Optical properties of Nd3+ in metaphosphate glasses

Journal of Non-Crystalline Solids 44 (1981) 137 - 148 North-Holland Publishing Company

137

OPTICAL PROPERTIES OF Nd 3+ IN METAPHOSPHATE GLASSES

M.J. WEBER, R.A. SAROYAN Lawrence Livermore National Laboratory, University o f California, Livermore, California 94550, USA and

R.C. ROPP Vitrex Corporation, 138Mountain Avenue, Warren, New Jersey 07060, USA

Received 12 November 1980

Absorption and fluorescence spectra and fluorescence lifetimes of Nd3+ ions were measured for the following polymeric metaphosphate glasses: [M(PO3)2]n, where M = Mg, Ca, Sr, Ba, Zn, Cd, and AI(PO3)3. Judd-Ofelt intensity parameters for f - f transitions were derived from the integrated absorption spectra and used to calculate the spontaneous emission probabilities from the 4 F3[ 2 state. Metaphosphate glasses exhibit systematic variations of refractive indices, opti-

cal intensity parameters, fluorescence lifetimes and linewidths, and stimulated emission cross sections with alkaline earth. The origin of these variations and their implications for tailoring spectroscopic properties by compositional changes are discussed. Neodymium laser action in metaphosphate glasses is also considered.

1. Introduction

The optical properties of paramagnetic ions in glass are strongly affected by the glass composition. For example, factor-of-five variations in the stimulated emission cross section and fluorescence lifetime of Nd 3÷ have been observed by changing the glass network former. For a given glass former, similar but smaller variations are observed by changing the network modifier cations [1,2]. The spectroscopic properties and possible laser action of Nd 3÷ in phosphate glasses have been the subject of several studies [ 3 - 5 ] . Here we report the linear and non-linear refractive index, absorption and fluorescence spectra, and fluorescence lifetime of Nd 3÷ in a series of polymeric metaphosphate glasses. Systematic variations in these properties occur with changes in glass composition. The effects of glass composition on the stimulated emission cross section and possible 4F3/2 ~ 4111/2 laser action of Nd 3÷ are also considered. The metaphosphate glasses investigated had a nominal formula of [M(PO3)2]n, where M was Mg, Ca, Sr, Ba, Zn, or Cd, and n implies a degree.of polymerization. These glasses are composed of equal moles of the divalent modifier oxide and the 0022-3093/81/0000-0000/$02.50 © North-Holland

138

M.J. Weber et al. / Optical properties of Nd 3+ in metaphosphate glasses

Table 1 Electronic configurations, ionic radii a, and relative field strengths (Ze/a 2) of cations. Electrons removed in forming ions are enclosed in parentheses Element

Electronic configuration

lon radius (A)

Mg

ls22s2p6(3s 2)

Mg2+ 0.66

4.6

Ca

ls22s2p63s2p6(4s 2)

Ca 2+ 0.99

2.0

Sr

ls22s2p63s2p6dl°4s2p6(5s 2)

Sr 2+

1.12

1.6

Ba

ls22s2p63slp6dl°4s2p6dl°5s2p6(6s 2)

Ba2+ 1.34

1.1

Zn

ls22s2p63s2p6dl°(4s 2)

Zn 2+ 0.74

2.7

Cd

ls22s2p63s2p6d1°4s2p6dl ° (5 s2)

Cd 2+ 0.97

2.1

A1

ls22s2p6(3s2p)

A13÷ 0.51

11.5

Nd

1 s22s2p63s2p6dl °4s2p6dl °f3(f)5 s2p6(6s2)

Nd 3+ 1.04

P

ls22s2p6(3s2p3)

pS+

0.35

Field strength

2.9 14.3

P2Os glass former; the phosphorus-to-modifier cation ratio is 2.0. One metaphosphate glass with a trivalent cation was included: Al(POs)s. For this glass P/A1 = 3.0. The electronic configurations of the cations studied and their ionic radii are given in table 1.

2. Glass preparation and chemical properties Samples were prepared by melting specially purified raw materials in an alumina crucible in air. The resulting melts were held for times sufficient, as determined experimentally, to ensure complete polymerization. Each melt was then cast in a graphite mold, chilled, the glass rod removed from the mold, and annealed. It was necessary to anneal at 10°C above the measured softening point, or strain relief did not take place. Each glass had its own critical annealing point, above its softenhag point, yet deformation of the glass rods did not take place. Two Nd a+ concentrations were added: 0.01 tool Nd 3+ and 0.0005 tool Nd 3+ per tool of M(PO3)2. The actual concentrations of Nd a+ incorporated into the glass were determined by spectrochemical analysis and are given in table 2. Neodymium must be added to the melt as Nd(POs)3. If either Nd:Os or NdPO4 were added, crystals of pyrophosphate appeared in the melt due to the reaction 2M(POs)2 + NdP04 ~ M2P207 + Nd(POs)s •

(1)

The number of pyrophosphate crystals appeared to be proportional to the amount of NdP04 added. Thus, the probable formulation for the glasses was [(1 - x) M(PO3)2 • x Nd(POs)sln •

(2)

M.J. Weber et al. / Optical properties o f Nd 3+ in rnetaphosphate glasses

139

Table 2 Physical properties of polymeric metaphosphate glasses Property

Mg(PO3) 2 Ca(PO3)2 Sr(PO3)2 Ba(PO3)2 Zn(PO3)2 Cd(PO3)2 AI(PO3)2

Wt.%Nd 0.59 Density (g/cm 3) 2.48 nD 1.5009 v 66 n2(10 -2° m2/W) 2.93

0.50 2.72 1.5544 66 3.39

0.45 0.33 3.26 3.67 1.5691 1.5926 67 66 3.40 3.67

0.58 2.99 1~5400 59 3.81

0.40 3.83 1.6218 56 4.99

0.59 2.60 1.5219 65 3.18

Further details concerning these glasses and their polymeric nature will be reported in detail elsewhere [6]. The solubility of Nd 3+ in these glasses was limited. This is illustrated in fig. 1 for the [(1 - x ) Ca(POa)2 "xNd(PO3)3]n system. The glass density increases linearly with x for x ~<0.11, but remained constant at higher concentrations. The solubility limit corresponds to a Nd density of ~8.4 × 102°/cm 3. Total impurity content of the raw materials averaged about 100 ppm, of which 60 ppm was Na. Transition metal content was less than 20 ppm with minor amounts of Si and A1 also present. The glass melts attacked the inner surfaces of the alumina crucible so that the finished glass contained about 1500 ppm total impurities. About 1200 ppm of this was A1. The other impurity increases, for example, Na, Si, A1, Fe, etc., mirrored the composition of the clay used as a binder in the manufacture of the crucibles. Preparation of mixtures of cations was not possible because each glass rejects "foreign" cations. Even Mg and Ca, or Ca and Sr were not compatible and each phase separated. The only usable compositions were the "simple" metaphosphate formulations. 2.82

'

r

'

I

'

,,I"

2.80 --

E ~ 2.78-

0.92 x + 2 . 7 0 /

/

'~ 2.76 --

•

J

f ,@

@----

J

I

'

I Nd3+ solubility ,~I

~

limit-" I

2.74 --

[

2.72'--

1

0.04

0.08

0.12

0.16

x rnols Nd (PO3) 3 per tool of glass

Fig. 1. Glass densities in the [(1 - x ) Ca(PO3)2 • x Nd(PO3)3] n system. The Nd 3+ solubility limit corresponds to 8.4 X 1020 Nd/em a.

140

M.J. Weber et al. / Optical properties of Nd 3+ in metaphosphate glasses

The hydrolysis stability of these glasses to boiling water rivals that of soda-lime glass at 0.053 mg/cm:/h. They appear to be 103 to 104 times more resistant than hydrolytic glasses of similar composition. The actual stability of these glasses could not be accurately determined since most, if not all, of the hydrolytic etching occurred at sharply det'med areas along the surface of the glass rod. It was proven by SEM techniques that these areas were those where the impurities were segregated as specific islands within the body of the phosphate glass. The rest of the glass area appeared to be untouched by hydrolysis attack. 3. Density and refractive indices Several physical properties of the glasses at 295 K are summarized in table 2. Densities were determined from the weight loss upon immersion. Refractive indices were measured with a precision refractometer. The Abbe number v is a reciprocal dispersion given by ( n o - 1)/(nz -- nc), where the subscripts D, F and C denote the index at the sodium and hydrogen line frequencies 589.3,486.1 and 656.3 nm. The refractive indices at other wavelengths were calculated from a simple dispersion formula using n o and v. Optical electric fields associated with the propagation of intense laser beams induce refractive index changes in materials. The total refractive index is given by n =no + n2I, (3) where no is the linear index, n2 is the nonlinear refractive index coefficient, and I is the beam intensity in W/m 2. Recent studies [7,8] have shown that reasonable estimates of n2 in the long-wavelength limit can be obtained from the expression K ( n D -- a)(n~ + 2) 2 n2 nDv[1.5 +(n~ + 2)(nD + 1) v/6nD] l/z ' (4) where the empirical parameter K is 2.8 × 10 -is m2]W. Values of n2 calculated from eq. (4) are included in table 2. 4. Spectroscopic properties 4.1. A b s o r p t i o n spectra

Absorption spectra of Nd 3÷ in the range 200-1000 nm were recorded for all glasses at 295 K with a Cary 17 spectrophotometer. The spectra were digitized, non-Nd contributions to the spectra removed, and the Nd absorption bands integrated using a system described in detail elsewhere [9]. The absorption of the base glass plus impurities begins at ~350 nm; the absorption coefficient is ~2 cm -a at 300 nm. The Nd 3÷ absorption cross section, obtained after subtraction of the host absorption and reflective and scattering losses, is shown in fig. 2 for the extremes of the alkaline-earth metaphosphate series. The bands in fig. 2 correspond to transitions from the 419/2 ground state to the [SL]J states listed in table 3. All absorption spectra were very similar, the greatest differences being small changes in the

M.J. Weber et al. I Optical properties o f Nd 3+ in metaphosphate glasses I I I 1 1 1 1 1 1 1 1 1 1

141

I l l l l l l l l l l l l l l l l l

Mg(P03) 2

L.X

v

.~_

0 I

i

I

I

[

I

i

r

I

I

I

I f

I

I

[

I

I

I

I

11

I

]

I

i

i

t

I

I

11

I

I

I

I

[

I

I

I

I

I

I

I

I

I

I

I

I

I

I

I

I

I

i

I

I

I

I

11

i

I

I

I

I

I

I

I

I

I

I

I

0

.g

3

BaIPOa)2 0

14 2

1

0 i

300

i

i

I

I

400

i

i

I

500

I

I

600

I

I

I

700

800

900

I

I

I

1000

Wavelength, nm

Fig. 2. Comparison of the absorption spectra of Nd a* in two alkaline-earth metaphosphate glasses at 295,K.

relative band intensities. Because of inhomogeneous broadening, the Stark structure is poorly resolved. The intensities of f - f transitions of rare earths in glass have been treated by the approach of Judd-Ofelt [10]. In this approach the line strength of a transition between two J states is given by

S(J;J') =

~ t=2,4,6

~2t I([o~L] J II u(t) l I [~'S'L'] J'>l s

,

(5)

where the coefficients ~22, ~24, £Z6 are phenomenological intensity parameters and

142

M.J. Weber et al. / Optical properties o f Nd 3+ in metaphosphate glasses

Table 3 Comparison of measured (Sm) and calculated (Se) absorption line strengths (10 -2o cm2) for Nd 3+in metaphosphate glasses at 295 K. X-is the wavelength of the band peak Band

~

Ca(P03)2 Sm

Sc

Zn(PO3)2 Diff.

Sm

Sc

Diff.

4F3/2

875

1.15

1.37

0.22

1.14

1.27

0.13

4F5/2, 2H9/2 4F7/2, 4S3/2

803 747

3.70 3.40

3.72 3.43

0.02 0.03

3.52 3.25

3_52 3.27

0 0.02

4F9/2

682

0.27

0.24

-0.03

0.27

0.23

-0.04

2HI1/2 4G5/2, 2G7/2

628 582

0.13 7.51

0.06 7.5 3

-0.07 0.02

0.12 7.86

0.06 7.87

-0.06 0.01

4G7/2, 4G9/2, 2K13/2 4 2 2G11/2~ G9/2, D3/2, K15/2 2P1/2, 2D5/2

525

2.23

1.99

-0.24

2.06

1.92

-0.14

477

0.60

0.40

-0.20

0.45

0.38

-0.07

429

0.28

0.20

-0.08

0.18

0.19

0.01

the (][U (t) I1> are doubly-reduced matrix elements of unit tensor operators calculated in the intermediate coupling approximation. The values of ~2 were found from a least-squares fit to the integrated absorption band strengths in the 4 0 0 - 9 5 0 nm region of fig. 2. Measured (Sm) and calculated (Se) line strengths for two representative glasses are compared in table 3. The largest differences occur for transitions to the 4F312 and (4G7/2, 4G9/2, 2K1312 ) states. The J u d d - O f e l t parameters are tabulated in table 4. The experimental error is the standard deviation associated with the quality of the fitting and does not include uncertainties in the Nd concentration or the measurement procedures. The goodness of the fit, the reduced chi square defined by ~ ( S c - Sm)2/(~ - 3 ) , where ~ is the number of bands used in the calculation (9 in this case), is included at the bottom of table 4. 4.2. Fluorescence spectra

Neodymium fluorescence was excited with a cw xenon arc lamp and observed with a grating monochromator equipped with a PbS detector. Examples of the 4F312 ~ 4111/2 spectrum at 295 K are shown in fig. 3; the variation in detection sensitivity was <3% over the spectral region shown. Individual Stark components are not observed in fig. 3 because of inhomogeneous broadening. The spontaneous emission probability A for electric-dipole transitions was calculated from the JUdd-Ofelt parameters via 641rae2 A ( J ; J ' ) - 3 h ( 2 J + 1) ~-3

n(n2 + 2)2 S ( J ; J ' ) .

9

(6)

Table 4 J u d d - O f e l t intensity parameters for Nd 3÷ in m e t a p h o s p h a t e glasses. Values for Nd (PO3)3 are from ref. [ 14] Mg(PO3) 2

Ca(PO3):~

Sr(PO3)2

Ba(PO3)2

Zn(PO3)2

Cd(PO3)2

Al(PO3)3

Nd(PO3)3

I22 (10 -2o cm 2)

5.3 ± 0.3

4.5 ± 0.4

4.3 ± 0.2

4.0 ± 0.2

5.1 ± 0.2

3.9 ± 0.2

6.3 ± 0.3

4.8 ± 0.5

I24 (10 -20 cm 2)

4.7 ± 0.4

4.8 ± 0.5

4.3 ± 0.3

5.4 ± 0.3

4.4 ± 0.3

4.2 ± 0.3

4.0 ± 0,4

3.2 ± 0.6

s26 (10 -20 cm 2)

4.3 ± 0.2

4.9 ± 0.2

5.0 ± 0,2

5.6 +_ 0.2

4.7 ± 0.2

4.6 • 0.2

4.6 ± 0.2

3.7 ± 0.5

0.0141

0.0269

0.0098

0.0088

0.0078

0.0096

0.0169

-

( S i n - Sc)2/6

Table 5 Spectroscopic properties associated with t h e 4 F 3 / 2 ---*4111/2 fluorescence transition o f Nd 3÷ in m e t a p h o s p h a t e glasses at 295 K. Measured fluorescence lifetimes are t h e first and third e-folding times. T h e relative absorption o f x e n o n flashlamp radiation given in the b o t t o m line is definea in the t e x t Property

Mg(PO3)2

Ca(PO3)2

Sr(POa)2

Ba(PO3)2

Zn(PO3)2

Cd(PO3)2

Al(PO3)3

ap,(nm) A~eff (nm) o (10 -20 cm 2)

1056 33.9 2.4 ± 0.1 0.47 431 390-410 1.13

1055 30.9 3.0 ± 0.2 0.49 358 315-370 1.09

1056 30.5 3.1 ± 0.1 0,50 358 310-360 1.02

1056 28,5 3.9 -* 0.1 0.49 290 310-320 1.15

1055 29.3 3.0 ± 0.1 0.49 393 330-390 1.05

1055 30.2 3.0 ± 0.1 0,49 340 320--340 1.05

105 3 31.2 2.7 ± 0.1 0.5 0 421 360-410 1.02

r R (its) r (its) Relative absorption

7~

144

M.J. Weber et al. / Optical properties o f Nd a+ in metaphosphate glasses

1.0

~

I

0.8

)2

0.6 8

0.4 B

0.2

Ba(P03)2 J ' " ' . . . ~

0 1020

1040

1060 1080 Wavelength, nm

11O0

120

Fig. 3. Comparison of the Nd 3+ 4F3/2 --+ 4111/2 fluorescence spectra of two alkaline-earth metaphosphate glasses. The intensity is normalized to unity at the peak. Temperature - 295 K; spectral resolution - 1.7 nm.

The stimulated emission cross section at the peak fluorescence wavelength ~p for the 4F3/2 ~ 4F 11/2 transition was calculated from 87r3e 2

~kp (n 2 + 2) 2

O(Xp)- 27hc /XXeff

~4

[U(4)] 2 d- ~ 6 [U(6)] 2}

(7)

n

and is given in table 5. Because of the asymmetry of the emission band in fig. 3, an effective linewidth A~keff, determined by integrating the fluorescence intensity and dividing by the intensity of Xo, was used in eq. (7) instead of the full-width halfmaximum linewidth [3]. Measured values of A~keff are tabulated in table 5. The radiative lifetime rR of the 4F3/2 state and the fluorescence branching ratio for the 4F3/2 ~ 4111/2 transition were also calculated and are included in table 5. The branching ratios to 419/2 ranged from 0.44 for Mg(PO3)2 to 0.40 for Al(PO3)3; corresponding ratios to 4113/2 were 0.084 and 0.094, respectively. The branching ratio to 4Ilsl2 was in the range 0.004 to 0.005 for all glasses.

4.3. Fluorescence lifetime The time dependence of rare-earth fluorescence decays in glass is not a single exponential because of site-to-site differences in the probabilities for radiative and multiphonon relaxation processes [11]. The first and third e-folding times of the 4F3/2 decay measured at 295 K are included at the bottom of table 5. The differences indicate the degree of site-to-site variation in transition probabilities. To avoid nonexponential decays due to self-quenching by ion-ion interactions, fluorescence

M.J. Weberet al. / Optical properties of Nd 3+in metaphosphate glasses

145

decays were measured using samples containing ~0.05 mol.% Nd. The observed range of fluorescence lifetimes is comparable to or slightly shorter than the calculated radiative lifetimes (because the Judd-Ofelt parameters are derived from all sites, the latter is some effective average). This agreement indicates that the quantum efficiency is near unity. Nonradiative decay can occur by multiphonon processes and/or the presence of a small amount of OH- which is a potential quencher of Nd 3+ fluorescence. Based on the results in table 5, the effects of these two nonradiative decay processes must be small. This is reasonable because: (1) measurements of multiphonon emission rates for rare earths [12] when extrapolated to the Nd 3+ 4 F3/2411s/2 energy gap predict only a small nonradiative contribution for phosphate glasses; and (2) the observed OH- bands in the infrared absorption spectra were very weak.

5. Discussion

The structure of phosphate glasses is dependent on the composition and preparation. The composition also governs the limits of glass formation and devitrification, the chemical durability, and other physical properties [6]. Our interest here is the effect of composition on the local fields at Nd a+ sites and the resulting optical properties. As seen from tables 2 and 5, these properties exhibit systematic dependences on the divalent modifier cation. In metaphosphate glasses with a one-to-one molar ratio of alkaline earth oxide to P:Os, each phosphorus-oxygen tetrahedron is linked to two other tetrahedra and one oxygen per tetrahedron is associated with a metal ion. This structure leads to the existence of long chains of tetrahedra which have been confirmed by X-ray studies. The long-chain phosphate molecules are entwined in much the same way as long thin organic molecules in polymers. The introduction of Nd203 causes cross linking of the phosphate glass structure, but the greater part of the glass mass probably remains in the form of chain polymers [5]. The mobility of these chains is sufficient for them to assume an arrangement around the Nd cation as ligands similar to that achieved in more complex, multicomponent glasses. The Judd-Ofelt intensity parameters are a function of crystal-field parameters, interconfigurational radial integrals, and energy separation of the 4f and opposite parity configurations. The angular part of the 4f wavefunction is sensitive to covalency changes, however, these effects are small. The largest effect of composition on the ~2 values arises through their dependence on the odd-order terms in the expansion of the local field at the Nd 3+ site. Small, highly charged ions polarize the neighboring oxygen anions more strongly which, in turn, increases the field at the Nd 3+ ions. If we assume an electrostatic model for the local field at Nd 3+, the values of ~ vary as R -(2t+2), where t = 1,3 for ~22, t = 3,5 for ~24, and t = 5,7 for ~26 and R is the ligand-Nd 3+ separation. Based on the ionic radii in table 1, neither the sensitivity or relative magnitude of the observed changes of the values of [2 with modi-

146

M.J. Weber et al. / Optical properties o f Nd 3+ in metaphosphate glasses

tier cation are consistent with such a simple model. The ~22 parameter involves the longer range terms in the crystal field potential and is the most sensitive to local structural changes [13]. For Nd 3+, the intensity of the 419/2 -~ 4Gs/2 transition is the principal determiner of f22. This transition satisfies the IAJI ~<2 rule for hypersenstive transitions [13]. From table 4, ~22 decreases with increasing ion size. In contrast, the other two intensity parameters show a monotonic increase with increasing ion size. [The small value of ~4 for Sr(PO3)2 is suspect and may be the result of a measurement difficulty or an incorrect Nd concentration determination.] Brachkovskaya et al. [14] have reported Judd-Ofelt intensity parameters for rare-earth metaphosphate glasses. In these glasses the rare earth plays the role of a network modifier. The ~2 values for Nd 3÷ are included in the ffmal column of table 4. They are approximately 20% smaller than the corresponding values for the other trivalent ion studied, A13÷. This is in contrast to the behavior of the divalent alkaline earths, where ~22 decreases and ~24 and ~26 increase with increasing ion size and atomic number. The 4Fa/2 fluorescence branching ratios are independent of ~22 and can be expressed in terms of the ratio ~24/~26 [1]. Since ~24 and ~2~ exhibit similar dependences on composition, variations in the values of ~ with compositional changes are small. The radiative lifetime of 4Fa/2 is inversely proportional to a linear combination of ~24 and ~26. The main reduction in r R through the alkaline earth series arises from the increasing magnitudes of ~24 and ~26. The increasing refractive index, which enters as n(n 2 + 2) 2 in eq. (5), also has a non-negligible effect. Deutschbein et al. [3] examined the properties of 500 phosphate glass compositions including the metaphosphates. Among the results of this work was a series of empirical rules governing the Nd 3÷ fluorescence spectra [4]. They noted that for a given modifier cation valency, the larger the cation the smaller the fluorescence bandwidth. This reflects a smaller effective Stark field at the Nd ion and/or a smaller range of site-to-site disorder. The decrease of Akeff with increasing cation size is well obeyed for the alkaline earth series in table 5 and illustrated in fig. 2. Zinc and cadmium, however, does not conform to this rule indicating that the structure and bonding variations are more complicated and differences in the electronic configurations (table 1) should be considered. The wavelength of the peak 4Fa/2 ~ 4111/2 fluorescence for all glasses with divalent modifier ions was within ~+1 rim. In the case of A1a÷, it is more strongly bonded to oxygen which reduces the covalency of the Nd-O bond. The reduced nephelauxetic effect shifts the center of gravity of the J states to higher energies which appears as a small lowering of kp. 5.1. Laser action

Metaphosphate glasses are chemically very durable and have other physical properties suitable for laser ion hosts, consequently they have been the subject fo several

M.J. Weber et al. / Optical properties o f Nd 3+ in metaphosphate glasses

147

studies [4,5,15]. The gain coefficient is proportional to a product of the stimulated emission cross section o and the population inversion between the initial and final laser levels. The inversion in Nd glass lasers is achieved by optical pumping using a broadband source, such as a xenon flasttlamp. Computer programs have been developed to model the excitation of Nd-doped glasses by xenon flashlamp radiation [16]. We have used this program and the absorption spectrum in fig. 2 to determine the inversion for a given product of Nd ion density and sample thickness. The relative absorption efficiency in the spectral range 340-950 nm for 5 X 102° Nd/cm 2 (a typical laser glass thickness-doping product) and a flashlamp current density of 1000 A/cm 2 is given in the final line of table 5. The numbers are relative to ED-2, a high-gain Li-Ca-A1 silicate laser glass. The variation of absorption efficiency for the different metaphosphate glasses was small, the extreme variations being only ~10%: The achievable population inversion is also affected by the fluorescence lifetime which shows a more pronounced variation with composition. The dependence of the inversion on r is not strong, however. For long pulses and weak pumping it is proportional to r, for pump pulse durations < < r it is independent of r. The lifetime is also a function of Nd concentration which must be adjusted to optimize pumping uniformity and efficiency [16]. The most promising method of tailoring the gain coefficient and saturation fluence is via compositional changes which affect the stimulated emission cross section. As seen from table 5, the cross section increases by ~50% in going from Mg to Ba. This variation is due to a combination of increasing intensity parameters [24 and ~26 and decreasing Aheff in eq. (7). The cross sections for metaphosphate glasses are in the low-to-middle range of cross sections observed in other phosphate glasses. They are all comparable to or larger than the cross sections observed in silicate laser glasses having similar modifier contents [ 17]. For short-pulse, high-power Nd lasers, a small nonlinear refractive index is desirable to reduce beam breakup due to self-focusing [8]. From tables 2 and 5, there is a tradeoff between cross section o and index nonlinearity n2 which have diverging trends. In practice, these and other properties are considered in selecting the most attractive laser glass [ 1,16]. Lempicki et a3. [15] have investigated high-Nd-concentration aluminum metaphosphate glass for laser action. The stimulated emission cross section for the 4Fa/2 ~ 4 I l l / 2 transition was determined two ways: from integrated absorption data and the Ladenburg-Fuchtbauer equation with: (1) partial decomposition of the emission spectra into transitions between individual Stark levels; and (2) no decomposition and an average over all Stark levels of the initial and final J manifolds. The two methods yielded difference o values of 1.96 × 10 -20 and 2.7 × 10 -20 cm 2, respectively; the corresponding predicted radiative lifetimes were 614 and 446 las. A low Nd concentration Nd concentration sample was not available to Check the predicted fluorescence lifetime. The Judd-Ofelt treatment offers a third way of predicting the emission cross

148

M.J. Weber et al. / Optical properties o f Nd a+ in metaphosphate glasses

section. Although the actual compositions of the glasses may not be identical, the results in table 5 are in very good agreement with those obtained by the second method o f Lempcki et al. This is not surprising because an average over Stark levels is more in the spirit o f the J u d d - O f e l t approach. The measured lifetime of the low Nd concentration sample in table 5 is in better agreement with the lower predicted radiative lifetime. We thank J. Lynch and R. Morgret for their assistance with the measurements and W. Sunderland for performing the chemical analysis of the Nd content in the glasses. The work of M.J. Weber and R.A. Saroyan was performed under the auspices of the US Department o f Energy under Contract W-7405-eng-48; the work of R.C. Ropp was performed at and under the auspices o f Allied Chemical Corporation, Materials Research Center, Morristown, N J, USA.

References [1] R.R. Jacobs and M.J. Weber, IEEE J. Quant. Electron. QE-12 (1976) 102. [2] N.B. Brachkovskaya, A.E. Grubin, S.G. Lunter, A.K. Przhevuskii, E.L. Raaben and M.N. Tolstoi, Sov. J. Quant. Electron. 6 (1976) 534. [3] O.K. Deutschbein, C.C. Pautrat and I.M. Svirchevsky, Rev. Phys. Appl. 2 (1967) 29. [4] O.K. Deutschbein and C.C. Pautrat, IEEE J. Quant. Electron. QE-4 (1968) 48. [5] M. Syczewski and K. Wieczffmski, Am. Soc. China. Polonorum. 49 (1975) 1059. [6] R.C. Ropp, to be published. [7] N.L. Boling, A.J. Glass and A. Owyoung, IEEE, J. Quant. Electron. QE-14 (1978) 601. [8] M.J. Weber, D. Milam and W.L. Smith, Opt. Engr. 17 (1978) 463. [9] R.A. Saroyan and M.J. Weber, SPIE Vol. 82, Unconventional spectroscopy (1976) p. 165. [10] W.F. Krupke, IEEE J. Quant. Electron. QE-10 (1974) 450. [11] C. Brecher, L.A. Riseberg and M.J. Weber, Phys. Rev. B18 (1978) 5799. [12] C.B. Layne, W.H. Lowdermilk and M.J. Weber, Phys. Rev. B16 (1977) 10. [13] R.D. Peacock, Struct. Bond. 22 (1975) 83. [14] N.B. Brachkovskaya, S.G. Lunter, A.K. Przhevuskii, E.L. Raaben and M.N. Tolstoi, Opt. Spectr. (USSR) 43 (1977) 411. [15] A. Lempicki, R.M. Klein and S.R. Chinn, IEEE J. Quant. Electron. QE-14, (1978) 283. [16] G. Linford, R.A. Saroyan, J.B. Trenholme and M.J. Weber, IEEE J. Quant. Electron. QE-15 (1978) 510. [17] M.J. Weber, J. Non-Crystalline Solids 42 (1980) 189.