Volume 44, number 2
OPTICS COMMUNICATIONS
15 December 1982
HARMONIC GENERATION WITH NON COLLINEAR LASER BEAMS. APPLICATION TO PULSE STACKING J. SAUTERET, T. DUVILLIER and A. ADOLF Commissariat a l'Energie Atomique, Centre d'Etudes de Limeil, B.P. No. 2 Z 94190 Villeneuve-Saint-Georges, France Received 29 September 1982
Harmonic generation in KDP crystals is of great interest in application to high power Nd laser chains. A non collinear beams technique has been investigated numericaUy and experimentally. It has been pointed out that an optimum separation angle can be found where tolerance on divergence of one beam is increased. The process provides angular separation of the fundamental and harmonic beams and allows a pulse stacking compression technique, which is described, and which could improve the performances of a laser chain.
1. Introduction There are several efficient ways to produce visible or ultraviolet (U.V.) pulses with peak power in the gigawatt range. One way is to use a nonlinear crystal to generate harmonics from the output of a neodymium power laser. It has been pointed out that the nonlinear interaction can mix two beams [1-3]. Most experiments use collinear beams and total energy conversion efficiency is up to 80% starting from a near infrared wave (I.R.) at 1.06/am to its third harmonic at 0.35/~m [4]. Considering this standard conversion we need to develope efficient techniques for the separation of the fundamental and harmonic wavelengths. This result is generally ensured by blocking the fundamental energy with glass filters. Then difficulties are encountered when filtering the second and third harmonics output energies: linear absorption losses, solarisation, self-focusing effects, two photons absorption losses in the glass filters. To obtain a higher efficiency in the conversion and filtering system we propose a new input configuration using non-collinear beams. In addition this configuration allows a pulse stacking compression technique which increases the power of the generated pulse. This paper describes the doubling scheme and shows that no additional components are required to sepa0 030-4018/82/0000-0000/$ 02.75 © 1982 North-Holland
rate the green beam from the I.R. beam (or the U.V. from the green and I.R.).
2. Non-collinear waves phase matching The doubling scheme shown in this work is based on a non-collinear beam conversion (see fig. 1). The optimum mixing of plane waves occurs when the vec-
oo2 rlo
n~t~ Fig. 1. Phase matching direction in a KDP type I crystal for second harmonic generation with non-collinear beams (noo~ and no2 to denotes the ordinary refractive indexes at to and 2to, 0 o is the phase matching angle of collinear conversion).
135
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OPTICS COMMUNICATIONS
torial phase matching condition is realized [5]: K 1 +K 2 =K 3 ,
(1)
where K 1 and K 2 are the wave vectors of the incident beams and K 3 is the wave vector of the generated beam. This technique can be used in either type of KDP crystals (I and II) to double or triple the I.R. beam frequency. The relation (1) becomes: K 1 cos ct' + K 2 cos(a - o/) = K 3 ,
(2)
K 1 cos01 + K 2 cos02 = K 3 cos03 .
(3)
The angles a and ~' are the angle between K 1 and K 2 and between K 1 and K 3 . The angles 01,2,3 are the angle between K 1,2,3 and the optical axis OA of the crystal. The curves represented on fig. 2 show the direction of the two incident wave vectors where relations (2) and (3) are verified. We have assumed that O A , K 1 a n d K 2 are in the
B/ ._d'(m~o)
8/
~m rd)~
j--U,~'= ~<2 /
~
' 07-0o(tara)
c/
15 December 1982
sante plane. Fig. 2 shows the values of the angles a and a' versus 01 - 02 for either KDP type I (or II) crystals in the doubling and tripling conditions (00 is the phase matched angle with collinear beams). The phase matching angles a, 0, are calculated from the refractive index in KDP given by Zernicke
[61. When a = 0, the collinear phase matching condition is met again. We must also consider another important case: it occurs stationary condition for the second beam (K 2, 02), which determines an optimum for its divergence.
3. Experimental results The experiments are performed using a CW Qswitch YAG laser. The experimental set up represented in fig. 3 is similar to the one described by Giordmain [2] except for a few modifications, one being the addition of a second power beam. The beam splitter BS divides the main beam (ab) in two separated beams (a) and (b) which intersect at an angle % that can be adjusted in the area where beam (a) and beam (b) intersect. Assuming that the angle oLa (in the air) and the thickness of the crystal are small then the volume of interaction is about the same like a collinear configuration and the optical delay between the two beam pulses is always small compared to the pulse duration. The detection of the harmonic produced in the crystal is made with a Polaroid film P in the focal plane of a lens L 1 . A dielectric mirror M 2 selects only the harmonic waves.
o,-00(.,,~,d) CW
~-'B'--
'
~'o
'
~-~2£{r..~)
Fig. 2. Phase matching curves for non-collinear beams: a) doubler type I crystal, b) doubler type 1I crystal, c) tripler type 1 crystal, d) tripler type 11 crystal. (c~ and c/ denote the angle between wave vectors K1, K2 and KI, Ka, respectively; 01--00 is the angle between the direction of K1 and the collinear phase matching direction. (In the type II conversion the ordinary wave propagates with the wave vector K 1). 136
t
@
,
----- .........
p
Fig. 3. Experimental set up. Nomenclature: (ab), (a), (b): source beam and incident beams; CW: YAG laser; BS: beam splitter; M1 mirror; L2 : movable lens for angular tolerance measurement; D: movable diffusor screen for phase matching rings observation; M2 : dielectric mirror; L 1: focusing lens; P: polaroid film in the focal plane of L 1.
Volume 44, number 2
OPTICS COMMUNICATIONS
15 December 1982
3.1. Phase matching condition
~
O•
~(mrd) 2
When a diffused screen D is inserted in front of the KDP crystal, each scattered light beam gives a cone o f emission at the second harmonic wavelength. Then two rings are observed in the focal plane (see fig. 4). These phenomena explained by Giordmaine [2] are used to determine the phase matching condition o f beanas (a) and (b). The fraction of non scattered light gives three green focal points. These points are respectively associated with the direction of the second harmonic produced by
~~
/
_J
K 1 + K 2 , K 1 + K 1 a n d K 2 + K 2. For the (K 1 + K2) phase matching the two rings are tangential each other in the K 3 direction which permits to tune the crystal at the correct angle. The different positions o f the rings observed in the focal plane allows to draw the experimental curve presented in fig. 5. The agreement for a doubling KDP type I is good as we can see in fig. 5.
(~=41.2
0~70o
I~
10
deg
40
0~-00(mrd)
3.2. Angular tolerances When the diffusor screen is removed it is possible to insert a lens L 2 in the beam (a) or (b) or (ab). This lens gives a divergent beam. In this case series o f bright harmonic bands are observed in the phase matching direction. The main lobe width o f the characteristic sinc2(CA0) phase matched pattern
Fig. 5. Experimental phase matching curves with noncollinear beams in a 2,o-type I KDP crystal (solid line) (broken lines are the theoretical prediction of fig. 2).
30
(mrd)
^^'J I
® s
"
i
i
i ®
1 '"'
Fig. 4. Harmonic generation rings obtained when a diffusor screen is inserted in front of the KDP crystal.
lb
:
:
"
5"0
"
;
o'(mrd)
Fig. 6. Angular tolerance of the incident beams in a 2w-type I KDP crystal (e = 10 ram); (ab), (a), (b) denote respectively tl~ source and the two incident beams. 137
Volume 44, number 2
OPTICS COMMUNICATIONS
gives the angular tolerance of each beam versus the angle o~'. The experimental results presented in fig. 5 and 6 show that the angular tolerance of the (b) beam is maximum when the angle 0, between OA and (a) is minimum as expected above. This is a particularly interesting non collinear configuration because angular tolerances in beams (a) and (ab) do not decrease significantly with respect to the tolerances observed in the collinear configuration.
4. Application The straight forward application of non-collinear beam frequency conversion is the spatial wavelength separation. In this technique 260 and 360 filters are not necessary before focusing the beam as shown in fig. 7. Consequently all the problems of selffocusing, polarisation, and losses in these filters are avoided. This technique allows also a pulse stacking compression. The energy of a power chain is delivered by a sequence of two pulses. Each pulse goes through the KDP crystal which is not tuned for collinear conversion. After two reflexions (see fig. 8) the first pulse is recombined with the second with appropriate delay time and angle a' in the crystal. Therefore two pulses are stacked up and generate the harmonic pulse.
Lens
!:
Fig. 7. Spatial separation of the incident harmonic beams in the focal plane of a lens.
138
15 Deccmbcr 1982
M;
o,
_rse
o
KDI~
-~.~ ......
Fig. 8. Base line of the pulse stacking technique (M: mirror; D: dielectric mirror; r is the delay time between the two incident pulses). The extraction of energy from a power chain with a pulse of duration rp is mainly limited by the B-integral. The same power chain can deliver two rp pulses separated in time by a few nanoseconds with a total energy which is almost twice the maximum energy of a single pulse. Consequently this technique allows a noticeable increase of conversion efficiency of the power chain.
5. Conclusion We have suggested in this paper the use of noncollinear beam conversion to generate high power harmonic pulses. With this technique glass filters can be avoided before focusing and pulse stacking compression increases the conversion efficiency. Extensive experimental verifications on a high power laser will be undertaken in our laboratories.
References [ 1 ] M. Bass, P.A. Franken, A.E. Hill, C.W. Peters and G. Weinrich, Phys. Rev. Lett. 8 (1962) 18. [2] J.A. Giordmaine, Phys. Rev. Lett. 8 (1962) 19. [3] P.D. Maker, R.W. Terhune, M. Nisenhof and C.M. Savage, Phys. Rev. Lett. 8 (1962) 21. [4] W. Seka, S.P. Jacobs, J.E. Rizzo, R. Boni and R.S. Craxton, Optics Comm. 34 (1980) 469. [51 D.A. Kleinman, Phys. Rev. 128 (1962) 1761. [6] F. Zernicke, J. Opt. Soc. Am. 54 (1964) 1215.