ANISOTROPIC REFRACTIVE INDICES OF CADMIUM SULFIDE THIN FILM ON A SLAB-TYPE OPTICAL WAVEGUIDE

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ANISOTROPIC REFRACTIVE INDICES OF

CADMIUM SULFIDE THIN FILM ON A SLAB-TYPE OPTICAL WAVEGUIDE

K. Sasaki, T. Shimizu, O. Nonaka, O. Hamano, M. Serizawa

To cite this version:

K. Sasaki, T. Shimizu, O. Nonaka, O. Hamano, M. Serizawa. ANISOTROPIC REFRACTIVE IN-

DICES OF CADMIUM SULFIDE THIN FILM ON A SLAB-TYPE OPTICAL WAVEGUIDE. Jour-

nal de Physique Colloques, 1983, 44 (C10), pp.C10-127-C10-130. �10.1051/jphyscol:19831027�. �jpa-

00223484�

ANISOTROPIC REFRACTIVE INDICES OF CADMIUM SULFIDE THIN FILM ON A SLAB-TYPE OPTICAL WAVEGUIDE

K. Sasaki, T. Shimizu, 0. Nonaka, 0. Hamano and M. Serizawa

Faculty of Science and Technology, Keio University, 3-14-1, Hiyoshi, Yokohama 22S, Japan

Résumé - Les indices de réfraction anisotropes de couches minces de sulfure de cadmium déposées par évaporation sous vide sur des guides d'onde optiques, ont été déterminés par l'analyse croisée des ondes TE et TM.

Abstract - Anisotropic refractive indices of vacuum evaporated cadmium sulfide thin films on slab-type optical waveguides were determined by an incorporated analysis of the TE and the TM waves.

1. Introduction

There have been many methods to determine optical constants of thin solid films, Ellipsometry/1/, Abeles'' method/2/ and Male*s method/3/

are famous because of their availabilities. In ellipsometry, degrees of freedom in polarization are skillfully joined to determining opti- cal constants of isotropic films. Majority of other methods are also concerned with optically isotropic films.

In the present study a new method to determine anisotropic refra- ctive indices of vacuum evaporated cadmium sulfide thin films is pro- posed. This method is an extended application of the previously repo- rted guided wave method with tapered isotropic films on slab-type op- tical glass waveguides/4,5/. In the present method an anisotropic ca-r dmium sulfide thin film was used as an example. Vacuum evaporated ca- dmium sulfide thin film deposited on fused quartz substrate at appro- priate temperature has microcrystalline wurtzite structure with the c- axis of each microcrystal oriented perpendicular to the substrate.

Other two axes are ambiguous in each crystal and can be averaged over as isotropic in the plane. This situation is expressed by a dia- gonal dielectric tensor. Optical guided waves for each polarization mode (the TE and the TM) in a single propagation mode slab-type wave- guide have each inherent propagation constants corresponding to a specific waveguide thickness. Smooth guidings of those waves through a region covered with a cadmium sulfide top layer film are prevented, except for specific top layer thicknesses(resonant thicknesses).

These situations are analyzed theoretically by dispersion relations considered as equations for unknown refractive indices in both pola- rization modes with an unknown dielectric tensor of the cadmium sul- fide thin film. Incorporation of both dispersion relations can give rise to determining the anisotropic refractive indices by substituti- ons of experimentally given resonant thicknesses of both modes into the relations.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19831027

JOURNAL

DE

PHYSIQUE

2. Theory

T h e o r e t i c a l a n a l y s i s i s performed by a s l a b - t y p e s i n g l e p r o p a g a t i o n mode waveguide w i t h a h i q h i n d e x t o p l a y e r f i l m t o b e d e t e r m i n e d a s

shown i n F i g 1.

G

I

: n3:

^{I I} _I

d ^j lcds nd

^I

FGUIDF ni SUBSTRAT E no

n3=1.00 y L ⁼

ii2 means anisotropic refractive indices.

n, ~ 1 . 5 5 nod46

F i g l , A model waveguide u s e d i n t h e a n a l y s i s .

I t i s supposed t h a t a n i s o t r o p i c p r o p e r t y of t h e t o p l a y e r i s e x p r e - s s e d by a f o l l o w i n g d i e l e c t r i c t e n s o r ( 1 ) .

D i s p e r s i o n r e l a t i o n s of t h e r e g i o n I1 a r e g i v e n by t h e f o l l o w i n g two e q u a t i o n s ,

2 2 2 2 2 2 2 2

where

h o

⁼

-(keno) , A 1

= (kOnl)

- p E , n E 2

= ( k o n 2 0 )

- p E ,

2 2 2

h.

=

(3,-

( k 0 n 3 )

,

^k,, = 2 X / A

, /\

i s a wavelenqth o f g u i d e d wave and m i s p o s i t i v e i n t e g e r

.

TM:

A

m2d = t a n [ ( n 2 0 h 2 n:nM2) t a n ( tan-' (n:Ao/ n

,'. A )-A,W] I

+tan-' (n20 2

A

3 / n : ~ M 2 ) + m x ( 3 )

2 2 2 2 2 2 2

where

h

0 =

p M

'.

,

= ( k o n l )

2-g

^{M , j\ M 2 =} ( k 0 n 2 0 ) -(n20/n2e )

2 2 2

X ? M ,

:

= a n - ( k 0 n 3 )

,

nZo and n 2e c o r r e s p o n d t o o r d i n a r y and e x t r a o r d i n a r y r e s p e c t i v e l y . C a l c u l a t e d d i s p e r s i o n c u r v e s f o r each mode a r e shown i n F i g 2. I n t h e f i g u r e , v e r t i c a l s t r a i g h t l i n e s c o r r e s p o n d i n g t o t h e i n c i d e n t p r o p a g a t i o n c o n s t a n t s

B O E

^and

FoM

^{i n}

t h e r e g i o n s I and I11 i n t e r s e c t e v e r y d i s p e r s i o n curvE a t s p e c i f i c t o p l a y e r t h i c k n e s s e s ( r e s 0 n a n t t h i c k n e s s e s ) dlE, d 2 E , d 3 E , . . a n d dlM, d2M, d 3 M . . . f o r t h e r e s p e c t i v e modes. A t t h e s e r e s o n a n t t h i c k n e s s e s , f o r t h e TE mode Equ. ( 2 ) i s reduced and a n unknown i n d e x n20 f o r t h e

n E 2 d m M = m S t 8 nZ0 = (m/i /2dmM) + ( ~ ~ ~ / k( 4 ) ~ ) Then from Equ. ( 3 ) a t r e s o n a n t t h i c k n e s s e s f o r t h e Trl mode,dmM, a n o t h e r i n d e x f o r t h e e x t r a o r d i n a r y wave n2e c a n b e g i v e n a s :

nze= 2.29 n

I

=I. 55

F i g 3 . x - r a y d i f f r a c t i o n F i g 2 . C a l c u l a t e d d i s p e r s i o n p a t t e r n of vacuum

c u r v e s . s o l i d l i n e ; TE evapoated cadmium dashed l i n e ; TM s u l f i d e t h i n f i l m . 3 . Experiment

(A) Sample p r e p a r a t i o n

Tapered cadmium s u l f i d e t h i n f i l m

w 3 s

d e p o s i t e d on a s i n g l e propaga- t i o n mode s l a b - t y p e waveguide a t S Q C from an alumina c r u c i b l e w i t h a t u n g s t e n h e a t e r , a t l70A/min d e p o s i t i o n r a t e . Tapered s t r u c t u r e was r e a l i z e d by d i f f r a c t i o n of e v a p o r a t e d m o l e c u l a r beam w i t h a k n i f e edge. I t was found t h a t t h e f i l m had p o l y c r y s t a l l i n e w u r t z i t e s t r u c t u r e by x-ray a n a l y s i s a s d e p i c t e d i n F i g 3 .

( B ) Measurement o f r e s o n a n t t h i c k n e s s e s

Resonant t h i c k n e s s e s f o r each mode were measured By a n exwer2mental s e t u p i l l u s t r a t e d i n F i g 4 . Damned o s c i l l a t i o n s w i t h c o n t i n u o u s v a r i a t i o n of t h e t a p e r e d t o p l a y e r t h i c k n e s s were r e c o r d e d by t r a n s - l a t i o n a l movement o f t h e waveguide w i t h a synchronous g e a r motor.

T y p i c a l t r a c e s of o s c i l l a t i o n s a r e s k e t c h e d i n F i g 5 w?th a c r o s s - s e c t i o n of t h e t a p e r e d t o p l a y e r f i l m . Used wavelength of t h e quided wave was an Ar l a s e r 5145a.

4 . R e s u l t s and d i s c u s s ? o n

S u b s t i t u t i o n s of r e s o n a n t t h i c k n e s s e s d i n F i g 5 f o r t h e TE mode and t h e p r o p a q a t i o n c o n s t a n t P o E / k 0 = YM532 f o r t h e 1 s t mode i n t h e

JOURNAL DE PHYSIQUE

r e g i o n I i n t o Equ. ( 4 ) gave n20 = 2.66 f o r t h e o r d i n a r y wave. I n t h e same w a y , s u b s t i t u t i o n of e a c h p a r a m e t e r i n Equ. ( 5 ) by t h e p r o - p a g a t i o n c o n s t a n t P O M / k O = 1.530 f o r t h e TM mode i n F i g 5 g a v e r i s e t o d e t e r m i n i n g a n o t h e r unknown i n d e x f o r t h e e x t r a o r d i n a r y wave ( n z e

= 2 . 3 3 ) . We c a n h a r d l y f i n d p a p e r s on o p t i c a l c o n s t a n t s of a n i s o t r o - p i c cadmium s u l f i d e t h i n f i l m s though t h e r e a r e s e v e r a l r e p o r t s on b u l k s i n g l e c r y s t a l s / 6 , 7 , 8 / . Determined i n d i c e s i n t h e p r e s e n t s t u d y a r e s m a l l e r t h a n t h o s e o f b u l k c r y s t a 1 , a s known g e n e r a l l y f o r s o l i d m a t e r i a l s . For t h e b u l k c r y s t a 1 , i t was r e p o r t e d t h a t ne)no f o r w a v e l e n g t h l o n g e r t h a n t h e a b s o r p t i o n e d g e ( 5 2 0 0 A j and n ) n f o r s h o r -

o e

t e r w a v e l e n g t h /9/. A r l a s e r 5145# u s e d i n t h e p r e s e n t s t u d y i s l o c - a t e d n e a r t h e a b s o r p t i o n e d g e , b u t d e t a i l e d comparison o r d i s c u s s i o n i s n o t g i v e n h e r e . T h e problem w i l l b e c l a r i f i e d by measurement of d i s p e r s i o n and t e m n e r a t u r e dependence of t h e i n d i c e s . A b s o r p t i o n c o e f f i c i e n t of t h e f i l m r e s u l t i n g i n t h e damping o s c i l l a t i o n i n F i g 5 c o u l d b e d e t e r m i n e d by i n t r o d u c t i o n o f complex r e f r a c t i v e i n - d i c e s and complex p r o p a g a t i o n c o n s t a n t s though c u t t i n g down i n t h e p r e s e n t p a p e r .

P i g 4. E x p e r i m e n t a l s e t u p . 1 ; p o l a r i z e r , 2; s l a b - t y p e waveguide, 3; f u s e d q u a r t z s u b s t r a t e , 4 , 6 ; p r i s m , 5 ; t a p e r d t o p l a y e r CdS f i l m , 7 ; d e t e c t o r , 8 ; p e n - r e c o r d e r .

-

LATERAL

POSITION (mm)

F i g 5 . O s c i l l a t i o n t r a c e s and f i l m c r o s s s e c t i o n . Acknowledgment- A u t h o r s w i s h t o e x p r e s s t h e i r t h a n k s t o t h e s u p p o r t s

of Nippon ALEF Co. L t d .

R e f e r e n c e s . 1. MULLER R . H . , P r o c . Symp. Recent Development i n E l l i p s - o m e t r y , S u f . S c i . 1 6 (1969) 1 4 .

2. ABELES F . , C . R . A C ~ . S c i . , 228 (1948) 553.

3. MALE D . , J . Phys. Radium 11 ( 1 9 5 0 ) 332.

4 . SASAKI K . , KUDO Y . ,

FUKUDAA.,

AWATA H . and HAMANO O . , Appl. Opt.

21 (1982) 3552.

5 . =SAKI K . , KUDO Y . , WATANABE H . and HAMANO O . , Thin S o l i d ~ i l m s

9

(1982) 297.

6. GOTTESXAN J . and FERGUSON W. C . H . , J . Opt. S o c . Am. 44 (1954) 368.

7. GOBRECHT H . and BARTSCHAT A . , Z e i t s c h r i f t f u r p h s y i k - f 5 6 ( 1 9 5 9 ) 1 3 1 . 8 . VITRIKHOVSKII N . I . , GUDYMENKO L. F. and -IAZNICHENKO ,.FA. S o v i e t

P h y s i c s - S e m i c o n d u c t o r s 2 (1968) 732.

9 . LANGER D . W . , J . Appl. g h y s .

37

(1966) 3530.