid optical damage problems, or as small as desired to avoid problems associated wlth optical absorption and thermal gradients. This freedom to choose the size of the crystal without affecting the eFFiciency is extremely important in the design and optimization oF nonlinear devices. Thus the flnal step in choosing the crystal dimensions is (5)
Choose the beam aperture.
Nonlinear optical materials for high power lasers
This can be chosen on to s a t i s f y any number of requirements, not a l l of which are coa~)atible.
For example, the aperture is minimized to
reduce the undesirable effects of absorption or made large to design around optical damage issues. I t may also be determined simply by the size of available crystals. In t h i s connection, i t is important to note that the damage threshold of a nonlinear crystal is not so much a function of the crystal i t s e l f , as i t is a function of the imperfections, impurities and stresses introduced during crystal growth. Thus there may be a s i g n i f i c a n t sample-to-sample variation in the damage threshold of an optical c r y s t a l , depending on that p a r t i c u l a r sample's individual chemical h i s t o r y . Table 1 l i s t s the optical damage thresholds for some common nonlinear materials, as supplied. Specific individual crystals grown with fewer impurities and imperfections w i l l e x h i b i t a higher damage threshold than indicated in t h i s table. On the other hand, less perfect examples w i l l be less resistant to damage. 3.
The Threshold Power I t is apparent that the threshold power appearing tn the brightness X (Eq. 16 and 17, and Figs. 2 and 3), ts the fundamental figure of merit which determines whether a material can be e f f i c i e n t with a given laser source. Physically, t t is approximately the peak total laser power required in a c i r c u l a r , d i f f r a c t i o n - l i m i t e d beam in order to reach about 40~ conversion efficiency. Thus, in selecting materlals for a p a r t i c u l a r process, i t is necessary (but not always s u f f i c i e n t ) that the threshold power of the materlal be s t g n l f l c a n t l y less than p/Q2 for the laser source. Clearly, the threshold power is a useful figure of merit for ranking nonlinear opttcal materials; the material with the lower threshold power is considered superior, because i t can reach a higher efficiency at i t s optimized shape. Because I t represents the opttmum balance between i n t e n s i t y and beam divergence effects, the threshold power is q u a n t i t a t i v e l y useful only to the extent that beam divergence is the primary source of dephastng. For example, in short pulse applications the laser bandwidth is the primary source of dephastng, and therefore requiring that the threshold power be low enough is a necessary, but i n s u f f i c i e n t condition for high efficiency. The importance of the threshold power is that d i f f r a c t i v e contributions to the beam divergence are always present, and therefore i t is always a relevant parameter. The threshold power for doubling a 1.064 pm laser using a Type I I process in KDP is about 80 MH. Thus, for a twice dlffraction-llmited
69
70
O. Eimerl et al.
Table I.
Material
DamaaeThresholds of Nonlinear Materlals
Damage Fluence
Remarks"
(31cm2)
LAP
g.8
LAP
13.4
d-LAP
9.2
d-LAP
13.0
KDP
5.0
KDP
15.0
KD*P
5.0
KTP
g.o
KTP
13.0
KTP
> 20.0
LtNbO3:MgO
Recrysta111zed twice
Recrysta111zed twice
Improved growth process
Hydrothermal Flux (BeJjing) Phosphate flux (PhJllps)
10.0
LIfO3
- 2.0
BaB204
13.0
SrxBal_xNbO3
6.0
KNbO3
7.0
Fujian x = .60, room temperature data
Data for I n s Gausslan pulses at 1064 nm. "Damage threshold depends on sample history and growth parameters. The threshold for other samples may therefore vary considerably from the data presented here.
beam containing about 500 m3 in 6 ns, the conversion efficiency optimizes at about 50%. The threshold powers for frequency doubllng in other materials are presented in Fig. 4 for some common uniaxial crystals, and the associated angular sensitivities and coupllngs, Be and C are
Nonlinear optical materiels for high power lasers
1000
I
71
I BzO4 (U)
KDP(11) ~ " "
i
.oP(,)
10 0.4
0.6
0.8
1.0
1.2
1.4
1.6
Wavelength (microns)
4.
The threshold power for second harmonic generation for some common unlaxlal crystals.
presented tn Figs. 5 and 6. Calculations for some btaxial crystals are given tn Figs. 7, 8 and g. The data used tn these calculations ts ltsted tn Tables 2 and 3. Htth the knowledge that Pth represents the mtntmal peak power needed to obtain roughly 50~ conversion e f f i c i e n c y , the uttllty
of a matertal for doubltng can be tmmedlately tnferred from these
graphs. The threshold power, of course, varies from materlal to materlal, but it ~Iso varies along the phasematchlng curve for each materlal.
For
example, In KOP Type II doubllng the phasematchlng curve Is a circle , e . constant, encloslng the polar, or z-axls.
Thls clrcle lies
paralle1 to the xy plane , and posltlon along the phasematchlng curve Is specified by ~, the angle between the radlus vector at a given polnt on the clrcle, and the x-axls.
Thus, ¢ - 0 where the phasematchlng curve
intersects the xz plane, and ~ - =/2 where It Intersects the yz plane.
Along the phasematchlng curve, the nonllnear coefficient for KOP,
dell, varles as cos(Z~), but the angular senslt|vlty BB - 8(Ak)/ae Is a
72
D. E i m e r l et al.
100
I
1
103 (I)
s=O4 (i)
10 r
KDP (I)
_> LJrea(11) 1 p-
o,II III I, 0.4
5.
0.6
J,
0.8
, IIL'N°°,~''l
1.0 Wavelength (l.U11)
1.2
1 1.4
1.6
The angular sensltlvlty, ~klBe, for the materials Included In Fig. 4.
10
I~
)J
I
J
I
8
A
6
-
,
\\--..~o,
(,)
4
>~ ,,=, 2
0 0.4
6.
,,,KDP (
0.6
1
0.8
1
1.0 Wavelength (pro)
~
1.2
1.4
1.6
The coupling C, (units: GH-I12) for the materials included in Fig. 4
73
Nonlinear optical materials for high power lasers Table 2.
OotJcal Constants for Selected UntaxJal Nonlinear Materials
(a) n2
1 + S1 + S2X2 + S3Z4 + S4X2/(X2-S~) + S6/(X2-S ~)
I
sI (DP
Jrea
LtIO 3
BBO
CD*A
LiNbO3
Sellmeter Parameters (~ tn um)
s2
s3
s4 12.99707
s5 20.0
s6
1.260476
0
0
1.133831
0
0
1.1823
0
0
0
0
0.01250
0.173205
1.51527
0
0
0
0
0.0240
0.173205
2.39503
0
0
0.696664
6.5703223 0.059542
0.052416
1.92106
0
0
2.261063
24.46665
0.003362
0.178943
1.7405
-0.0155
0
0
0
0.0184
0.1338
1.3730
-0.0044
0
0
0
0.0128
0.1249
3.227935 20.0
0.01011279
s7 0.1137646
0.008653247 0.110875
0.6278496 -0.018220 0.0002813 0.780817
0.1407699 0
0.6236063 -0.009339 0.0019654 0.724959
0.141485
1.392928
-0.026301 -0.000087 2.520353
0.2170176 0
0
1.313283
-0.020484 -0.000237 2.266851
0.2097321 0
0
(b) d36 KDP
0.39
Urea
1.17
LtNbO3
Nonllnear Oottcal Constants (om/V) d15
dll
d22
4.43
LI IO3
B~ CO*A
0
0.2
1.40
0.60 4.64
2.45
74
O. Eimerl et al.
Table 3.
Ootlcal Constants for Selected Biaxlal Nonlinear Materlals (a)
n2 l
I + SI + s2X2 + s3~4 + s4~2/(X2-s~) + s6/(X2-S~)
s1
KTP
d-LAP
LFa
(a)
Sellmeler Parameters (X in um)
s2
s3
s4
s5
s6
s7
2.0129
-0.01664 0
0
0
0.03807
0.2070
2.0333
-0.01695 0
0
0
0.04106
0.2224
2.3209
-0.01763 0
0
0
0.05305
0.2441
2.2352
-0.00683 0
0
0
0.0118
0.1208
2.4313
-0.0143
0
0
0
0.0151
0.1463
2.4484
-0.0115
0
0
0
0.0172
0.1513
-1.606
-0.00131 -0.00083 2.44644 0.056364 0
0
-2.449
-0.00610 -0.00149 3.600]6
0.063803 0
0
-0.230344 0.00580 -0.07841 1.47954 0.111192 0
0
These Sellmeler parameters give accurate indices only in the region of
transparency, 0.19 - 1.2 ~m (b)
Nonlinear Ootlcal Constants (Dm/V)
KTP
0 0 5.4
0 0 4.15
0 0 11.4
0 6.3 0
5.1 0 0
0 0 0
LAP
0 0.4 0
0 0.92 0
0 -0.84 0
-0.58 0 -0.84
0 -0.58 0
0.4 0 -0.58
LF
0 0 0.95
0 0 -I.08
0 0 1.58
0 -I.08 0
0.95 0 0
0 0 0
constant.
Therefore the threshold power is a minimum where the coupling
def f is a maximum, namely at ~ = O.
In general, the optimum
operating point for a nonlinear materlal
is that point along the
phasematchtng curve where the threshold power is a mtnimum, but this is
75
Nonlinear optical materialsfor high lower lasers not necessarily the potnt at which def f ts a maximum. For the example of KDP, t t ts true that the threshold power ts a mtntmum where def f Is a maximum, because Be ts a constant along the phasematchtng curve. In general, for untaxtal materials, the angular s e n s i t i v i t y ts always a constant along the curve, and so tn general, for untaxtal materials, the optimum operating point ts that which maximizes deff. On the other hand, the angular s e n s i t i v i t y for btaxial materials varies in a nontrtvtal manner along the phase matchtng curve, and the optimum operating point ts not tn general gtven by the maximum of deff. The maxtmum efficiency obtainable wtth a particular mater|a1 ts obta|ned for that crystal orientation along the phasematchtng curve where the threshold power ts a mtntmum. There are some circumstances where t t may be desirable to operate at some other potnt, but I t wtll seldom be advantageous to do thts. Posstble motivations for choosing a non-optimal operating potnt tnclude: (a) avoiding or reductng orientation-dependent effects such as stimulated Raman scattering, photorefracttvtty, nonlinear self-focussing, thermal expansion and thermal stresses, and ltnear optical absorption, (b) avotdtng poss|ble complications tn the cutttng, 104
lOa
LAP(l)-
Z,,o!
/ /
F- lo-'
E
10"3 0.4
[ 0.6
0.8
1.0
1.2
1.4
1.6
Wavelength(microns) 7.
The threshold power for second harmonic generation for the btaxtal crystals, lithium formate monohydrate (LF), KTP, and d-LAP.
D. Eimerl et al.
76
100 (
I
l
i
I
I
E
> C Q
=
~
I
C
o.i 0.4
KTP (im)
I
I
I
I
I
0.6
0.8
1.0
1.2
1.4
1.6
W~elength(~m)
8.
The angular sensitivity, a~klee, for the materlals included in Fig. 7 I 14
-
12
-
f
J
I
]
ee
o =
8
0 4
-
L
I
I KTP
)
0 0,4
9.
0.6
0.8
1,0 Wavelength (~ m)
1.2
1.4
1.6
The coupling C, (untts: GH-112) for the materials included in Fig. 7
Nonlinear o~ical mate~all ~r high powerla~m polishing and coating of the crystals, and (c) tn the case of very large crystals, Increasing the yield of useful crystals from freshly grown crystal boules.
In many circumstances, these are not Important
considerations whereas htgh conversion efficiency ts desirable. Therefore, the threshold powers quoted here are the mtntmum along the phase~tchtng locus, and therefore they represent the htghest efficiency configurations for the material. Occasionally, another ftgure of mertt Is quoted for nonlinear materials, namely, deff/2 n3. This figure of mertt ts essentially the square of the coupling, C2, and Is Insufficient on tts own to determine whether a material wtll be e f f i c i e n t tn a particular application. For this reason, C alone Is not the appropriate parameter to rank nonlinear materials for applications, although I t may be useful to bastc research on new materials. Thls emphasizes that, In appllcattons, the 11near opttcal properties play as Important a role as the nonlinearity; research atmed at developing new materials for spectftc applications must address the linear opttcal properties equally wtth the nonlinear opttcal properties. Near noncritical wavelengths, the angular s e n s i t i v i t y ts very small. and the behavtor of the threshold power ts determined by the effective coupling. For untaxtal crystals, the coupllng goes to zero for both Type I and Type I I coupllng for crystals tn the classes ~m2, "[, 622. 32. and 422. For the remalntng classes, the coupllng C rematns f t n t t e only for Interactions Involving two o-rays, and one e-ray. Thus, the coupllng goes to zero for Type I coupllng tn positively btrefrtngent crystals, and for Type I I coupltng In negatively btrefrtngent crystals. Thus. for KDP ~2m), the threshold power goes to zero for Type I coupling at the noncritical wavelength of 514 nm, but for the Type I I process, both G6 and def f go to zero, and the threshold power rematns f t n t t e at the noncritical wavelength, near 700 nm. Table 4 11sts the noncritical wavelengths for the ~ t e r t a l s In Ftgs. 4 and 7. along wtth thetr transparency range. The data presented tn the ftgures terminates at the noncritical wavelength tn the u l t r a v i o l e t , and Just beyond the absovpt|on edge tn the Infrared. The Importance of the 11near opttcal properties ts clearly Illustrated by the calculations for KTP (Ftgs. 7, 8, and 9). For Type I doubling the coupllng ts r e l a t i v e l y small, and the angular s e n s i t i v i t y ts qutte large, and the threshold power ts large, around 10 GH. However, for Type I I doubllng the coupllng C ts large, and In the regton between
77
78
D. Eimerl et al.
T a b l e 4.
Havelength
N o n c r l t l c a l Havelenath f o r Second H~rmgnJ~ Generatlon Material
(nm)
Propagation
Type
Axis a
Coupling (pmlV)
327
LF
8
II
0.95
378
LIIO 3
y
I
4.43
386
LF
y
II
--
400
LIIO 3
y
I
--
409
BBO
y
I
0.2
464
d-LAP
8
I
--
480
Urea
--
I
--
488
d-LAP
y
I
--
519
KDP
(x÷y)/42
I
527
BBO
--
II
589
Urea
(x+y)/42
II
626
d-LAP
8
II
0.39 -1.17 --
658
d-LAP
y
II
718
LF
=
I
--
736
KTP
8
I
--
737
KDP
--
I
--
801
KTP
=
I
--
990
KTP
8
II
5.1
I045
CD*A
(x+y)142
I
0,6
1062
LINbO3
y
I
4.6
I081
KTP
=
II
6,3
(a) For b l a x l a l c r y s t a l s ny > nB > n .
0.4
For u n i a x l a l c r y s t a l s
(xyz) are c r y s t a l l o g r a p h i c coordinate systems.
about I ~m and 1.1 ~m the phasematching curve intersects the low bJrefrlngence (xy - ab) plane where the angular s e n s i t i v i t y is small. KTP has two n o n c r i t i c a l wavelengths, one at each end of t h i s spectral region.
The threshold power goes to zero at these n o n c r i t i c a l
wavelengths and because the angular s e n s i t i v i t y is small between them, the threshold power remains low throughout the e n t i r e 1 - 1.1 l~m band. S i m i l a r l y f o r l i t h i u m formate monohydrate, there is a n o n c r l t i c a l wavelength close to 900 nm, but l i t h i u m formate does not have a low
N~limNIr optical mamnals~r highpowerleINl~
79
btrefrtngence plane, and therefore the threshold power dips to zero near 900 nm, but quickly rises to large values on either stde of t h i s n o n c r i t i c a l wavelength.
On the other hand, LAP does have a low
btrefr|ngence plane, and t h i s gives rise to a low threshold power band ~ust below 500 nm, where the Type I coupltng ts large and the angular s e n s i t i v i t y ts small. Thts band ts very narrow, about 20 nm wtde, and ts qutte far tnto the UV, where the absorption at the second harmonic near 240 nm may be s i g n i f i c a n t . LAP also has Type I I n o n c r i t i c a l wavelengths, but the coupltng vanlshes for these configurations. There ts no wavelength at which t t s threshold power dtps to zero. Graphs such as Ftgs. 4 and 7 tn effect summarize the technology of nonlinear opttcs. I d e a l l y , t t would be desirable to have a sutte of materials such that for whatever process ts being considered, a low threshold power matertal would be available. However, from Ftgs. 4 and 7 t t t s clear that over most of the W - v i s i b l e spectrum low threshold power materials are lacking. These graphs also show that untaxtal materials are not, tn general, as wavelength-flexible as btaxial materials. Each new uniaxtal material brtngs one noncritical wavelength where the threshold power can be low, and a small band of wavelengths to the red from t h i s wavelength where the threshold power is small.
On the other
hand, a btaxtal crystal has the potential for two r e l a t i v e l y close n o n c r i t i c a l wavelengths. Thts ts I l l u s t r a t e d by the KTP curves in Fig. 7. Such a crystal exhtbtts a band of low threshold power behavior, bounded by the two n o n c r i t i c a l wavelengths.
Between the two noncritical
wavelengths, the phasematchtng curve Intersects a low btrefrtngence plane, where the angular s e n s i t i v i t y is small.
To have two n o n c r i t i c a l
wavelengths close together, a btaxtal crystal must have two indices of r e f r a c t i o n close together, and both must be s t g n t f l c a n t l y d i f f e r e n t from the t h i r d . In other words, the crystal must be close to untaxtal. signature of a low btrefrtngence plane (and therefore of two close
The
n o n c r i t i c a l wavelengths) in a btaxtal matertal ts that i t s opttc angle be small but not zero, perhaps not larger than about 45 deg. The smaller the optic angle, the closer the crystal is to untaxtal, and the narrower the band of low threshold power. On the other hand, for larger opttc angles the separation between the noncritical wavelength becomes large (as in ltthtum formate) and the low threshold power band does not r e a l l y e x t s t . In any case, the potential for two n o n c r i t i c a l wavelengths tn btaxtal crystals makes them more a t t r a c t i v e than untaxtal materials as candidates for the desired suite of nonlinear materials. Other thtngs betng equal, the technology of nonlinear opttcs benefits more from a new
D. Eimerl et
80
al.
btaxtal crystal whose linear optical properties are close to, but d i s t i n c t from, unlaxlal behavior, than from a new unlaxlal material.
4.
Database on Non!lnear Ootlcal Matertal~ He have seen above that the threshold power is the c r i t i c a l
figure of
merit in ranking nonlinear materials for applications, and that graphs of the threshold power as a function of wavelength are a very useful aid in summarizing the technology of frequency doubling from a materials standpoint.
Of course, similar sun~rtes can be generated for any
three-wave interaction; for example third harmonic generation by mixing the f i r s t and second harmonics has been studied for the KDP famtly of tsomorphs 3 and the results published.
Hhtle t t is useful to summarize
the threshold powers of commonly available materials, i t would be much more useful to summarize the capability of all known nonlinear materials.
Also, i t would be useful to generate a summary for frequency
mixing and optical parametric oscillators as well as for frequency doubling.
Only with thts information, can an informed choice be made
regarding which known materials should be developed.
Also, from such
graphs, i t will be evident which spectral regions are under-represented by nonlinear opttcal materials. To this end, a database has been constructed which contains the nonllnear coefficients and Sellmeter data for every known nonllnear material for which such data is available in the l i t e r a t u r e . 7 About one hundred materials are s u f f i c i e n t l y well-characterized for inclusion in this database, and some materials are represented more than once to reflect conflicting data in the l i t e r a t u r e ,
This database in accessed by
a btaxtal phasematchtng code which calculates the phasematchtng curve for each matertal and phasematchtng type requested, and determines the minimum threshold power along the phasematchtng curve.
Note that for
btaxtal crystals the coupling tn more than one octant of the index ellipsoid must be calculated.
The code is completely general, and treats
the general three-wave interaction and all phasematching types.
The code
calculates the threshold power for each material, and prints out a l i s t of those materials for which phasematchtng is possible, ordered by their threshold power. The data represented in Figs. 7, 8, and 9 was generated using this expert system.
A f u l l e r description of this expert system
will be published elsewhere. In establishing this database, a thorough review of the l l t e r a t u r e was necessary, and'many of the Sellmeter parameters were calculated from the l i t e r a t u r e data for the f i r s t time.
A surprising discovery was made
Nonlinearo~ical materials~r high powerlasers that there ts a coefficient d~ ~ o 1n - values . . . . . Is tables II report
81
s i g n i f i c a n t disagreement regarding the nonlinear of KDP t t s e l f , where the spread tn reported 0.39 pmlV to 0.78 pm/V, whereas the standard reference 0.63 pmlV. There are relatlvely few absolute
determinations of the nonllnear coefficients of KDP and I t s tsomorphs, and most were made tn the 1960's. The early experiments used a focussed beam geometry, and t h e i r i n t e r p r e t a t i o n ts complicated by the effects of beam walk-off, and the nonuniform laser proflle near the focus. The most tellable measurements are more recent and use dlffractlon-llmtted or stngle mode, hlgh energy, pulsed lasers to measure the conversion e f f i c i e n c y of hlghly collimated beams. The advantages of a large aperture and collimated geometry are: (1) beam walk-off Is n e g l i g i b l e , (2) there is no d i f f r a c t i o n as the beam propagates through the sample, and (3) the beam divergence can be made much less than the acceptance angle of the sample. The plane-wave experiments a l l agree to within 2% on the nonlinear coupling of KDP. For Type I I doubltng the coupling is C =
o.g5
GW-1/2
(18)
which corresponds to d36
-
0.39
pm/V
(19)
The large aperture results for C tn the 11terature also agree exactly wlth our (unpubllshed) experience wlth frequency conversion of the NOVA laser. Unfortunately, d i f f e r e n t authors use d i f f e r e n t deftnlttons of the d - c o e f f i c i e n t ; the d e f i n i t i o n used here ts the same as that in Zerntke and Midwinter. 8 The d e f i n i t i o n s used the other collimated beam experlmentsg'10 differ from thls by a factor of two, and quote 0.78 pm/V. The discrepancy between the co111mated beam, hlgh intensity experiments and the other determinations of d36 remains unexplained. 5.
Hlcrocrvstal Characterization Technlaues Characterization Is an essentlal element In the development of new
nonllnear optlcal materlals.
The minimum data requlred are the angular
s e n s l t l v l t y and the nonlinear coupllng throughout the transmlsslon range of the material. From these data the threshold power can be computed, and the material can be ranked against other, known nonlinear materials. Until recently, this characterization was posstble only wtth crystals about 10 mm tn size, s u f f i c i e n t to permit a precise determination of the
D. Eimerl et al.
82
Individual components o f t h e d-tensor, and also of the refractive indices throughout the transparency range of the crystal.
I t was necessary to
grow crystals of htgh opttcal quality at about the 1 cm3 size in order to compute the threshold power and thereby to rank the material against other materials.
However, we22 have recently developed new techniques
of mtcrocrystal characterization which can determine the necessary parameters ustng I r r e g u l a r l y shaped crystals just 50 - 250 microns tn size.
Using these new techniques, i t is posstble to measure the relevant
matertal parameters without the costly and time-consuming step of crystal growth to the 10 m scale.
Often, crystals of sufficient size are
obtained as a routine result of chemical synthesis.
By avoiding the
Intermediate crystal growth step, these techniques provide a rapid and cost-effective way to evaluate a new nonlinear matertal at an early stage of study.
Subsequent crystal growth efforts can then be directed towards
materials whtch have been already characterized at the mtcrocrystal scale, and are therefore known to possess attractive properties. He have developed two new microcrystal devices and characterization techniques which apply Fully to all crystal symmetries Including blaxtal crystals, and indeed, their power lies in the ease with which they handle such o p t i c a l l y complex materials.
The f t r s t instrument determines the
ltnear opttcal properties using the double splndle stage refractometer, 14 a modification of a polarizing microscope used in opttcal mineralogy to characterize minerals.
The double sptndle stage
refractometer determines the refractive indices throughout the visible and near infrared with an accuracy of about 0.0001.
The sample must be a
stngle crystal, but i t s shape can be nonsphertcal, and its slze can be as small as 25 microns.
Crystallttes of 50 to 100 micron dimensions are
preferred, depending on their btrefrtngence.
The same instrument is also
capable of determining thern~optlc coefficients in the range 0.0001 "K-1.
The second new devlce is a nonlinear optlcal
gontometer,22 which measures the nonlinear opttcal properties and phasematchtng characteristics d i r e c t l y on small mlcrocrystals (slze). Hlth thts instrument, the phasematchlng locus for any three-wave process can be dtrectly measured.
I t also determlnes the nonlinear coupling and
the angular s e n s i t i v i t y along that locus.
An extension of the instrument
allows i t to determine the temperature and wavelength s e n s | t l v t t y of the crystal as well.
The sample for this instrument must also be a stngle
crystal, which may be asphertcal.
The sample stze can be as small as
100 microns, but the accuracy of the data is highest for crystals 250 - 500 microns tn size.
83
Nonlinear optical materials ~ r high power lasem
6.
The DQuble $otndle Stage Refractometer
The double sptndle stage refractometer ts a modification of the (stngle) sptndle stage mlcroscope developed by Bloss. 12'13 I t ts e s s e n t i a l l y a polarizing transmission microscope wtth coil|mated i l l u m i n a t i o n of the sample. The sample ts held tn a small temperature controlled cell along wtth another small reference c r y s t a l . As the orientation of the crystal ts changed, the transmission through the crossed microscope polarizers varies. By determining the mtcrocrystal orientations for complete e x t i n c t i o n , the optic axes of the crystal can be found, and the mtcrocrystal can therefore be oriented o p t i c a l l y .
In
p a r t i c u l a r , t t can be oriented so that any one of the three principal optical directions l i e s tn the plane of the microscope stage ( h o r i z o n t a l ) , and perpendicular to the direction of l i g h t propagation { v e r t i c a l ) . Once the principal opttcal directions of the sample have been determined, the sample can be oriented so that the relevant index of refraction for l i g h t parallel to the ( v e r t i c a l ) axis of the microscope ts any one of the three principal lndtces. otl immersion methods.
These can then be determined by
Typically otl immersion methods are, however, subject to systematic errors associated wtth the degradation of the otl over time. The r e f r a c t i v e index of an otl ts affected by the loss of v o l a t t l e components, contamination, and other unavoidable aging processes. Accurate work therefore requires that the Immersion o t l s be calibrated regularly. I f thts c a l i b r a t i o n ts not carried out with every experiment on a mtcrocrystal, systematic errors can occur. Thts c a l i b r a t i o n error is eliminated t f the r e f r a c t i v e index of the otl ts determined tn s t t u , at the same ttme and temperature as the sample is measured.
To thts
purpose, a reference crystal ts tncluded wtth the sample tn the immersion o t l , and is used to determine the refractive index of the o11.
In
essence, the double sptndle stage compares the r e f r a c t i v e index of the sample d i r e c t l y wtth the r e f r a c t i v e index of the reference c r y s t a l . Thus the systematic error associated wtth the use of an immersion otl ts v i r t u a l l y eliminated. Figure 10 shows how a untaxtal crystal on a sptndle axis serves as a mlcrorefractometer to obtaln the ol1's refractive index for a particular wavelength of light. The reference crystal is precisely mounted with its unique (optic) axls perpendicular to the spindle axls and aligned in a plane parallel to the microscope's polarizer. As the reference crystal Is rotated on the spindle, the full range of indices are observed - from light vibrating parallel to the optic axis, n e. to light vibrating
O. Eimerl et al.
84
S
z
III
.....
~
// I
I !
//
I ip
S
$
fs
~
,•
jl
| I I
//
#S 4¢
! st
10. The ordinary (o), and extraordinary (e) polarlzatlons for a plane wave In a unlaxlal crystal wlth wave normal s.
perpendicular, no .
Once an otl ts found which matches the desired
r e f r a c t i v e index of the unknown crystal at the wavelength of i n t e r e s t , the reference crystal Is rotated by angle e unttl tndex n(e) matches the o t l .
I t s extraordinary
The mutual r e f r a c t i v e indices of the
standard, oii and unknown are then determined from Eq. (20).
n(e) -
n~n0 2 stn2B)i/2 (n e 2 cos2e + no
(20)
Here, e Is the angle between the direction of index matching and the optic axls of the reference crystal and ne and no are the prlnclpal refractive indices of the reference crystal at the wavelengths of Interest.
The procedure may be repeated for addltional wavelengths untll
a s u f f i c i e n t number of data points to characterize the dispersion curve are determined.
At least four data points are required, and preferably
about eight evenly separated wavelengths should be used. Because a
Nonlinearoptical materials~r high powerlase~
85
reference crystal has a 11mtted range of r e f r a c t i v e tndtces, several posstble reference c r y s t a l s , spanntng the range from 1.335 to 1.908 are 11sted tn Table S. A schemttc drawtng of a sptndle stage microscope configured for thts type of refractoeetry ts shown tn Ftg. 11. The most elegant prevtous r e a l i z a t i o n of the "double sptndle stage refractometer" constructed to date ts described by Nedanbach. 14 However, thts and prevtous devtces have been 11mired to v l s t b l e 11ght. 15'16 To assess frequency conversion characteristics for near tnfrared and u l t r a v i o l e t 11ght, accurate values of r e f r a c t i v e tndlces tn those spectral regtons are necessary. Stmple extrapolations of dispersion data measured tn the v t s t b l e are usually Inadequate for thts purpose. Therefore, a feature of our sptndle stage refractometer destgn was a CCD camera coupled to one port of the microscope that permitted tmagtng of the reference and unknown crystal from 0.38 to 1.10 pm on a t e l e v i s i o n monttor. The tndtces of refraction for the reference crystals were also measured through thts spectral regton on larger samples cut for prlsm spectrometry. Refractive tndtces collected at a sertes of wavelengths are least-squares f t t to the Sellmeler equation: n2 - A + _ L _ + X2+C
DX2
(21)
where X ts the wavelength in I~m and n is the principal r e f r a c t i v e index of i n t e r e s t . To assess the accuracy of our apparatus over the f u l l range of wavelengths, we measured the r e f r a c t i v e tndlces of several known materials. Including deuterated 1-argintne phosphate (d-LAP). 4 Accurate dispersion data for the three principal indices of LA*P have been determined previously by prlsm spectrometry. 4 The Individual
Table ~,
Compound
Reference Crystals for Solndle Staae Refractometrv
ne
no
NaNO3
1.335
1.585
CaCO3
1.486
1.658
BaB204
1.553
1.670
ZnCO3
1.621
1.849
Lt103
1.754
1.908
86
D. Eimerl et al.
FP
~ )
FP
[ Camera Reference spindle
,~
Sample spindle
Graded interference...........!......... !
filter
..........
Lamp i ~
I I . Schematic of splndle stage refractometer (oll cell not shown).
Pl
and P2 - polarizers; F.P. - focal plane.
refractive index values determined by sptndle stage refractometry deviate from the more accurate prism values by as much as 0.002. However, these deviations appear to be random, and are due in part to the uncertainty in determining the precise match of standard, unknown and o i l . The Sellmeter formula (Z]) and values of the refractive indices were obtained at each wavelength by use of b e s t - f l t curves. The data are shown in Fig. 12. Table 6 shoes that these values, reported for the Nd:YAG fundamental and second harmonic wavelength, compare more favorably to the prism data, with a standard deviation of 5 x 10-4 . The main source of errors are related to sample quality.
Strain,
poor surface quality and the shape of the grain all affect the quality of the conoscoplc 13 figure used to orient the crystal.
In addition, an
unambiguous match between oll and crystal is dependent on the graln's boundaries, with sharp and clean surfaces at the edges providing the most sensitive conditions.
87
Nonlinear optical materials for high power lasers 1.680
1.490 3,000
S,O00
8,000 Wavelength (A)
11,000
12. D1sperslon of d-LAP. The curves are a Sellmeler f i t to the data.
Table 6.
Refractive Indices for LA*P Determined bv Minimum Deviation
(M.D.) and Solndle Staae Refractometrv (S.S.) for Selected Havelenqths
Principal Index n
nB
n
7.
Y
X(vm)
nM.D.
ns.s.
1.064
1.4960
1.4941
0.532
1.50go
1.5089
1.064
1.5579
1.5577
0.532
1.5759
1.5754
1.064
1.5655
1.5651
0.532
1.5846
1.5845
The Nonllnear Ootlcal Gonlometer Untll recently, the most common approach to new nonlinear optlcal
materlals has relied on powder SHG methods to identify new phasematchable second harmonic generators. 17 Large crystals of attractive candidates are then grown for careful evaluation of refractive index dlsperslon 18 and nonllnear coefflclents. Ig
From this "global" Informatlon, the
theoretlcal efficiency for mlxlng any pair of incident wavelengths can be
88
D. Eimerlet al. computed. 20 To date, over one hundred materta]s have been characterized at this level of detatl.11'21 However, this characterization method is quite slow because SHG powder tests on t h e i r own give i n s u f f i c i e n t , and often q u a n t i t a t i v e l y unreliable data, and progress is made at the rate that r e l a t i v e l y large crystals can be grown. The nonlinear optical gonlometer in contrast permits accurate characterization of a new matertal s u f f i c i e n t to rank i t against other nonlinear materials without requiring r e l a t i v e l y large crystals. The nonlinear optical gontometer determines the phasematchtng curve for any frequency conversion process of i n t e r e s t , and measures the coupling and angular s e n s i t i v i t y along that curve. I t requires only one high q u a l i t y , single crystal several hundred microns in size. Such crystals are often available at the t n t t t a l stages of synthesis without spectal e f f o r t , and e x h i b i t the same phase matching properties as larger c r y s t a l s . This level of material characterization is intermediate between powder SHG measurements on the one hand, and detatled ltnear and nonlinear s u s c e p t i b i l i t y determinations on the other. In a d i r e c t phasematchtng measurement, a laser beam (or beams) is passed through a c r y s t a l , and the angular orientation of the crystal is adjusted u n t t l a sharp increase in harmonic l t g h t i n t e n s i t y c h a r a c t e r i s t i c of phasematchtng is found. 23 For a given incident wavelength, and a given set of polarizations, the continuous set of such orientations comprises the phasematchtng locus. 24 Three basic kinds of information about phase-matched harmonic generation can be obtained from crystals by direct measurements, as I l l u s t r a t e d in Figs. 13-16. The slmplest is the position of the phase matching locus for a given process, i . e . Type I , I I or I I I mtxfng 6 of the wavelengths of i n t e r e s t . Figure 13 shows a set of phasematchtng loci for doubllng, t r i p l i n g and quadrupling of the Nd:YAG fundamental in a 1 nln diameter crystal of a new blaxtal harmonic generator, L-argtntne f l u o r i d e (I.AF). In a classic paper, 25 Hobden obtained loci such as this in ( r e l a t i v e l y ) large crystals of some other compounds by direct measurement, but only to confirm the accuracy of loct computed from r e f r a c t i v e index data. The data in Fig. 13 represent the d i r e c t determination of the phasematchtng locus of a microcrystal of LAF in the ~b~ence of r e f r a c t i v e index data. In LAP, the phasematchtng 1oct for doubling 1064 nm are almost c f r c u l a r e l l i p s e s enclosing the low index axis (¢), as shown in Fig. 14. The effective coupling varies along these l o c l , and in Fig. 14
Nonlinearopticelmaterialsforhighpowerlasers
~
3
0
)
TypeI
13. Phasen~tchlng Iocl for doubling, tripling and quadrupling 1.06 l~n obtained In a l nvn diameter crystal of L arglnlne fluoride.
The 3~
Type I locus Is not shown since It nearly overlaps 2= Type II. Asterisks mark the optic axis positions.
the maxima of def f are represented by dark circles, whereas the zeros are represented by open ctrcles. The low symmetry of UkP allows four Independent relevant d-tensor components, and the complexity in the variation of def f ts shown in Ftg. 15 and is a consequence of the interference and cancellations of the contributions from these four components. These data were used in Ref. 4 to determine the relattve signs of the d-tensor components, and to locate the optimum phasematchtng direction (marked IIA tn Ftg. 14). By monitoring the Intensity of SHG along the locus, the variation of def f can be obtained. By careful comparison with a standard, the approximate value of def f ts obtained. Flnally, by dlrectly scanning the crystal orientation In a dlrectlon orthogonal to the locus, the angular sensitivity can be determined from the phasematchlng "signature" as shown In Fig. 16. The direct measurement technique makes the characterization of unlaxlal materials nearly trivial because the phase matching Iocl are simple cones about the unique axis, the effective coupling varies slnusoldally along the locus, and the angular sensitivity is a constant. The real power of the technique Is realized in the characterization of blaxlal crystals, which exhibit nontrlvlal variations of coupling and
90
O. Eimerl et al.
=o
14. The phasematchlng loci for second harmonic generation in LAP are e11Ipses encloslng the low index axls (~).
The closed circles
represent local maxima in def f, and open circles represent zeros of def f •
angular acceptance along a locus, and whose loci can have complicated topologles.25
This data, along with the location of one or two
crystallographic planes determined by x-ray diffraction on the same sample, is sufficient to determine the orientation of cuts to produce desired doublers or mixers from large crystals once they become available. In certain cases, i t is possible to determine the signs and magnitudes of individual d coefficients by combining x-ray data and the positions of maximum or vanishing nonlinear coupling when the crystallographic point group is known.26 Of course, this level of characterization gives information only about the processes directly studied, and thus is less general than prism and wedge measurements. On the other hand, from a series of direct
91
Nonlinear optical materials for high power lasers 1
~2~1
I
I
I
I
IA
m
J e,o
A
z x
=
,s
0°
60°
120•
180~
240~
300~
I
I
I
I
I
LAP 20} II
lid
IIC
|
I,,
o 0
II
liB
0°
15. V a r i a t i o n for
60"
180°
o f second harmonic I n t e n s i t y
Type I I
calculated
120°
doubltng of curve.
o f the d - t e n s o r
240°
300°
360°
along the phasematching locus
1.064 ida t n d-LAP. The s o l i d
ltne
is the
These d a t a were used t o d e t e r m i n e t h e r e l a t i v e
components f o r
d-LAP.
sign
D. Eirnerl eta/.
92 LAP: Type U A
-10
0
10
Angle to plate normal (degrees)
16. Angular acceptance data for d-LAP Type I I at the point IIA of Fig. 14, where the coupllng C Is a maximum. Solld line Is least squares f i t to the function sJnc2 (I/2I~BL).
measurements at discrete wavelengths, the behavior of the materlal for other processes can often be assessed by Interpolation. I t is important to note the smallest crystal slze for which i t is theoretlcally posslble to make direct phase matching measurements. The sole criterion which must be satisfied is that the true phasematching positions be distinguishable from subsidiary intensity maxima where the coherence length is locally maximum, but not infinite.
For this to be
true, the slze of the particle must exceed the inverse of the angular sensitivity: >> 2~/~e
(22)
For example, for Type II doubllng of 1.06 ~m in potassium dihydrogen phosphate (KDP) which has an angular sensitivity of 2500 cm-I/rad , a particle size of 100 microns is sufficient to resolve the phase matching locus.
I t is, perhaps, surprising to note that this criterion is exactly
the same as the one derived by Kurtz and Perry17 to determine when phasematched SHG dominates the powder signal of a material.
Thus, I f
materials are synthesized with crystallite sizes large enough to determine whether or not they are phasematchable by a powder test, then i t is possible to obtain much more precise information about their
93
Nonlinear optical materials ~ r high power laserz
properties by direct measurements.
The sample handling methods we
currently employ allow us to study particles as small as 300 l~m in diameter, but improvements which w t l l permit the study of 100 I~n sized samples appear feasible. Samples for d i r e c t phasematchtng measurements can be produced by a variety of methods. I n l t l a l attempts at crystal synthesis, either by high temperature melt growth or by evaporation or cooling of solutions, often result in polycrystalline masses with single crystal domains a few hundred microns in size. In addition, submllllmeter sized samples produced by fast fiber pulling technlques 27 or by growth in caplllarles 2B are ideal for these studies. Hhile i t is possible to make measurements on c r y s t a l l l t e s in t he i r natural habits or on cleavage plates, we have found i t convenient to grind samples into a spherical or elllpsoldal shape, in part because i t is much simpler to estimate the optical path length as a function of orientation in a spheroidal sample. In addition, a well rounded sample presents an entrance surface which is nearly normal to the laser beam for all orientations, making refraction corrections less serious. Finally, manipulation of the crystal orientation for mounting (see below) is much easier for rounded samples. Figure 17 shows the morphology of a typical sample after rough grinding in a commercially available sphere former. Subsequentpolishing by tumbling with fine g r l t or solvent etching is often possible.
In any
case, scattering due to poor surface quality is greatly reduced by immersing the sample in an index matching f l u i d when measurements are made. This also reduces the lensing effect of the spherical sample since the focal length of a sphere of radius r and index nA immersed in a f l u i d of index nBls given by F - rnA/2(nA - n B ) . The refractive indices of the f l u i d and sample can usually be matched to better than 0.Ol. although for very birefringent samples this may necessitate changing the matching f l u i d for different phase matching types. Samples are permanently bonded to the glass fibers in particular orientations with respect to the principal di el ect ri c axes. Figure 18 shows a crystal mounted on a glass fiber and suspended in immersion f l u i d and shows that the transparency of even a roughly ground sample is reasonable when immersed in a f l u i d with a near index match. The positions of the principal axes of the refractive index ellipsoid of the small c r y s t a l l i t e are located by principal and optic axis interference figures, using the same techniques as the spindle stage microscope. 12'13 These principal axes are labelled ~, ~ and y with the convention that
94
D. Eirnerl eta/.
17. Spheroldal sample of barlum metaborate produced by a i r tumbling.
n
< nB < n .
Typically, two orientations are s u f f i c i e n t to
obtain the entire locus for any frequency mixing or doubling process in a biaxial crystal.
In the f i r s t , the crystal is mounted with the glass
fiber parallel to the 8 axis (perpendicular to the optic plane, using the convention n
< nB < ny ). In the second, the fiber is parallel to the highest index direction (y). For uniaxial crystals, a single orientation, either with the optic axis parallel or perpendicular to the f i b e r , is usually s u f f i c i e n t to obtain a particular locus. The apparatus for measuring SHG in small crystals is shown
Nonlinear optical materials for high power lasers
95
18. Crystal immersed in refractive index matching fluid.
schematically In Fig. 19.
Part of the laser beam is s p l l t off and
doubled (with low efficiency) in a separate nonlinear crystal.
The
doubled light intensity serves as a normaIizatlon slgnal to account for laser power fluctuations.
The second harmonic signal from the sample is
detected in a photomultipller, using a ground fused s i l l c a plate to diffuse and depolarize the detected light and calibrated neutral density f i l t e r s to attenuate the signal into the linear range of the detector. The second harmonic and normalization signals are collected, averaged and digitized for analysls.
As the phasematchlng curve is traced out, the
96
D. E i m e r l
et al. r. . . . . . .
A
A
;.2
I ,
2
~ i,
I F1
/
F2 PMT
T,~®.
;
w21
.
1
Boxcar trigger
I Normalization
signal
19. Schematic of apparatus for phasematchlng measurements. A:
aperture; PD: photodiode; KTPI and 2: doubling crystals;
HI,W2: waveplates; Fl, F2: f i l t e r s ; L: 20 cm focal length lens; P: polarizer.
The segment enclosed by the dashed line is inserted for
3~ and 4~ experiments.
azimuthal (¢) and polar (8) angles of the crystal in the iaboratory frame are recorded. The coupling C is determined from the signal for points exactly along the phasematching curve, Ip
=
[Cp.I p . l l n c]
2
(23)
Here lin c is the incident intensity, and the point P(e,¢) lies on the curve.
The optical thickness of the sample Ip is calculated by
modeling the sample as an ellipsoid.
The accuracy of this calculation
for typical samples is about 5%, although very occasionally, an oddly shaped sample results from the grinding process, and the e11ipsoidal f i t is less accurate.
Phase mismatch and walK-off are negligible because the
confocal parameter of the focused beam greatly exceeds the crystal size, as does the walkoff length due to double refraction.
The absolute
magnitude of the coup]ing is obtained by careful comparison with a suitable standard.
The angular sensitivity at the point P is measured by
scanning along the arc at P perpendicular to the phasematchlng curve.
If
is the angle describing location along this arc then
Ip(~) ~ sinc2(~p~)
(24)
Nonlinear optical materials ~ r high power l a i r s
where slnc(x) . s l n ( x ) / x , and ~p Is the angular s e n s i t i v i t y at the point P. The qualtty of the f i t to the phase matching signature (24) is a criterion for Judging crystal qualtty and the r e l i a b i l i t y of the angular s e n s i t i v i t y and intensity data. HJth the methods described above, phase matching angles can be determined to = 25 mrad, angular s e n s i t i v i t i e s to better than 20"I. and def f values in good qualtty samples to 25% for second harmontc generation at 1.064 microns. The major sources of error for the angular acceptance and intensity measurements are the sample surface qualtty, and the uncertainty tn opttcal path length. For work in the u l t r a v i o l e t , the relattve dispersion of available transparent immersion otls exacerbates the tndex mismatch problem. The accuracy of Cp is reduced to z 50%, but this is stt11 accurate enough to evaluate and rank the material. I f very accurate values of JCpI2 are obtained, i t is sometimes possible to deduce values of the Individual d-coefficients by f i t t i n g the observed varlatlon of Cp along the phasematchlng curve. Of course, one must know the crystal class of the sample must to reduce the number of independent d-coefficlents. The accuracy of the magnitude of Cp Is often marginal for this purpose, but much can be deduced from the 1ocatlon of i t s maxima, and of those zeros not required by crystal symmetry. Relatlve, signed values for individual d-coefflclents were obtained using this method for two materlals, d-LAP,4 and NaLaF4.26 K1elnmansymmetry8 reduces the number of unknowns, and is usually well within the uncertainty of these measurements. For blaxlal crystals in point groups I, 2, m, and mm2, some convention must be chosen for the positive direction of the polar axls to uniquely define the relative signs.
For unlaxial crystals in 3, 3m, 6 and 4 i t is
necessary to find the 1ocatlon of the maximum def f relative to the (lO0) or (010) directions. Nlth the optlcally oriented crystal mounted on a gonlometer head, i t is straightforward to determine the complete relatlonshlp between the optical and crystallographlc axes by x-ray dlffraction. 12 8.
Oraanlc Nonllnear Materials for ICF Aoolications The laser required for an economlcally vlable power station using ICF is large. Energyof I - 10 MJ in a nomlnally lOns pulse, with a beam divergence not greater than 0.1 mrad, at a wavelength in the near u l t r a v i o l e t and posslbly large frequency bandwidth are currently thought to be requlred. I'2 This wavelength range can be reached by frequency
97
D. Eimerl et al.
98
conversion of an e f f i c i e n t infrared laser. For the overall laser system to be cost-effective, the frequency conversion must be very e f f i c i e n t .
That is, the nonlinear materlal must
have a low threshold power, and must not have significant absorptions at any of the relevant wavelengths.
However, all materials which satisfy a
particular threshold power criterion are not equally suitable in practice.
In the f i r s t place, detalled calculatlons show that a very
nonllnear material would necessarily be configured as a thin plate to avoid back-converslon. 2g Thin plates are mechanlcally weak and cannot be fabricated Into large area plates, 11mltlng the Indlvldual aperture size.
In the second place, the cost of the laser driver increases
significantly with the the sum of the areas of a11 the output apertures. There is a minimum value (and therefore a minimum cost) for the total aperture which is determlned by materials limlts on the intensity or fluence.
Thus, the total area w111 be affected by damage thresholds of
optlcal elements, and by any other Intenslty-llmltlng effects such as two-photon absorption, st|mulated Raman or Br111ouln scattering and self-focusslng and/or phase-modulatlon.
The last three processes are
determined by the chemical composition and structure of the material, while the damage threshold is determined by the presence of inclusions, defects, or impurities incorporated during crystal growth. Thus, ICF applications call for a hlgh damage threshold (20 - 40 J/cm2 at 10 ns, a11 wavelengths), 1'2 an effective coupllng about 2 - 4 times as large as that of KDP, and a low absorption.
The
angular sensitivity, stimulated Raman gain, and nonlinear refractive index must be comparable to or smaller than those of KDP. The material must be inexpensive to grow, fabricate and pollsh, would preferably be posslble to antl-reflection coat.
We believe that a11 of these
conditions can be met by certain molecular crystals of slmple organic compounds. Many organic crystals with second harmonic generatlng properties are known, II'21'30 and are of interest prlmarily due to their large nonllnearlty, the SHG moiety is a conjugated ring or its derivative. However, the conjugated ring is not sultable for ICF because i t exhibits photochemical processes in the near ultravlolet, as well as losses due to 11near and nonlinear absorption losses.
However, since the nonlinearity
required is not much larger than that of KDP, other SHG molties can be used, such as the conjugate C02 group. Indeed, using the expert system described earlier, we calculated the threshold power of all (suffIclently well characterized) known materials ? for doubling or
Nonlinearoptical materials~r high powerlasers
99
t r l p l l n g 1.064 I~m. He found that h a l f the known materials with threshold powers less than 40 HH (recall KDP = 80 HH) were ~ l e c u l a r , organic crystals containing small, conjugated, ionic groups attached to chtral carbon centers.7 Hhen these groups are i n t r i n s i c a l l y acentric, they have much larger hyperpolarJzabtltttes than nonconJugated u n i t s , such as the phosphate ion. The nonlinear coupling in such crystals is therefore l i k e l y to be adequate. Holecular c h i r a l l t y guarantees that the crystals w t l l be acentrtc, and most crystals f a l l into point groups 2 or 222. Examples of t h i s kind of moiety are shown in Fig. 20. Crystals containing these molecules can be grown easily from aqueous solution as salts with various metallic or organic countertons or as zwttteriontc crystals. Horeover, such crystals are mechanically harder and more stable in a i r than KDP. On the other hand, structural differences among these compounds lead to a range of btrefrtngence and optic angles. This is i l l u s t r a t e d in Tables 7 and 8, which describe the linear and nonlinear optical properties of various l-Argtntne compounds.31 In the molecular "gas" model, the antsotroptc components of the optical properties of the crystal are given by summing the contributions of Individual molecules fixed in space. The v a r i a t i o n In the btrefrtngence and optic angle r e f l e c t s the d i f f e r i n g relattve orientations of the individual molecules. In general, chtral organic molecular crystals e x h i b i t a wtde v a r i e t y of phase-matching properties, such as angular s e n s i t i v i t y and n o n c r i t i c a l phase-matching wavelengths, but these properties depend on the structural details of the crystals and cannot be eastly engineered. Thus, the angular s e n s i t i v i t y , and the noncritical wavelengths are the major unknowns in thts class. However, because the chemical moieties in
H NH2
R'--
R'--.
--
I NH~,
R"/C ~
+..)c
--R
N
H Carboxyl
Guanadyl
Hlstadyl
20. A t t r a c t i v e chemical moieties for generation of 355 nm l i g h t in our molecular engineering approach to new nonlinear materials for laser fusion experiments.
D. Eimerl et al.
100
these crystals are similar and they are all lonlcally bonded, many other properties which rely less c r l t l c a l l y on structural details w111 show marked regularlties. In partlcuIar, their mechanlcal strength, and the linear and two-photon absorption properties, which arise from slmllar spectroscopic transltlons, are not expected to vary strongly from crystal to crystal. Of course, these properties may well have an orlentatlonal dependence which varles with structure. Thus, In following this strategy, the focus of ICF research is on the 11near optlcal properties: adequate nonllnearlty is more common than s u f f i c l e n t l y low angular sensitivity. In fact, most of the compounds we have examined have adequate blrefrlngence for second- and thlrd-harmonlc generation of 1.064 ~m, but most have a larger angular s e n s l t l v l t y than KDP because the blrefrlngence Is slgnlflcantly larger. He have found several crystals with nonlinearitles 2 - 4 tlmes greater than the d36(KDP). Table 7 gives the phase matching parameters for several crystals we have characterized recently using the mlcrocrysta111ne techniques. These Include L-arglnlne phosphate (LAP), L-arglnine fluorlde (LAF), and dlammonlum tartrate (DAT). Crystals of DAT and ~F T~ble 7.
ProDertles of some ionic oraanlc crystals for doubllna 1.064 um
Material
Type
LAP
I
0.99
6900
63
II
0.93
4]00
26
I
1.24
4900
21
II
0.93
4100
26
I
0.53
5700
154
II
0.37
2150
47
LAF
DAT
.
.
.
.
KDP
(a)
.
.
.
.
.
.
.
.
.
.
.
deff(pm/V)(a)
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
(cm-I/rad)
.
.
.
.
.
.
.
.
.
.
.
.
.
.
Pth(MW)
.
.
.
.
.
.
.
.
.
.
.
.
I
0.25
4900
500
II
0.35
2500
70
Maximumdef f for the given type.
Based on d36 - 0.93 pm/V.
.
.
.
.
.
.
.
.
.
.
.
.
Nonlinear optical materials for high pOwer lasers
101
and other compounds have been grown by slmple evaporatlon or coollng technlques to volumes between I and 10 cm3, and crystals of LAP to about 100 cm3 and larger. 9.
Oottcal prooert1~s of Chtral Actd Crvstals
The u l t r a v i o l e t edge ts determined by strong ~ - ~* t r a n s i t i o n s associated wtth the small conjugated groups. Thts edge ts generally at wavelengths lower than 250 nm for carboxylate or guanadyl groups, and may be somewhat redshtfted for tm|dazolyl (Ftg. ZO). However, LAP exhtbJts a s i g n i f i c a n t absorption feature 4 (1-3 ~/cm) in the region between 250 and 300 nm. Thts Js probably due to n - ~* t r a n s l t t o n s . The wavelength of these t r a n s i t i o n s Jn carboxyllc actds has been shown to depend s i g n i f i c a n t l y on the molecular structure, 3Z but very l t t t l e Information ts known about thetr behavtor tn other kinds of organic salts. In the near infrared, (0.9-1.5 Fm) overtone absorptions of N-H, O-H, and C-H stretching vibrations can be qutte strong. These crystals are extensively hydrogen and consequently have overtone absorptions whtch lead to losses of 10-20~/cm at the Nd:YAG fundamental wavelength. 33 DeuteratJon can reduce thts absorption s i g n i f i c a n t l y . 4
C-H stretching
overtones are s i g n i f i c a n t at 0.910 and 1.2 t~m. These covalently bonded protons are not as easily replaced by deuterium, however. L i t t l e information is available concerning two photon absorption tn organ|c s a l t s . Stmple symmetry arguments suggest that the same v - v* t r a n s i t i o n s which determine the 1 photon UV edge are also s i g n i f i c a n t l y two photon active. (In fact, they must be Jf these t r a n s i t i o n s are to flgure strongly in the x (Z) response.) Thus, the two photon edge Is expected to begin around 400 nm, making the strength of such transltJons an Important tssue for generating harmonics tn the near u l t r a v i o l e t . The nonllnear tndex determines the threshold | n t e n s i t t e s for catastrophic s e l f focusing. I t correlates strongly wtth the size of the l i n e a r Index and tts dispersion.
Heasurements on LAP at LLNL tndtcate
that nZ ts not s i g n i f i c a n t l y d i f f e r e n t than what would be predicted by r e f r a c t i v e index scaling. 34 Table 8 contatns data on the nonlinear refract|ve index nZ for LAP, KDP and potassium t t t a n y l phosphate (KTP) for comparison. High frequency, narrow Raman resonances can lead to low thresholds for stimulated Raman scattert~q (SRS).
Intense transverse SRS can cause
D. Eimerl et al.
102
Table 8,
Nonlinear refractive index (n 2) values for some freauency
doublinq crystals. (a)
~rvstal
~
Dz(X1013cm3/era)
KDP
1.49
1.0 - 3.6
LAP
1.55
1.87 - 3.04
KTP
1.77
2.5 - 5.7
(a) taken from Ref. 40. significant energy loss or even physlcal damage to the nonllnear crystals. 35 Of primary concern in organic crystals are aliphatic C-H vibrations in the 2900 cm-I region. These can have spontaneous Raman scattering intensities 2-3 times larger than other Raman active vibrations in these crystals, e.g. the carboxylate symmetric stretch at 1460 cm-l. 36 However, typlcal magnitudes of the a11phatlc C-H mode scattering cross sections in these crystals are not known, nor have the linewldths been quantltatlvely documented.
He may estimate the potential
SRS gain by noting that the C-H modes (2858 cm- I ) in the allphatic hydrocarbon decalln have an SRS gain coefficient of 0.7 cm/GH.35 (By comparison, the gain coefficient of the phosphate symmetric stretching mode in KDP is approxlmately 0.2 cmlGH.)35 The relevance of this estimate is uncertain because the linewldths of such vibrations in crystals may be much smaller than those of liquld deca]in. Nonetheless, i t demonstrates the potentlal impact of these modes on SRS thresholds. In summary, the group of chlral, ionic, organic crystals contains a significant number of materlals which have moderately large nonllnearlties (I-2 pm/V), favorable phase-matching properties for vislble or near ultravlolet, and which grow easily into large, high optlcaI quallty crystals.
The simple engineering approach of attaching
103
Nonlinearopti~l mmteHals~r high powerlase~ Small, conjugated 1onto groups to chtral carbon centers to produce new crystals of thts type ts far from exhausted. There ts evidently no i n t r i n s i c constraint imposed by optical damage, and the nonlinear r e f r a c t i v e tndex, the two-photon absorption and the stimulated R~uMn scattering strength are expected to be similar to those tn materials wtth similar l i n e a r refractive indices, UV edges and chemical moieties. The promise of thts class ts that t t may provide a set of nonlinear materials, al1 more nonlinear than KDP. and wtth a range of phasematchtng properties and noncritical wavelengths. A suite of such materials spanning the v i s i b l e and UV spectrum would represent a s i g n i f i c a n t advance tn the technology of frequency conversion of htgh power lasers. A summary of a study of crystals of other salts of L-argtntne has been published. 31 10. L-Aratntne Phosohate L-Argtnlne phosphate ts an example of the chtral organtc materials we have been studylng for laser fuston applications. Both LAP and tts deuterated analog, O-LAP, grow eastly from aqueous solution, are monocltntc, space group P21, and also they are phasematchable for a l l processes where KDP is phasematchable. Hith the posstble exception of harmontc generation to wavelengths shorter than about 270 nm, thetr threshold powers are smaller than those of KDP or barium borate by a factor of 2 or 3. In the absence of opttcal absorption, then, these materials are considerably more e f f i c i e n t , for a given laser source, than KDP. They are r e l a t i v e l y Inexpensive, posses a htgh damage threshold, and achieve higher efficiency than KDP using a smaller crystal volume. Table 3 sumartzes t t s linear and nonlinear opttcal properties, and Fig. 21 shows phasematchtng curves. The undeuterated crystal has substantial absorption at 1064 nm, between 5 and 20 ¢/cm, depending on the polarization.
Thts absorption ts
due primarily to overtones of OH and NH vibrational excitations, yet not to CH vibrations. The absorption can be removed by deuteratton, and for deuteratton levels above 95~ the absorption is less than 1 ¢/cm, which ts s u f f l c t e n t l y low for many applications Including ICF. I t ts not necessary to deuterate the CH sites, but only the NH and OH sttes, which ts eastly accomplished by r e c r y s t a l l t z a t t o n from aqueous solution. The deuteratton of the OH and NH sttes can be brought a r b i t r a r i l y close to 100¢ by thts procedure. A thorough study of the crystal growth and scaltng of D-LAP Is betng carrled out by Cleveland Crystals, Inc. Htgh opttcal q u a l l t y crystals suttable for harmonic generation have been grown as large as 7 x 8 x 4 cm.
104
D. Eimerl et a/.
Y
0 2~,4~ 10
20' 30 0 40: 50 60
70: 80 90 CZ
0
10
]L t
20 30 40
50
6"0
70
80
90
0
0
10
20 30 0 40 50 60 70 80 9O O~
10
20 30
40 ~ 50
60
70
80
90
21. Empirically determined phasematching loci for LAP. The solid lines are the same loci calculated from the Se]Imeier Formula. (a) 2~ Type I, (b) 2~ Type I I , (c) 4~ Type I, (d) 3~ Type I, (e) 3~ Type I f .
Nonlinear optical materials~r high power lairs TWO interesting features of D-LAP have emerged recently.
The f i r s t
ts that as currently grown, I t exhibits a weak blue fluorescence under Irradiation with 355 nm ltght, but extensive tests at thts wavelength indicate that they do not experience damage or solartzatton.
On the
other hand, under shorter wavelength 11ght they darken, apparently undergoing a photochemical process.
The wavelength where thts
photochemistry sets in Is not yet known, but t t ts certainly below 300 nm and we belteve that t t is near 270 nm.
He believe that the UV-tnduced
photochemistry below 270 nm may be intrinsic to the crystal, In which case the crystal would be generally unsuitable for UV applications below thls wavelength. On the other hand, the blue fluorescence seen In 355 nm experiments Is observed to have a strong dependence on position In the crystal, and Is certainly associated wlth inclusions. There Is no correlation between the sources of fluorescence and damage.
The chemical
nature of the fluorescing inclusions has not yet been identified, but It is likely that they are other organic molecules, such as aldehydes, or perhaps benzene rlng compounds and their derivatives, such as tryptophan. The fluorescence spectrum matches closely that of guanadyl, suggesting that energy Is transferred from absorbing inclusions to the guanadyl Ion, which then fluoresces. It may be possible to reduce the fluorescence by purifying the starting materials for crystal growth. Note that thls fluorescence Is not necessarily a disadvantage. For example, the output of a third harmonic generator wlll cause fluorescence, which will be monotonic In the 355-nm output energy. The fluorescence can therefore be used to sake an In sltu measurement of the conversion efficiency without the need for calorimetry In the target chamber. In fusion experiments, this would be of considerable value. The second interesting attribute of d-LAP concerns Its temperature bandwidth. The temperature bandwidth Is very large where the linear temperature sensitivity BT ts zero.
a&k/aT
(25)
In contrast to untaxtal crystals, in btaxtal crystals such as
LAP the temperature s e n s i t i v i t y varies along the phasematchtng curve. For LAP, t t actually has a zero, for both second and third harmonic generation of 1064 nm, and for both Type ! and Type I I processes.
At
these points on the phasematchtng curve, the temperature bandwidth ts very large. direction.
These points are close to the optimum phasemtchtng The threshold power at this zero ts about an order of
D. Eimerl et al.
106
magnitude larger than the minimum threshold power quoted earller, but is nonetheless low enough to provide efficient conversion.
For example, for
Type I I second harmonic generation, the minimum threshold power is about 30 MH, whereas at the zero of the temperature s e n s i t i v i t y , I t is about ]70 MH. Thus LAP and d-LAP are capable of temperature-insensitlve operation, at some cost in the threshold power, or efficiency. The posslbl]ity of large temperature bandwidth makes d-LAP a candidate for medium average power devices. However, under thermal load, the crystals w i l l also generate stress, and the presence of a cleavage plane makes i t vulnerab|e to thermal-stress-induced fracture. The eIastlc constants and thermal expansion of LAP have been measured recent]y, 37 and used to ca|cu|ate i t s resistance to therma] fracture. 5 Again, this varies along the phasematchlng curve, but at the location of the zero of the temperature s e n s i t i v i t y , i t Is about as resistant as KDP to thermal fracture. Therefore, we have concluded that d-LAP, whose absorption and thermal fracture properties are similar to KDP, does not derive any slgnlf|cant advantage over KDP In average power appIicatlons, despite its potentla]ly high temperature bandwidth. d-LAP Is currently under development for fusion applications.
In
addition to favorable optical properties, I t Is amenable to cutting, poItshlng, dlamond-turnlng and sol-gel anti-reflectlon coating. I t is currently our leading harmonic generation material for future laser fusion experiments. 11. Hioh Averaoe Power Material@ Under average power conditions, the optical absorptlon of the nonlinear material causes thermal gradients which disturb phasematching and can cause thermal fracture. 5 Thermal effects are described by two figures of merit, the thermal dephaslng parameter, and the fracture temperature. The thermal dephaslng parameter, Hm, relates the thermal dephaslng (In radlans) to the average power and the dimensions of the crystal. Hm
-
8K / =I~T
(26)
where K is the thermal conductivity, and ¢I Is the optlca] absorption.
The fracture temperature is a material figure of merit whIch
ranks materlals by their reslstance to thermal fracture. mechanlcally isotroplc material,
For a
Nonlinear optical materials ~ r high power l a i r s
&TF -
3SF(1-v)I2E¢T
107
(27)
where SF ts the surface fracture stress, v Is r a t i o . E Is Young's modulus, and ~T Is the thermal expansion c o e f f i c i e n t . Because fracture stress depends on the defects In the surface, the fracture temperature figure of merit ts defined for a p a r t i c u l a r d i s t r i b u t i o n of surface defects. Physically, the fracture temperature describes the fracture point of a thtn plate of i n f i n i t e area. whose surface has a p a r t i c u l a r d i s t r i b u t i o n of defects, tn which a quadratic temperature p r o f i l e has been established between the mtdplane and the surface. As the height of the quadratic temperature p r o f i l e ts increased, the surface stress increases, and at some point exceeds the surface strength. The fracture temperature describes that point. I t ts a materlal figure of merit describing an idealized s i t u a t i o n , and t t does not necessarily descrtbe the fracture point of real plates. In antsotroptc materlals the fracture temperature and the thermal dephastng parameter depend on the orientation of the plate. 5'3g For example, the fracture temperature of KDP ts shown tn Ftg. 22 as a function of o r i e n t a t i o n . Most nonlinear materials dtsplay the same large anlsotropy In t h e i r a b i l i t y to withstand thermal gradients; a summary of the results for some common materials ts given tn Table 9. 12. Future Directions Thts paper has reviewed progress In new, p o t e n t i a l l y inexpensive materials for nonlinear optics tn the wavelength range 300 - 1200 nm. The theoretical analysis has shown that the threshold power ts the essential parameter tn the frequency conversion of collimated laser beams, and thts single parameter serves to rank ~ t e r t a l s . Using the database and expert system, two points became clear.
F i r s t , that t t ts
not posstble for a materlal wtth a t y p t c a l wavelength dependence to t t s r e f r a c t i v e indices to be Ideal for a11, or even most, nonlinear opttcal processes. Second, that there ts a lower l t m t t on nonlinear opttcal technology represented by the fact that the smallest threshold powers for processes tn the v t s t b l e part of the spectrum are tn the tangle of i0 100 1414. Achieving htgh conversion efficiency wtth a matertal wtth a threshold power tn thts range, requires either a very htgh peak power laser, 1 - 10 GH, or a laser which ts close to d i f f r a c t i o n 11mtted, and which also has f l a t temporal and spattal p r o f i l e s . The technology of nonlinear optics w t l l beneftt most from a suite of nonlinear materials
D. Eimerl et al.
108 20
18
t
i
I
I
I
I
I
i
i
I
I
r
50
60
70
80
= 45 ° 16
o
14
¢ = 30
12
°
0 D
10 E O= 15 ° ,.,=
LL
(~= 0 °
0
I
o
lO
I
J
I.
20
30
40
90
Polar angle, 9
22. The fracture temperature of KDP as a function of orientation. nonllnear materials display a similar anisotropy.
Table 9.
Fracture Temoerature of Nonlinear Materials
Material
Range
epm (deg.)
KD*P
4-20
36 (I)
17
54 ( I I )
5 7
ATF ('C)
LiNbO3
4-11
- 90 (I)
LilO 3
5-19
31 (I)
10
BBO
20-285
23 (I)
200
32 ( I I )
90
Most
Nonlinear optical materials ~ r high power l a i r s
such that for any p a r t i c u l a r combination of wavelengths, a low-threshold-power ~ t e r J a l is available. Blaxtai ~ t e r t a l s have a greater potential than untaxlal materials for providing a range of low threshold power. The opttmal bJaxtal material, from t h i s perspective, has a low optic angle, so that t t possesses a low btrefrtngence plane. Ustng the molecular engineering strategy to develop new blaxlal materials, we found that I t ts r e l a t i v e l y straightforward tn organic materials to engineer materlals which are transparent from below 300 nm to 1200 nm, and which posses nonlinear couplings of 1 - 3 pm/V. The more d t f f l c u l t parameter to engineer ts the btrefrlngence. In thts sense, developing materials for high power applications ts more a program tn ltnear opttcal properties than In nonlinear opttcal properties. Unttl a deeper understanding of crystal structure of molecular crystals ts developed, we would expect that the ltnear opttcal properties w i l l conttnue to be the most important parameter of new nonlinear opttcal materials. Hlgh average power materlals must not only meet the threshold power requirement, but they must also withstand thermal gradients. The most important parameter for this application is therefore the 11near optlcal
absorption. In organ|c materlaIs the hydrogen vibrational overtones will necessarily lead to significant (about O.OOl/cm) absorption In the near infrared, because I t Is not posslble to remove all the protons from the crystal. He have consldered the possib111ty of organic materials without hydrogen, such as perfluorlnated materials, but very few of these are known, and I t Is not known whether they form acentrlc crystals. The lowest absorption w111 probably be found In the inorganic materlals, but as yet no slmple synthetic strategy exists for acentrlc Inorganic crystals. Eventually, I t w111 be necessary to address the problem of crystal structure of both organic and inorganic materials, together with the optical structure-property relations necessary for guidance. Unfortunately, crystal structure continues to be an impenetrable subject, and progress in nonllnear materlals wlll langulsh whlle an understanding of structure is lacklng. On the other hand, In the foreseeable future the most frultful area for ICF and other hlgh power appllcatlons w111 continue to be the organic molecular crystaIs of the type already under study. It Is entirely posslble that within thls class, low threshold power materlals w111 be found for most Interestlng appllcatlons.
109
110
D. Eimerl et al.
Acknowledqements I t Is a pleasure to acknowledge the c o n t r i b u t i o n s of D. Mllam and R. Gonzales, who carrled out the measurements of the damage thresholds.
AoDendIx:
Jacobl Function Routines
The f o l l o w l n g routines f o r the Jacobl e111ptlc functions are based on the i n f i n i t e product representations given in Ref. 40.
Although not
optimized for speed, they are e a s i l y f a s t enough f o r most applications in nonllnear optics.
The number of loops required f o r convergence diverges
as the laser brightness, X, becomes large.
For m < 10-4 , double
precision Is suggested, and f o r m < 10-7 , the a n a l y t i c s o l u t l o n f o r the conversion e f f l c i e n c y should be used i f posslble. ( I ) Comolete E111otlc Integral K(m) def fnkm(m)
'
Assumes that 0 < m < 1
qkn - sqr(m) : qkm- 2 " a t n ( l ) qkmloop: qkp - sqr(l-qkn'qkn) : qkn - (1-qkp)/(1+qkp) : qkm - qkm*(l+qkn) i f qkn > Ie-14 then go to qkmloop fnkm , qkm end def (2) Jacobi Functlons sn.cn.dn(u.m) '
Subroutine f o r sn cn dn Jacobl functions
pl - 4*atn(1) : mpr - 1-m : km - fnkm(m) : kmpr - fnkm(mpr) q - exp(-pl*kmpr/km) : x - u*pl/km : cp - cos(x) sn - 2 * s t n ( x / 2 ) * s q r ( s q r ( q / m ) ) cn -
2*cos(xl2)*sqr(sqr(q*mprlm))
dn -
sqr(sqr(mpr))
Jacloop:
qJ-q*qn
da -
l+qj*qJ
sn -
sn*(dl-d2)/dd
if
abs(d2)
: qn -
1
: qn-q*qj
: db - 2 * q J * c p
> le-14
: cn -
:dd - da-db
cn*(dl+d2)/dd
: dl
-
l+qn*qn
: d2 -
2*qn*cp
: dn - d n * ( d a + d b ) / d d
then goto Jacloop
end sub
Disclaimer This Document was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor the U n i v e r s i t y of C a l i f o r n i a nor any of t h e i r employees, makes any warranty, express or implied, or assumes any legal l i a b i l i t y or r e s p o n s i b i l i t y f o r the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents
111
Nonlinearo~ical matenals ~rhighpowMlase~
that its use would not infringe privately owned rights.
Reference
herein to any specific commercial products, process, or service by trade name, trademark, manufacturer, or otherwise, does not necessarily constitute or imply i t s endorsement, recommendation, or favoring by the United States Government or the University of California. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government hereof, and shall not be used for advertising or product endorsement purposes. References 1.
J. Holzrichter, E. M. Campbell, J. O. Ltndl, and E. Storm, "Research with High-Power Short-Navelength Lasers", Science 229, 1045 (1985).
2.
J. F. Holzrtchter, D. Etmerl, E. V. George, J. 8. Trenholme, N. N. Simmons, and J. T. Hunt, "Htgh Power Pulsed Lasers", J. Fuston Energy 2, S (1982) D. Elmerl, "E1ectro-optlc, Linear, and Nonllnear Optlcal Properties of KDP and I t s Isomorphs", Ferroelectrlcs 72, 95 (1987)
3. 4.
5.
D. E1merl, S. Velsko, L. Davis, F. Nang, G. LoJacono and G. Kennedy, "Deuterated L-Arglnine Phosphate: A New Efflclent Nonllnear Crystal", submitted to J Qu. El. D. Elmerl, "High Average Power Harmonic Generation", I . E . E . E . J . Quant. Electron. 0E-23, 575, (1987)
6.
O. Elmerl, L. Davis, S. Velsko, E. K. Graham and A. Zalkln, "Optlcal, Mechanlcal, and Thermal Properties of Barium Borate", O. App1. Phys. 62, 1968 (1987)
7.
D. Etmerl, "Frequency Conversion Materials From A Device Perspective", Proc. SPIE 681, 2 (1986) F. Zerntke and E. Midwinter, Aoolted Nonlipear Oottc}, (NIley, New York, 1973)
.
9.
R. S. Craxton, S. D. Jacobs, O. E. Rtzzo, and R. Boni, "Basic
Properties of KDP Related to the Frequency Conversion of ll~m Laser Radiation", I . E . E . E . J . Quant. Electron. OE-17, 1782 (1981) 10. D. Bruneau, R. M. Tournade, and E. Fabre, "Fourth Harmonic Generation of a Large-Aperture Nd:Glass Laser", Applied Opttcs 24, 3740 (1985) 11. S. K. Kurtz, J. ~erphagnon, and M. M. Choy, "Nonl|near D i e l e c t r i c S u s c e p t i b i l i t i e s " , tn Landolt-Bornstein New Series Vol. 11, p. 671 (Springer Verlag, N.Y., 1978); J. Jerphagnon, S. K. Kurtz, and J. L. Oudar, Landolt-Bornstetn new Series Vol. 18, p. 456 (1984).
112
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Prlnciples and Practice,
Cambridge Unlv. Press, N.Y. (1981). 13. F. Donald Bloss, An Introduction to the Methods of Opttcal Crystallography, Holt, Rhtnehart and Hlnston, N.Y. (1961). 14. O. Medanbach, "A New Mtcrorefractometer Spindle-Stage and i t s Application", Fortsch. Miner., 63, 111 (1985). 15. J.-L. Crovtster, "Methode de Measure Rapide des t r o i s Indices de Refraction Principaux des Mineraux en Grains", Bull. Miner. 103, 40 (1980). 16. V. G. Fekllchev and N. V. Flortnsky, "A Universal Set to Determine Refractive Indexes by the Theodoltte-lmmerston Method", Isv. Akad. Nauk, CCCP, Ser Geol. 12, 106 (1965). 17. S. K. Kurtz and T. T. Perry, "A Powder Technique for the Evaluation of Nonlinear Optlcal Materials", ~. ADo], phvs. 39, 3798-3813 (1968). 18. M. L, Bond, "Measurement of the Refractive Indtces of Several Crystals", J. Apol. Phys. 36 (5), 1674-1677 (1965). 19. S. K. Kurtz, "Measurement of Nonlinear Optical S u s c e p t l b t l t t i e s " , Ouantum Electronics, Vol. IA, H. Rabin and C. L. Tang, eds. (Academic Press, New York, 1975). 20. J. Q. Yao and T. S. Fahlen, "Calculatlons of Optimum Phasematch Parameters for the Blaxial Crystal KTiOP04", J. App1. Phys. 55(I), 65-68, 1984. 21, S. Slngh, "Nonllnear Optical Materlals", In The Handbook of Laser Science and Technology, Vo1. I I I , M. J. Heber, editor (CRC Press, Boca Raton, FL., 1986) pp. 3-248. 22. S. Velsko, "Direct Assessment of the Phasematching Properties of New Nonlinear Materials", in Laser and Nonllne~r Ootlcal Ma~erl~1~, L. DeShazer, ed., Proc. SPIE 681, 25-29 (1986). 23. J. A. Giordomalne, "Mixing of Light Beams In Crystals", Phys. Rev. Lett. ~ ( I ) , 19-20 (1962). 24. P. D. Maker, R. H. Terhune, M. Nisenoff, and C. M. Savage, "Effects of Dispersion and Focusing on the Production of Optical Harmonics", Phys. Rev. Lett. ~(1), 21-22 (1962). 25. M. V. Hobden, "Phasematched Second Harmonic Generation in Biaxlal Crystals", J. Aopl. Phvs, 38, 4365-4372 (1967). 26. S. Velsko and D. Eimer], "Phasematched Second harmonic Generation in Sodium Lanthanum Fluoride", 3. Appl. Phys., 62(6), 2461-2465 (1987). 27. R. S. Feigeison, H. L. Kway, and R. K. Route, "Single Crystal Fibers by the Laser-Heated Pedestal Growth Method", In Infrared Ootlcal Materials and Fibers I l l , Proc. SPIE, Vol. 484, P. Klocek, ed.
Nonlinear opti~l materials for high power lasers
28. J. 8adan, R. Hterle, A. Pertgaud and P. Vtdakovtc, "Growth and Characterization of Holecular Crystals", in Nonlinear Oottcal Pronerttes of Oraantc Molecules and Crystals, Vol. 1, D. S. Chemla and 3. Zyss, eds. (Academic press, Orlando, FL, 1987). 29. D. Elmerl, unpublished 30. R. T. Twelg and K. Jaln, "Organic Materlals for Optlcal Second Harmonic Generation", in Nonlinear Ootlcal Prooertles of Oroanlc and Polvmerlc Materlals, David T. Hllllams, ed. (American Chem. Soc., Hashlngton, DC, 1982). 31. S. B. Monaco, L. E. Davis, S. P. Velsko, F. T. Hang, D. Elmerl, and A. Zalkln, "Synthesis and Characterization of Chemical Analogs of L-Arglnlne Phosphate', J. Cryst. Growth 85, 252 (1987) 32. H. Szyper and P. Zuman, "Electronic Absorption of Carboxylic Acids and their Anions", Anal. Chlm. Acta85, 357 (1976). 33. S. Velsko and D. Elmerl "New SHG Materlals for High Power Lasers" Proc. SPIE 622, 171 (1986). 34. R. Adair and L. Chase, private communication. 35. H. L. Smith, M. A. Heneslan, and F. P. Mllanovlch, "Spontaneous and Stimulated Raman Scattering in KDP and Index-Matchlng Fluids", in The Laser prooram Annual Reoort, UCRL-50021-8S, (1986). 36. DMS RamanlIR Atlas of Oroanlc Comoounds, B.Schrader and H. Meier, eds. (Verlag Chemle, GmBH, 1974). 37. H. Haussuhl and D. Elmerl, to be published 38. C. Chen and G. Llu, "Recent Advances in Nonlinear Optical and Electrooptlcal Haterlals", Ann. Rev. Mat. Sct. 16, 203 (1986). 39. D. Elmer1, "Thermal Aspects of High Average Power Electroopttc Switches", Z.E.E.E. 3. Quant. Electron. 0E-23, 2238 (1987) 40. I. S. Gradshteyn and I. H. Rhyzlk, "Tables of Integrals, Series and Products', Academic Press, New York and London, 1965 Ed., Equations 8.119 and 8.146 (22, 23, and 24).
113