BIREFRINGENGE INDUCED BY SPATIAL DISPERSION IN ALKALI HALIDES

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BIREFRINGENGE INDUCED BY SPATIAL

DISPERSION IN ALKALI HALIDES

C. López, C. Zaldo, F. Meseguer

To cite this version:

JOURNAL

DE

PHYSIQUE

Colloque

C7,

supplément

au

nO1O, Tome 46, octobre

1985

page C7-475

BIREFRINGENCE INDUCED BY SPATIAL DISPERSION IN ALKALI HALIDES

C. Lopez, C. Zaldo and F. Meseguer

I n s t i t u t o de Fcsica de2 Estado SbZido (CSIC) and Departmento de ~ p t i c a y Estructura de Za Materia, Universidad Autonoma de Madrid, CantobZanco,

28049 Madmd, Spain

Résumé - L'anisotropie optique induite par la dispersion spatiale des cristaux de KI, Cs1 et KBr proche à leur bord d'absorption a été mesurée par des experiments de transmission optique. La biréfringence a une grande dispersion proche au bord d'absorption de ces matériaux. En ajustant les resultats avec un modèle mi rosc on obtient le paramètre de courbure anisotropique (warping) 7 2

-Ttqu:

Le paramètre de warping est beaucoup plus petit pour le KBr que pour les iodures.

Abstract

-

Optical anisotropy induced by spatial dispersion of KI, Cs1 and KBr single crystals near their absorption edge has been measured by means of optical transmision experiments. The birefringence has strong dispersion near the absorption edge of these materials. By fitting the results with a microscopical model one obtains the warping parameter

Y2

- ) 1 3 . The warping parameter is much more smaller in KBr than for iodides.

1 - INTRODUCTION

The dielectric constant

c

is normally written in terms of the frequency and wavevector q. However, as the light in the optical region has wavelengths much larger than the lattice parameter a, one argues that spatial dispersion effect (SDE) would be negligible. However, optical experiments involving reflection, transmision,Raman and Brillouin spectra indicate SDE 111. Experiments on birefringence induced by spatial dispersion (BISD) have been done in zinc-blende (ZB) type semiconductors 12-51 and explained in terms of the warping of the valence band / 2 / . Recently, BISD has been measured in KI 161. The results show SDE of the same order as that detected for ZB-type semiconductors.

In this paper, we present the results obtained for KI, Cs1 and KBr at room temperature near their absorption edge. The results are explained in terms of a microscopic model that enables us to obtain the warping parameter of the exciton band.

II

- THEORY

For wavelengths in optical region the wavevector q is about three orders of magnitude smaller than the size of the first Brillouin zone. Therefore we can develope the dielectric tensor

c

i.tCiXq) in function of q.

eijcw,q) = cij(-)

+

i)1 ijk qk $ a i j k l qk 41 (1)

where the third rank tensor

)liek. is zero for crystals with inversion symmetry.

For materials that belong to 23m, 432 and m3m ciassesQijkl is described by three independent constants a l l l l

,a

1122 andîilZl2. We w ~ l l consider several cases:

C7-476 JOURNAL

DE

PHYSIQUE a) For q 11 (001) €(O,q, =

€

ta))

+

q2

0

a , , 2 ,

0

O

O

a,,,,

O

1

No birefringence is detected between the transversal components of€(U,q). The same occurs for qll(ll1).

b) For q11 (110)

a a a

€tu,q) =

c

(d

+

(q2~2)

an,,

a ,

+a,,,

O

O

2

a,,,,

O

1

The birefringence between the transversal compocents of the dielectric tensor

Cll0

and

€ 001

is:

2

A € =

€

,Io

-

Cool

= 2 n A n =

(allll

-

2û!1212)(q /2) ( 4 ) The microscopical theorv developed by P. Yu and M. Cardona / 2 / explains the BISD in terms of the q-induced splitting of the valence band. As the absorption edge of alkali halides is dominated by excitons we have considered the dielectric constant as an harmonic oscillator at

r15

exciton. We have used the expression (3) of reference 6 for fitting Our experimental results. From that, we obtain the warping parameter

( y 2

-)1

3 ) that is also defined in reference 6.

III

-

EXPERIMENTAL PROCEDURE AND RESULTS

The samples used were rectangular prisms with (110), (liO),and (001) faces and with thickness about 1 cm. Prior to BISD measurements thermal annealing, in order to avoid light depolarization induced by residual strains, has been performed. As explained in reference 6 we have obtained the BISD by measuring different configurations.

Figure 1 shows the different configurations used. The light intensity recorded bv the photomultiplier can be written as:

where

9

is the angle between the polarizer and (110) axis. Il ( ) means parallel (crossed) polarizers.

b

is the phase shift of light between parallel and perpendicular polarization to the (110 Iaxis and 1 is the incident light intensity. For

IL

no BISD is detected and only residualObirefringence by strains (RBS) appears.' For

It5

and 1i5 both BISD and RBS are detected. Figure, 2 shows (circles) the result obtained for CsI.

Fig. 2

-

Intensity of light transmited by Cs1 (circles) and Cs1 with KC1 uniaxial strained induced compensator (USIC) (triangles) and Cs1 with LiF-USIC (squares) placed between crossed polarizers. The continuous line is a guide for the eye.

In order to measure the sign of the BISD we have compared the signal

1:-

obtained for the sample with that obtained for the sample plus a compensator in the W

region. We have used as compensator KC1 and LiF uniaxially strained along (100) direction 171. Squares and triangles in figure 2 show the results. From that we deduce that nliO

<

n for Cs1 and KI. For KBr no BISD has Seen detected and therefore no sign

'

0

9

'

BISD has been obtained. Figure 3 shows (n

-

- n ) for Cs1 in function of the light energy close to exciton frequency. TkhOresu!??i show strong dispersion near the absorption edge. Continuos line shows the fit done bv using formula (3) of reference 6. Table 1 displays the values obtained for

(

-

b)

and

D

(see reference 3). Together with the position of the lowest exclton and its oscillator strength C for KI, Cs1 and KBr at RT. For KBr BISD is soOsmall that it was not possible

fg

obtain reliable values of (

y

2-

Y

) ,

JOURNAL

DE

PHYSIQUE

Fig. 3 - BISD for Cs1 as a function photon energy. The solid line is fit with equation ( 3 ) of reference

TABLE 1

KBr 6 . 6 2 6 . 6

---

<o. 02

REFERENCES

/1/ Agranovich,. V.M. and Ginzburg, V.L. in Crystal optics with spatial dispersion and excitons, Springer Verlag, 1984.

/2/ Yu, P.Y. and Cardona, M., Solid State Commun. 9 ( 1 9 7 1 ) 1 4 2 1 ; and Computational Solid State Physics, Plenum Pub. Co., New York 1972.

/ 3 / Bettini,M. and Cardona,M., 11th Int. Conference on Physics of Semiconductors, Warsaw, Poland ( 1 9 7 2 ) .

/ 4 / Baillou, J . . Rev. Phys. Appl. 17 ( 1 9 8 2 ) 377.

/ 5 / Deiss, J.L., Daunois, A., Chouiyakh, A. and Gogolin, O., Solid State Commun. 53 ( 1 9 8 5 ) 7 9 .

/ 6 / Meseguer, F . , Cardona M. and Cintas A., Solid State Commun. 50 ( 1 9 8 4 ) 371.