Temperature dependence of polariton dispersion in LiTaO3

Volume 4, n u m b e r 1

TEMPERATURE

OPTICS COMMUNICATIONS

DEPENDENCE

OF

T.S. CHANG, B C.JOHNSON,

POLARITON E. A M Z A L L A G * * ,

September 197I

DISPERSION

IN

LiTaO3*

R.H. PANTELL

Microwave Laboratory, Stanford, California 94305, USA and M. R O K N I a n d L. S. W A L L

DeparD~lent qt' Physics, Stanford, California .94305, USA Received 1 July 1971

T e m p e r a t u r e tunability of a polariton mode is r e p o r t e d for the f i r s t time. Using s p o n t a n e o u s , as well as s t i m u l a t e d n e a r - f o r w a r d R a m a n s c a t t e r i n g e x p e r i m e n t s , we have o b s e r v e d the shift of the polariton d i s p e r s i o n curve a s s o c i a t e d with the 200 c m - 1 f e r r o e l e c t r i c mode in LiTaO3 towards lower f r e q u e n c i e s , as t e m p e r a t u r e is r a i s e d f r o m r o o m t e m p e r a t u r e to 306oc. This behavior can be quantitatively explained through the c l a s s i c a l - o s c i l l a t o r d i s p e r s i o n t h e o r y .

The spontaneous Raman spectra of LiTaO 3 were obtained by Kaminov and Johnston [1,2]. The Al-symmetry 200 cm -I mode was shown to be a soft mode whose frequenqy goes to zero as the Curie temperature of 900°K is approached [2,3]. Spontaneous scattering from polaritons associated with this mode (infrared active) was also reported by Khashkhozhev et al. [4], the investigated polariton frequency range being 141 to 191 crn -I. It is the purpose of this letter to extend the frequency tuning range to lower frequencies and to investigate the temperature dependence of the polariton dispersion curve resulting from the variation of the soft mode frequency with temperature. We also wish to report on tunable stimulated polariton scattering in LiTaO 3. The crystals used in these experiments were grown by the Czochralski technique and were cut with faces perpendicular to the principal axes. The samples are typically 2.0 cm a-axis crystals with a cross section of 4 mm× 4 ram, and with uncoated ends polished flat and parallel within a few seconds of arc In the spontaneous near-forward Raman scattering experiments, the source was the 5145-A line of a Coherent Radiation Lab argon laser, operating at about 200 roW. A Jarrell-Ash double-grating Raman spectrometer was used * Work partly s u p p o r t e d by C o n t r a c t s NSF GT 24062 and U.S.O.N.R. NOCO14-67-A-0112-0039. ** On leave f r o m L a b o r a t o i r e de P h y s i q u e des Solides, Facult~ des Sciences, P a r i s , F r a n c e .

72

along with a dry-ice cooled RCA photomultiplier. As in ref. [5], the Stokes light emerging from the sample is directed by an adjustable mirror through a pin-hole, which defines a scattering angle, 0, inside the crystal. In the stimulated case, the source was a I MW QTswitched ruby laser, the experimental setup being similar to the one used in ref. [6]. In both experiments the incident laser beam was polarized along the c axis of the crystals. Fig. la shows the typical behavior of the spontaneous polariton lines at room temperature, for different values of the scattering angle, 0, inside the crystal. A tuning range from 62 to 193 cm -I was obtained as 0 was varied from 0.68 to 5.36 degrees. Fig. ib shows the continuous shift of the spontaneous polariton line for a constant angle 0 = 1.9 ° , when temperature is raised from 27 to 306oc. The dispersion characteristic (u- k diagram) can be deduced from the experimental data, using the wave vector conservation equation

(I) k2 = 4v 2 (uLn L - usns )2 + 8v 2 u L usnLns(I

-cos

0)

w h e r e UL, uS a r e t h e l a s e r a n d S t o k e s f r e q u e n c i e s in c m - 1 , a n d n L , n S a r e t h e c o r r e s p o n d i n g r e f r a c t i v e i n d i c e s . T h i s h a s b e e n d o n e on fig. 2, for four different temperatures, 27,100,200 and 3 0 6 o c , u s i n g t h e r e f r a c t i v e i n d e x d a t a of B o n d [7]. T h e v a r i a t i o n of n L a n d n S in t h e t e m p e r a t u r e r a n g e of t h i s w o r k a r e w i t h i n 1 9 of t h e i r v a l u e s a t r o o m t e m p e r a t u r e a n d a r e n e g l e c t e d [8]. No

Volume 4, number 1

OPTICS COMMUNICATIONS

September 1971

54

i:0.46. /

160

T= 270C 121

T=27°C

8 = 1.2 °

e= 1,9 =

T=IO0°C

0=1.5 °

~ID

~

200°c

0=2.3= . ~

T = 306°C

179 t

I

200

8=3.1o

[

150

~

I00

I

50

v(cm -I )

(0)

J

0

I

200

I

150

I

I00

1

50

I

0

z.' ( ¢ m - I )

(b)

Fig. 1. Typical p o l a r i t o n s p e c t r u m of LiTaO 3. The s m a l l e r peaks to the left of the p o l a r i t o n m o d e s r e l a t e to the b a c k w a r d s c a t t e r i n g s f r o m polished f a c e s of the c r y s t a l . (a) t e m p e r a t u r e is fixed at 2 7 o c , 0 v a r i e s f r o m 0.68 ° to 5,36o; (b) 0 i s fiKed at 1.9 ° , t e m p e r a t u r e v a r i e s f r o m 27°C to 306°C.

e x p e r i m e n t s w e r e a t t e m p t e d at h i g h e r t e m p e r a t u r e b e c a u s e of the b r o a d e n i n g of the p o l a r i to n line and the d e c r e a s e of its intensity.

Using the c l a s s i c a l o s c i l l a t o r model for the d i e l e c t r i c r e s p o n s e , the d i s p e r s i o n r e l a t i o n can be written as: 73

Volume 4, number 1

OPTICS COMMUNICATIONS

f 27 °C / / lO0 °C

200

0.2.7"

-

./

/

180

160 I40

'

,oo

, . ~ " 200 °C

°

8o, ,~-~//'// I 60 ,f/; i r

I

~/%,-~ ,./ u

"¢"~

20

0

'

STIMULATED Ji('l~l""~ ~ ' ~ - - - ~~. DATA? -/'~r~ ~ ' ~

KL ,

4000

I

8000

I

I0,000 k(cm -I)

,

T('C) .;9~(cm-') SF ~ 2oo 30.0

i

200 306

',

_

175 160 I

16.000

,

r

59.2 46.9 I

,

I

.....

20,000 24,000

J

Fig. 2. Experimental and calculated d i s p e r s i o n curves of polaritions in L~TaO 3 at different t e m p e r a t u r e s . O , I , x and&: experimental data at 27°C, 100oc, 200oc and 306oc, r e s p e c t i v e l y . V: room t e m p e r a t u r e data of Khashkhozhev [4]. Data from stimulated experiment are marked. The calculated curves and numerical values of ~F and SF are explained in the text.

)

(2)

where the subscript F denotes the "ferroelectric" mode, is the strength of the j mode located at frequency uj, and ~ is the frequency independent contribution to the dielectric constant due to high frequency electronic resonances. The lossless model considered here was found to be appropriate to fit the experimental data, as pointed out by Benson and Mills [9] for most materials. The temperature dependent contribution to the dispersion has been assumed to come from the 200 cm-I ferroelectric mode. Scott et al. [10], deduced from the generalized Lyddane-SachsTeller [ i i ] relation that one can write

Sj

SF(T) u2(T) ~ const = G •

(3)

T h e r o o m t e m p e r a t u r e v a l u e s of eoo, S j w e r e o b t a i n e d f r o m t h e i n f r a r e d r e f l e c t i v i t y d a t a of B a r k e r et al. [2] a n d t h e v a l u e s of uj f r o m r e f . [1]. T h e v a l u e of G f o r L i T a O 3 i s f o u n d to b e 1.2× 106 c m -2 (SF = 30, v F = 200 c m -1 at 27°C). By i n s e r t i n g t h e s e n u m b e r s i n t o eq. (2) a n d u s i n g t h e t e m p e r a t u r e d e p e n d e n c e of u F g i v e n in r e f . [2] w e h a v e p l o t t e d the t h e o r e t i c a l c u r v e s of fig. 2 ( s o l i d l i n e s ) , w h i c h a r e s e e n to b e in g o o d a g r e e m e n t with the e x p e r i m e n t a l data. This a g r e e m e n t t e n d s to j u s t i f y t h e two a s s u m p t i o n s m a d e :

74

September 1971

(1) t h e t e m p e r a t u r e d e p e n d e n c e of t h e p o l a r i t o n d i s p e r s i o n c o m e s mainly f r o m the soft mode, (2) the m a i n c o n t r i b u t i o n to t h e de d i e l e c t r i c constant comes also from that mode, as assumpt i o n w h i c h w a s m a d e to o b t a i n eq. (3)[10]. The e x p e r i m e n t a l data for the s t i m u l a t e d s c a t t e r i n g a r e a l s o s h o w n on fig. 2. At r o o m t e m p e r a t u r e , a n g l e t u n a b l e s h i f t s of 60 to 112 c m w e r e o b s e r v e d . T h e d a t a a r e in a g r e e m e n t with t h o s e o b t a i n e d in t h e s p o n t a n e o u s c a s e . M a x i m u m c o n v e r s i o n f r o m t h e p u m p to t h e S t o k e s w a s l o c a t e d a r o u n d 0 = 0.68o, w h e r e t h e i d l e r f r e q u e n c y i s a b o u t 65 c m -1. T e m p e r a t u r e t u n a b i l i t y , a s w a s o b s e r v e d a l s o in t h e s t i m u l a t e d c a s e , p r o v i d e s a way of o b t a i n i n g t u n a b l e , c o h e r e n t r a d i a t i o n at b o t h the S t o k e s and p o l a r i t o n f r e quencies In the s p o n t a n e o u s e x p e r i m e n t s , t h e p o l a r i t o n l i n e b r o a d e n s and i t s i n t e n s i t y d e c r e a s e s a s s c a t t e r i n g angle or t e m p e r a t u r e is i n c r e a s e d . F u r t h e r s t u d i e s of t h e s e e f f e c t s a r e now in p r o g r e s s , which will p r o v i d e i n f o r m a t i o n r e g a r d i n g t h e r e l a t i v e i m p o r t a n c e of e l e c t r o n i c and i o n i c c o n t r i b u t i o n s to t h e p o l a r i t o n s c a t t e r i n g p r o c e s s [9].

We are grateful to Professor D. L. Mills for helpful discussions.

REFERENCES [1] i . P . K a m i n o w a n d W . D . J o h n s t o n J r . , Phys. Rev. 160 (1967) 519. [2] W . D . J o h n s t o n J r . and I . P . K a m i n o w , Phys. Rev. 168 (1968) 1045. [3] H. I. Levinstein, A.A. Ballman and C.D. Capio, J . A p p l . Phys. 37 (1966) 4585. [4] Z.M.Khashkhozhev, V.V. Lemanov and R. V. P i s a r e v , Soviet Phys.-Solid State 12 (1970) 941. [5] H . E . P u t h o f f , R . H . P a n t e l l , B.G.Huth and M.A. Chacon, J . A p p l . Phys. 39 (1968) 2144. [6] J . M . Y a r b o r o u g h , S.S. Sussman, H . E . P u t h o f f , R.H. Pantell and B.C. Johnson, Appl. Phys. L e t t e r s 15 (1969) 102. [7] W . L . B o n d , J . A p p l . Phys.36 (1965) 1674. [8] H.Iwasaki, T.Yamada, N.Niizeki, H.Toyoda and H.Kubora, Japan. J. Appl. Phys. 7 (1968) 185. [9] H . J . B e n s o n and D . L . M i l l s , Phys. Rev. B1 (1970) 4835. [10] J . F . S c o t t , P . A . F l e u r y a n d J . M . W o r l o c k , Phys. Rev. 177 (1969) 1288. [11] W.Cochran a n d R . A . C o w l e y , J . P h y s . Chem. Sol. 23 (1962) 447. [12] A. S. Barker J r . , A . A . B a l l m a n and J . A . D i t z e n b e r g e r , Phys. Rev. B2 (1970) 4233.