Inelastic light scattering in halide and oxide glasses: Intrinsic Brillouin linewidths and stimulated Brillouin gain

240

Journal of Non-Crystalline Solids 102 (1988) 240-249 North-Holland, Amsterdam

INELASTIC L I G H T S C A T r E R I N G IN H A L I D E AND OXIDE GLASSES: INTRINSIC B R I L L O U I N L I N E W I D T H S AND S T I M U L A T E D B R I L L O U I N GAIN J. SCHROEDER, L.G. HWA, G. K E N D A L L * and C.S. D U M A I S Department of Physics and Center for Glass Science and Technology, Rensselaer Polytechnic Institute, Troy, N Y 12180-3590, USA

M.C. S H Y O N G Department of Electrical Engineering, University of Rhode Island, Kingston, RI 02881, USA

D.A. T H O M P S O N Research and Development Division, Coming Glass Works, Coming, N Y 14831, USA

Brillouin scattering measurements on various multicomponent halide and oxide glass compositions were performed as a function of composition, lattice temperature and configurational temperature. The intrinsic Brillouin linewidth measurements, the Brillouin intensities and the Brillouin frequency shifts allowed the calculation of phonon attenuations, the Pockels' elastoopic coefficients and the stimulated Brillouin scattering gain coefficients. From the parameters obtained in the above measurements we are able to calculate the threshold energy for the onset of stimulated Brillouin scattering in halide and oxide glasses. The results show that the threshold power for stimulated Brillouin scattering is larger in some of the halide glass compositions than some of the silica based glasses. This finding has important ramifications as a selection criteria for halide-based glasses versus oxide-based glasses in their use as possible single mode waveguide materials. The phonon attenuation values of some of the halide glasses, as measured from the linewidth data have magnitudes that correspond more to a liquid than to a solid. These anomalous phonon attenuation findings will be discussed in the light of existing theories.

I. Introduction

The light scattering properties of various halide and oxide glasses have been measured as a function of annealing time and temperature. The typical Rayleigh-Brillouin scattering spectrum of glass exhibits five identifiable components, two frequency shifted doublets comprising the longitudinal and transverse components of the Brillouin spectrum and a strong unshifted central line, the Rayleigh component. The origins of the Rayleigh scattering spectrum are microscopic density and concentration fluctuations in the glass. The Brillouin linewidth measurements, the Brillouin intensities and frequency shifts allowed the calculation of p h o n o n attenuation, Pockels' elastooptic coefficient and the Stimulated Bill*

Permanent Address: Dept. of Physics, State Univ. of New York, Albany, NY, USA.

0022-3093/88/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)

louin gain coefficient. Brillouin linewidths obtained experimentally range between the limit of 52 MHz for a BeF2 glass and 213 MHz for a zirconium-barium-lanthanium-fiuoride glass. If the optical power launched into a fiber exceeds some critical threshold level, then stimulated emission will occur. These may be Stimulated Brillouin Scattering (SBS) or Stimulated Raman Scattering (SRS), although our primary interest is Stimulated Brillouin Scattering. In this non-linear optical process a significant proportion of the optical power traveling along the fiber may be converted into a second lightwave, shifted in frequency, traveling backwards towards the source. This effect is an additional intrinsic non-linear loss mechanism. The critical threshold power is determined by the effective core area A, the small signal attenuation constant of fiber ap, and the gain coefficient for the stimulated scattering process g, by the approximation relation

J. Schroeder et aL / Inelastic light scattering in halide and oxide glasses

2 0 A a p / g . Our measurements and ensuing calculations show that the threshold power for the onset of Stimulated Brillouin Scattering in some halide glasses is greater than the best silica glass at their respective working wavelengths for minimum loss. The non-linear optical process of Stimulated Brillouin Scattering has been identified as an additional loss parameter (i.e. "Brillouin Crosstalk") in single mode optical waveguides. This effect must be considered in the design of optical communication systems using low loss fibers. PTh =

241

for the slowly varying complex Fourier amplitudes of the optical electric field E and density wave p on the fiber core axis [3] and they are: 3Es/3Z

= - ik2p*E L + aEs/2,

O O * / 3 r = - i k , E ~ E s - CO,

(3) (4)

where F-1 is the acoustic phonon lifetime resulting in a spontaneous Brillouin scattering linewidth of A F B = F / ~ r at (fwhm), and a is the attenuation coefficient. The coupling coefficients are given by: ,OF/2~0 k I = k 2 2VA ,

2. Theoretical background

qrrt 3p12

k2The theory of light scattering on the basis of thermodynamic fluctuations in glass was extensively discussed by Schroeder [1]. The phonon lifetime r is related to the measured natural linewidth by the expression: = 1/arB,

(1)

where AF B is the natural Brillouin linewidth. Note that the observed Brillouin linewidth is a convolution of the natural linewidth due to the finite phonon lifetime and the instrumental linewidth. However, only the magnitude of the natural linewidth is dependent on the type of glass that the phonons are contained in while the instrumental width is constant [2]. The phonon attenuation coefficient a is calculated from the following expression: A F B = OIVL/~ ,

(5)

XO

'

(6)

where P12 is the longitudinal elastooptic coefficient, O is the average density, and c o is the free space permittivity. The Brillouin gain coefficient can be calculated by using [4]: g = 2qrrtVP?z/C~k2pVLA_F'B,

(7)

where n is the refractive index, c is the speed of light, X is the incident wavelength, p is the density, VL is the sound velocity, Pa2 is the elastooptic coefficient, and AF B is the Brillouin linewidth. For a fiber length such that apL >> 1, the critical threshold power for Stimulated Brillouin Scattering is given approximately by: Pvh ~-- 2 0 A a p / g .

(8)

(2)

where VL is the longitudinal sound velocity. Stimulated Brillouin scattering can be described entirely classically as a coupled three-wave interaction involving the incident lightwave, a generated acoustic wave, and scattered lightwave or Stokes component. The three waves obey the energy conservation law which relates the three frequencies: vA = PL - - PS and maximum power transfer occurs when the wavevector mismatch is zero, namely kA = k L - k s here the subscripts L, S, A, refer to the laser, Stokes and acoustic frequencies, respectively. The usual starting point for a quantitative description of SBS are the coupled wave equations

3. Measurement and deconvolution techniques The methods employed to obtain the Brillouin spectra of halide and oxide glasses are laser excitation (argon-ion) operating at 0.488 ~m coupled to a stabilized multi-pass high contrast F a b r y - P e r o t interferometer with a photon counting detection system and associated data handling electronics. The entire F a b r y - P e r o t is contained in a thermally stabilized box and the whole system (laser, interferometer, detector and optics) is mounted on a vibration isolated opti~al table. The detector consists of an ITT-FW 130 photomultiplier tube cooled to - 2 0 o C. The dark count of this pho-

242

J. Schroeder et al. / Inelastic light scattering in halide and oxide glasses

tomultiplier tube in the cooled state is persistently about 0.4 counts/s and it has a quantum efficiency of 10% at 0.488/~m. The current generated by the photomultiplier is shaped, amplified, discriminated and converted to c o u n t s / s and the data of subsequent scans are stored in a 1024 channel multi-channel analyzer of the Burleigh DAS-1 system. This Burleigh DAS-1 system scans the F a b r y - P e r o t and assures long-term stability of the interferometer by providing servo-control for the piezo-electric stacks of the Fabry-Perot. The scattering experiments reported here were done in a three-pass mode with mirrors of 93% reflectively resulting in a finesse of about 80, a contrast of about 108 and overall measured transmission of about 0.40. The high contrast of about 108 was especially important in being able to measure the transverse Brillouin lines in some of the strong scattering heavy-metal fluoride glasses. The auxiliary parameters of refractive index and density were independently measured by determining the angle of minimum deviation of a ample that had been immersed in some well characterized index matching oil (i.e. parafin oil, cyclo-hexane, etc.), and from the measured angle the refractive index of the sample is calculated. The density was determined by an Archimedean technique where cyclo-hexane was the working fluid. Prior to measurement all samples were polished on three sides and then immersed in water-free parafin oil in a glass scattering cell to minimize any parasitic scattering and also to protect the delicate surfaces from water vapor attack. The velocities can be calculated from the Brillouin shifts with the aid of the Brillouin equation given by [5]:

here AVL,x is the Brillouin splitting (either longitudinal or transverse) in GHz, v0 to the incident frequency, C the velocity of light in vacuum, n the index of refraction at 0.488 /~m, and 0 the scattering angle. For a glass the velocity is independent of the direction of propagation and only one longitudinal and one transverse acoustic branch exist. In a glass the elastic strain produced by a small

stress can be described by two elastic constants, C]] and C44. Using the Cauchy relation that 2C44 = CIa - C12 allows one to determine C12. For pure longitudinal waves, C H = pV 2 and for pure transverse waves, C44 = pV 2, where 0 is the density, and Ve and VT the longitudinal and transverse velocities. The coupling between light and sound is described by Pockels' elastooptic coefficient, which gives the overall intensity and polarization properties of the scattering. The Pockels' cefficients are determined with respect to the S i O 2 glass from the Brillouin intensity measurements [1,2]. Problems with the Brillouin linewidth measurements arise from the fact that effects such as the instrumental resolution function, the scattering geometry and the velocity anisotropy, would broaden the Brillouin line over that caused by the phonon lifetime effect (natural Brillouin linewidth), by an amount AF. Consequently, the deconvolution techniques become important in order to recover the natural Brillouin linewidth. The observed Brillouin component profile is a convolution of Gaussian function and Lorentzianshaped spectrum. This instrumental width results from a convolution of several contributions such as the finite frequency width of the laser, the finite acceptance angle of the light gathering optics and the F a b r y - P e r o t interferometer. Fortunately several techniques exist that allow the deconvolution to obtain the natural Brillouin linewidth [6-9]. In this work we followed the method proposed by Leidecker and LaMacchia [6]. This technique involves approximation of the scattering function S(v), the light source function I(v), and the spectrum analyzer T(v), by analytic functions with adjustable parameters. The scattering function S(v) and the light source function I(v) are the Lorentzian function and Gaussian-shaped function, respectively. The transmission function for the F a b r y - P e r o t interferometer is given by Airy's function in the form:

oc

1

1 + F sin 2 Z 2

(1o)

J. Schroeder et al. / Inelastic fight scattering in halide and oxide glasses

where F = 4 R / ( 1 - R) 2, R is the reflectivity, and the definition of the finesse f = ~rv~-/(1 - R ) we can rewrite (10) as: 1

T ( v ) cc 1+

(11)

f sln~

1 1 +

f(e - tvp )

that is closely Lorentzian (when the F a b r y - P e r o t plates are flat and exactly parallel), a~ can be estimated in terms of the ratio of the analyzer width to the source width from eqs. (13) and (14) as follows: a I = t(o)(~r~/~r~)

where 8 is the phase difference. In practice, if f > 30 (in our work f - - 80) and the Airy function reduces to a Lorentizian function: 1 1 +

[ arF~/2 ] (12)

The source and the analyzer have a characteristic total width, the instrumental width A/"I. Leidecker and LaMacchia [6] have shown that characterization of the experimental distortions by a single parameter, the "instrumental width", is valid under only special conditions; usually, an additional parameter measuring the shape of the instrumental function is also necessary. The instrumental width is determined by the full width at half maximum of the Rayleigh line observed when scattering from a diffuse object such as ground glass is taken. Then the instrumental width z~FI and the characteristic line shape a I are given by:

243

(15)

and AFt AFI = ~ f ( a l ) ,

(16)

where f ( 0 ) = {ln 2} 1/2 and a v p = oc. The values of the Laser linewidth and the linewidth broadening due to the F a b r y - P e r o t interferometer was measured to be 20 MHz and 1.2 G H z for the free spectral range of 57.3 GHz, respectively. The relation between the true width A F B of the scattering maximum and its observed width AFOBs is: AFB = AF°BS -- F [ AF°Bs/AFI a, ] AFI"

(17)

For large a I, AF B = AFoB s - AF I, as a I -~ m, since the relevant line shapes are Lorentzian in this limit. Because the linewidth of F a b r y - P e r o t interferometer (1.2 GHz) is much greater than the laser linewidth (20 MHz), therefore, the above approximation is not unreasonable.

4. Results

ar~

lt(aFp) ] + it(0))

xf [(aFFp/t(aFp))2+ (Z~FC/f(0))2]1/2 ' (13) avp ] A F ~.(aFv) ] FP

[\ g(aFp) )2 + (g(0) ] where f ( a ) is a Voigt function standardization parameter, a v e is a parameter due to the F a b r y - P e r o t and AFc is the linewidth of the laser. In the case that the analyzer has a line shape

Tables 1 to 3 summarize the results of light scattering, density, index of refraction, Brillouin linewidth and phonon attenuation in halide and oxide glasses at 0.488 /,m and 300 K. The Brillouin linewidth is of the order of 102 MHz. The highest value is 213.6 MHz for ZBL glass and the lowest value is 52.5 MHz for BeFz glass. Fig. 1 shows that 6 K 2 0 . 9 4 S i O 2 and 8 K z O . 9 2 S i O 2 glasses give within the limits of error the same phonon attenuation as the annealing temperature and duration are varied. Fig. 2 gives a plot of phonon attenuation with respect to the square of the longitudinal sound velocity. It is evident from this figure that each different glass family exhibits a linear behavior with respect to these particular variables. Tables 4 to 6 give the gain coefficient,

J. Schroeder et al. / Inelastic light scattering in halide and oxide glasses

244

20

i

15

El

15

[]

A

A

13

U 0 x

Z

I0

2 x

11

-n

z

z

5

O z 0

9 Z

0 Z 0 -r.

0

gk

0

7

I 590

I

530

I

I

I

I

1

2

3

( LONGITUDINAL

650

4

VELOCITY) 2 x 1011 r]L(CM/SEC)2j

Fig. 2. Phonon attenuation versus the square of longitudinal sound velocity for halide and oxide glasses: D, halide glasses; ©, silicate glasses; v, glasses with lower percentage of B203; A, glasses with higher percentage of B203.

TEMPERATURE ( ° C ) ANNEALING Fig. 1. Phonon attenuation versus annealing temperature for 6K20_94SIO 2 (n) and 8 K 2 0 - 9 2 S I O 2 ( 0 ) glasses.

Table 1 Light scattering results for halide glasses at 0.488/~m and 300 K Sample

P ( g / c m 3)

n

VL (m/s)

611 (GPa)

Ara (MHz)

I Pa21

a (1/cm)

SiO 2 ZBL ZBLA ZBLAN HBL HBLA HBLAPC BeF 2 95BeF 2 - 5 T h F 4

2.203 4.672 4.579 4.301 5.78 5.83 5.10 2.01 2.10

1.462 1.530 1.548 1.521 1.514 1.554 1.524 1.28 1.31

5944.2 3979.0 3968.4 4270.0 3608.9 3470 4035 4634.1 4638.5

77.85 73.97 76.00 78.41 75.28 70.3 83.0 43.16 45.18

156 213.6 98.7 96.0 151.4 162.3 179.5 52.5 74.8

0.270 0.255 0.128 0.196 0.149 0.128 0.150 0.398 0.380

8.25 x 1.69 x 7.82 x 7.07 x 1.32 x 1.47 x 1.40 x 3.56 x 5.07 x

102 103 102 102 103 103 103 102 102

Table 2 Light scattering results for oxide glasses at 0.488/~m and 300 K Sample xLi20

zA1203

p ( g / c m 3)

n

yB203

(1) (2) (3) (4) (5) (6)

94.27 91.79 91.77 81.80 89.28 84.31

0.13 0.13 0.13 10.09 0.12 0.12

1.9434 1.9439 1.9025 2.0753 1.9823 2.0541

1.5056 1.5053 1.4946 1.5324 1.5189 1.5455

4.97 7.46 7.48 7.48 9.98 14.97

VL

C11

A/'~

(m/s)

(GPa)

(MHz)

4364 4351 4050 5109 4662 5205

37.01 36.80 31.20 54.18 43.08 55.64

100 116 113 124 138 104

I P12 I

a (1/cm)

0.2661 0.3017 0.2641 0.2870 0.3244 0.1437

7.199 x 102 8.342x102 8.795x102 7.624x 102 9.322x102 6.248 x 102

J. Schroeder et al. / Inelastic light scattering in halide and oxide glasses

245

Table 3 Light scattering results for oxide glasses at 0.488 ~m and 300 K Sample

T ( o C)

t (h)

O ( g / c m 3)

n

VL (m/s)

CH (GPa)

~Cg (MHz)

I P121

a (1/cm)

(1) 6 K 2 0 94SIO 2 (2) 6 K 2 0 94SIO 2 (0) 8K 2° 92SIO 2 (1) 8K20 92SIO 2 (2) 8K20 92SIO2 (3) 8 K 2 0 92SIO2 (4) 8 K 2 0 92SIO2 10K20 90SIO 2 10K20 90B203 30K20 70B203

637.8 604.8 547 627 603.5 589.5 574.3 573.4 -

78.56 231.8 59.96 103.42 141.793 345.68 84.66 -

2.2416 2.2519 2.2703 2.2725 2.2716 2.2696 2.2702 2.2991 2.0281 2.2699

1.4781 1.4781 1.4845 1.4844 1.4846 1.4844 1.4846 1.4923 1.5037 1.5231

5458 5465 5330 5335 5332 5321 5339 5039 4190 4839

66.78 67.26 64.50 64.68 64.58 64.26 64.71 58.37 35.61 53.16

184 186 175 190 177 170 187 208 104 134

0.2546 0.2533 0.2254 0.2432 0.2818 0.2333 0.2558 0.2278 0.2173 0.2028

1.06 × 103 1.07 x 103 1.03 × 103 1.12× 103 1.04 × 103 1.00 × 103 1.10 × 103 1.30×103 7.80 × 10 2 8.70×10 2

Table 4 Gain coefficient g, scattering loss % (from Landau-Placzek measurement) and threshold power PYh for the onset of stimulated Brillouin scattering in halide glasses normalized to a typical threshold power for SiO2: R

_ D(0.488 i x r n ) / D ( 0 . 4 8 S ~m) 1 - - ~Thtsample) / ~ T h ( s i o 2 )

and

R e = P(x~x). . . . . i/P(~Ss,c~m)"

?t is working wavelength Sample

g × 1011

a(2.s5 ,am)

p(0.488 'am)

R1

p(2.55 ~,m~

R

0.114 a) 0.0184 0.0053 0.0325 0.0787 0.318 0.152 0.0139 0.0936

14.99 63.06 30.13 87.43 678.9 3224.8 1439.8 8.44 78.84

1 4.21 2.01 5.83 45.29 215.1 96.05 0.56 5.26

147.5 a) 84.7 40.3 117.4 910.2 4317.8 1936.8 11.29 105.7

1 0.574 0.273 0.796 6.17 29.3 13.1 0.077 0.717

S(dB/km)

Yh(10 3w)

Yh~lo 6v¢)

(m/W) SiO 2 ZBL ZBLA ZB LAN HBI HBLA HBLAPC BeF2 95BeF 2 - 5 T h F 4

4.482 2.832 1.713 3.608 1.127 0.96 1.023 16.06 11.54

a) Calculated at 1.55/zm

Table 5 Gain coefficient g scattering loss % (from Landau-Placzek measurement) and threshold power PTh for the onset of Stimulated Brillouin Scattering in oxide glasses normalized to a typical threshold power for SiO2:

R1 = e(0.488~m)/p(0.488~m) Th tsample) /

Th (SiO2)

and

Sample xLi zO

yB203

zA1203

(1) (2) (3) (4) (5) (6)

94.27 91.79 91.77 81.80 89.28 84.31

0.13 0.13 0.13 10.09 0.12 0.12

4.97 7.46 7.48 7.48 9.98 14.97

R2

~

p(l.55"am)/e(l.55t~ml Wh (~mple) /

Th (SiO2)

g × 1011 ( m / W )

0~(1.55 'am)

--Vhoo 3w)

19(0.488/~m)

R

12.88 14.29 11.74 10.93 12.66 3.441

0.483 0.708 2.266 0.608 0.288 0.04

22.13 29.23 113.8 32.78 13.40 6.90

1.47 1.95 7.59 2.188 0.894 0.461

sldS/k°)

1

D(1.55 ~m)

--Thll,, 6~

R

217.2 287.0 1118.2 322.3 131.8 67.3

1.473 1.946 7.581 2.185 0.893 0.457

J. Schroeder et a L / Inelastic light scattering in halide and oxide glasses

246

Table 6 Gain coefficient g, scattering loss a~ (from Landau-Placzek measurement) and threshold power Prh for the onset of Stimulated Brillouin Scattering in oxide glasses normalized to a typical threshold power for SiO2: R

and

_ p ( 0 . 4 8 8 ~ m ) / p ( 0 . 4 8 8 ttm) l -Th(~mple ) / Zh(slo2)

R2

~ ( 1 . 5 5 ~ t m ) / p ( 1 . 5 5 #rn) = ~Th(~mple)/ Th(sio2) "

Sample

(1) (2) (0) (1) (2) (3) (4)

6 K 2 0 94SIO 2 6 K 2 0 94SIO 2 8 K 2 0 92SIO 2 8 K 2 0 92SIO 2 8 K 2 0 92SIO 2 8 K 2 0 92SIO 2 8KzO 92SIO 2 1 0 K 2 0 90SiO 2 1 0 K 2 0 90B203 3 0 K 2 0 70B203

T( o C)

t(h)

637.8 604.8 547 627 603.5 589.5 574.3 573.4 -

78.56 231.8 59.96 103.42 141.793 345.68 84.66 -

g )<1011 ( m / W )

a(1.55/~m)

D (0.488/zm) Irh(10_3W )

R1

p(1.55/Lm)

R2

3.905 2.783 3.354 3.587 5.181 3.704 4.038 3.122 8.169 4.675

0.254 0.467 0.073 0.163 0.309 0.222 0.360 0.087 0.026 0.025

38.38 98.86 12.06 26.73 35.18 35.35 52.60 16.40 1.865 7.745

2.56 6.60 0.805 1.784 2.348 2.359 3.511 1.095 0.124 0.517

376.8 972.1 126.1 263.3 345.5 347.2 516.5 161.4 18.4 76.09

2.55 6.59 0.85 1.784 2.342 2.354 3.502 1.094 0.125 0.517

scattering loss and threshold power for the onset of Stimulated Brillouin Scattering in halide and oxide glasses normalized t o S i O 2. The gain coefficient is of the order of 10 -11 ( m / W ) . Scattering loss was calculated at 2.55 /~m and 1.55 # m for halide and oxide glasses, respectively [10-12], the threshold power of the glasses was calculated at 0.488 # m and their respective working wavelengths for minimum loss [12]. The ratios R1 = p ( 0 . 4 8 8 ,ttm)/ ]o (0.488 /xm) a n d T h (sample)

ua

o

3

Z 13 /

2

o

[21 f

a o

/

,

/ /

t

I

/ /Q

J

/

/

O/

kiqt -I

i

0

i

I

2 PHOTOE

LAST t C

I

I

4 PARAMETER

Zh(10_6w)

for SBS than the best silica glasses. In fig. 3, the relative threshold power for SBS, as calculated from gain coefficient is given as a function of photo-elastic parameter. A linear correlation is observed between the relative threshold power and photoelastic parameter.

5. D i s c u s s i o n

T h (SiO2)

/ z

R o = p(~orking . . . . length)//p(a~l.55 ,m) are also ~.iven in ~ ~(Sample) -~ t~(Si02) tables 4 to 6. They clearly sliow that " s o m e " of the halide glasses have a higher threshold power

O

S(dB/km)

I

6

x 10-4(GPa-S~:C/CMI

Fig. 3. Relative threshold power vs photoelastic parameter 2 (PVL//n 7P12) for halide and oxide glasses: rn, halide glasses; ©, silicate glasses; zx, Borate glasses.

The intrinsic Brillouin linewidth measurements give the phonon attenuation values. Typical longitudinal acoustic phonon attenuation values for crystalline solids and for liquids are about 10 -5 cm -1 and about 1 0 4 c m 1, respectively. Our results in tables 1, 2 and 3 on phonon attenuation values show typical magnitudes for halide and oxide glasses to be about 10 3 c m - a . Hence, halide and oxide glasses exhibit almost liquid-like attenuation phenomenon. This suggests that the F ions in the halide glasses can move about rather freely in their lattice with liquid-like mobilities. N o t at all an unreasonable concept if one invokes the ideas embodied in the free volume model as envisioned in the work of Cohen and Grest [13-15]. The measured value of Brillouin linewidth, Ac, in bulk silica glass is 156 M H z at 0.488/~m. The linewidth varies inversely with the square of the wavelength, consequently, at 2t = 1.55 /~m, Ar =

J. Schroeder et al. / Inelastic light scattering in halide and oxide glasses

15.5 MHz. This agrees with Cotter's result for bulk silica glass [3] and table 2 also shows that the threshold power for BeF 2, ZBL and Z B L A glasses is on the order of tens of microwatts. Again Cotter's prediction are reconciled [3]. Recently, Shibata et al. [16] carried out direct Brillouin gain coefficients measurements on three different single mode fibers at 0.828 /~m. Their measurements show that the calculated Brillouin linewidth for the silica core fiber is 215 M H z at 0.828 #m; resulting 649 M H z at 0.488 /~m. This calculated value of AF B for silica core fiber is significantly different from our measurement on bulk silica glass. This discrepancy in the linewidth result may be due to broadening effects on the natural linewidth brought by an interaction in the total waveguide structure, namely, imperfections in the core-cladding interface [16,17]. Two possible mechanisms exist that could account for the attenuation of sound in glass. First, the anharmonic or three phonon interaction of B~Smmel and Dransfeld [18]; secondly, the structural relaxation mechanism of Anderson and BiSmmel [19]. The anharmonic model gives the damping rate F for longitudinal waves in the form

+

(18)

Here Y0 is the averaged dimensionless Grtineisen constant which measures the anharmonicity, T the temperature, 0 the density, w and v c the frequency and velocity of a sound wave, and c o and I- are the heat capacity and relaxation time, respectively, of a thermal phonon mode. The damping rate F is related to the Brillouin linewidth A~ and the acoustic attenuation constant a by F = avc = ~rAIB. The structural relaxation mechanism advanced by Anderson and BiSmmel to explain ultrasonic absorption is fused silica has the damping rate F given by:

F-

G~o(co/12) 1 + (w/f2) 2"

(19)

Here G is a temperature-independent constant representing the strength of the relaxation and f2 is the transition rate or frequency of a structural relaxation. (The particular structural transition postulated by Anderson and B/Smmel is a reordering of the S i - O - S i bond angle.) Here some of the

247

oxygen atoms can perform a transverse motion between bonding silicon atoms for which two potential minima exist (double potential well). The double potential well has a central barrier of activation energy E which can only be overcome by a thermally activated process, then the transition rate for jumping between minima is the product of the zero point vibrational frequency ~01 in one well and the Boltzmann probability of jumping the barrier: namely, ~2 = ¢01 e x p ( - E / k B T

).

(20)

Or if ~01 << kBT/h, then the Eyring form ~2= ( k B T ) / h e x p ( - E / k B T ) is applicable. In testing both models, Pine [9] finds that the anharmonic model appears to fit the data better (with fewer parameters), whereas the acoustic losses are not uniquely explained by a structural relaxation mechanism. Our result in fig. 1 shows that the local structure varies with different annealing temperature and time but we still have the same longitudinal acoustic phonon attenuation values within the limit of error [20]. This may suggest that the anharmonic model is more correct in explaining the observed longitudinal acoustic phonon damping behavior. The observed longitudinal acoustic phonon attenuation values in all of the glasses are much larger than these for a crystalline solid. In figs. 2 and 4 some type of correlation is observed to the attenuation values with the sound velocity squared (or the elastic constant cll divided by density). In fig. 4 we show the attenuation normalized with the frequency for each sample versus the velocity squared and again a linear behavior is seen within the bonds imposed by the error bars. The phonon attenuation seems to decrease with increasing sound velocity and each family of glasses shows a particular grouping. There is no obvious correlation of the phonon camping with lattice stiffness as obtained from the measured longitudinal elastic constants. A large change in the phonon attenuation, especially in the halide glasses, is seen while the density normalized longitudinal elastic constant changes at best by a factor of two. To understand this effect it may be necessary to invoke a strong resonance [22] and this tends to favor an anharmonic damping mechanism [9].

248

J. Schroeder et al. / Inelastic light scattering in halide and oxide glasses 0 tD

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42

(CM/SEC} Fig. 4. The phonon attenuation normalized with the frequency for each sample versus the velocity squared (the elastic constant Cll divided by density): ra, halide glasses; o, silicate glasses; v, glasses with lower percentage of B203, A, glasses with higher percentage of B203.

Temperature m a y not be sufficient a significant perturbation with which to study acoustic d a m p ing and its relation to structural relaxation. A m u c h stronger perturbation m a y be obtained by using pressure on glasses and perhaps this should be employed to study acoustic d a m p i n g [21]. The threshold power for Stimulated Brillouin Scattering has been calculated in halide and oxide glasses. Our results in fig. 3 show that the threshold power depends on the photoelastic properties of the medium. This linear correlation between threshold power and the photoelastic parameter indicates that SBS in halide and oxide glasses can be described by the dynamical theory.

6. Conclusion It has been shown that Rayleigh-Brillouin scattering measurements in fiber optic materials is a valuable technique with which to improve our

u n d e r s t a n d i n g of the non-linear optical effects that m a y occur in these materials if they are used for waveguide purposes. Some of the halide compositions show a higher power threshold for the onset of Stimulated Brillouin Scattering than the best silica-based glass, but the same glasses are not prime candidates for long range optical waveguide use since their loss characteristics as determined for Rayleigh scattering are not at a m i n i m u m value. Nevertheless, these materials are still i m p o r t a n t when crosstalk due to Stimulated Brillouin or Stimulated R a m a n scattering becomes a limiting factor. The p h o n o n attenuation values for halide glasses as determined from Brillouin linewidth measurements are of such a magnitude that the glass behaves m o r e with liquid-like lattice characteristics than characteristics representative of crystalline solids. The exact mechanism by which relatively high p h o n o n attenuation persists in a glass still require more study and perhaps low temperature experiments in the p u m p e d liquid helium range or high pressure experiments could offer new insights into these questions. This work was supported in part by National Science F o u n d a t i o n G r a n t No. DMR-85-10617 ( M R G ) , Air F o r c e C o n t r a c t R A D C / E S M F19628-86-K-0007 and two of us (G.K. and C.S.D.) wish to acknowledge the financial support f r o m the N a t i o n a l Science F o u n d a t i o n - Research Experience for U n d e r g r a d u a t e s (Materials Research) G r a n t No. DMR-87-12847.

References [1] J. Schroeder, Treatise on Material Science and Technology, Vol. 12, eds. M. Tomazawa and R.H. Doremus (Academic Press, New York, 1977) p. 151. [2] J. Schroeder et al., Mater. Sci. Forum 19/20 (1987) 653. [3] D. Cotter, J. Opt. Commun. 4 (1983) 10. [4] E.P. Ippen and R.H. Stolen, Appl. Phys. Lett. 21 (1972) 11. [5] L. Brillouin, Ann. Phys. (Paris 17 (1922) 88. [6] H.W. Leidecker and J.T. Lamacchia, J. Acoustic Soc. Am. 43 (1967) 737. [7] D. Walton, J.J. Vanderwall and H.C. Teh, Sol. St. Commun. 42 (1982) 737. [8] G.E. Durand and A.S. Pine, IEEE, J. Quant. Electron. 4 (1968) 523.

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[9] A.S. Pine, Phys. Rev. 185 (1969) 1187. [10] M.M. Broer and L.G. Cohen, J. Lightwave Technol. LT-4 (1986) 1509. [11] J. Schroeder et al., Electron. Lett. 23 (1987) 1128. [12] J. Schroeder, R.K. Mohr, C.J. Montrose and P.B. Macedo, J. Non-Cryst. Solids 13 (1973/1974) 313. [13] M.H. Cohen and G.S. Grest, Phys. Rev. B20 (1979) 1077. [14] M.H. Cohen and G.S. Grest, Phys. Rev. Lett. 45 (1980) 1271. [15] W.M. Macdonald, A.C. Anderson and J. Schroeder, Phys. Rev. B31 (1985) 1090. [16] N. Shihata, R.G. Waarts and R.P. Braun, Opt. Lett. 12 (1987) 269.

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[17] T.C. Rich and D.A. Pinnow, Appl. Opt. 13 (1974) 1376. [18] H.E. B/3mmel and K. Dransfeld, Phys. Rev. 117 (1960) 1245. [19] O.L. Anderson and H.E. B/3mmel, J. Am. Ceram. Soc. 38 (1955) 125. [20] J. Schroeder, C.J. Montrose and P.B. Macedo, J. Chem. Phys. 63 (1975) 2907. [21] J. Schroeder, Phys. Rev. B (1987) in press. [22] D. Heiman, D.S. Hamilton and R.W. Hellwarth, Phys. Rev. B19(12) (1979) 6583.