HAL Id: jpa-00223202
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Submitted on 1 Jan 1983
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PHOTOACOUSTIC STUDY OF GUIDED MODES IN LiF THIN FILMS
J.-P. Goudonnet, E. Arakawa
To cite this version:
J.-P. Goudonnet, E. Arakawa. PHOTOACOUSTIC STUDY OF GUIDED MODES IN LiF THIN FILMS. Journal de Physique Colloques, 1983, 44 (C6), pp.C6-275-C6-280. �10.1051/jphyscol:1983643�.
�jpa-00223202�
JOURNAL DE PHYSIQUE
Colloque C6, supplCment au nO1O, Tome 44, octobre 1983 page C6- 2 7 5
PHOTOACOUSTIC
STUDYOF GUIDED MODES IN LiF THIN FILMS
J.P. Goudonnet a n d E.T. Arakawar
Laboratoire de PhotocSZectrici
L6,FucuZ
te!des Sciences Wirande,
E . P. 1 3 8 ,21004
Dijon Cedex, France
'XeaZth and SaIety Division, Oak Ridge IiationaZ Laboratory, Oak Ridge Tennessee
37850, U.S.A.Resume
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Des modes l u m i n c u x s o n t e x c i t e s d a n s d e s f i l m s d e L i F . D e s m e s u r e s p h o t o a c o u s t i q u e s p e r m e t t e n t d e d e t e r m i n e r l ' i n d i c e d e r & f r a c t i o n , l ' a n i s o - t r o p i e o p t i q u e , l ' e p a i s s e u r e t l a r u g o s i t e d e s f i l m s .A b s t r a c t - L i g h t modes a r e e x c i t e d i n L i F f i l m s . P h o t o a c o u s t i c m e a s u r e m e n t s a l l o w t o d e t e r m i n e r e f r a c t i v e i n d e x , o p t i c a l a n i s o t r o p y , t h i c k n e s s a n d r o u g h n e s s o f t h e f i l m s .
I - INTRODUCTION
I n v a r i o u s e x p e r i m e n t s o n i n t e g r a t e d o p t i c s , d i e l e c t r i c f i l m s a r e u s e d a s p l a n a r l i g h t g u i d e s /1,2/. The main p a r a m e t e r s d a r a c t e r i z i n g s u c h f i l m s a r e t h e o p t i c a l c o n s t a n t N = n - j k , t h e t h i c k n e s s d a n d t h e r o u g h n e s s c o e f f i c i e n t s . The a t t e n u a t e d t o t a l r e f l t x i o n (ATR) method h a s b e e n shown t o b e a u s e f u l t e c h n i q u e i n s t u d y i n g t h e p r o p a g a t i o n o f t i e o p t i c a l modes i n t h e s e f i l m s a n d s e v e r a l a r t i c l e s / 3 , 4 / h a v c d e s c r i b e d t h e t h e o r e t i c a l a n d e x p e r i m e n t a l a s p e c t s o f t h e method. More s p e c i f i c a l l y H o r n a u e r a n d R a e t h e r (H.R.) /5/ h a v e r e p o r t e d r e s u l t s on l i g h t modes e x c i t e d i n a s y s t e m o f q u a r t z / ~ g / ~ i F / a i r l a y e r s , a n d d e r i v e d t h e r o u g h n e s s p a r a m e t e r s
6
a n d o o f t h e L i F f i l m f r o m t h e r e l a t i o n w h i c h d e s c r i b e s t h e a n g u l a r d i s t r i b u t i o n o f t h e d i p o l e s r a d i a t i o n f r o m t h e a i r s i d e o f t h e f i l m . Comparing them t o t h e c o r r e s p o n d i n g e x p e r i m e n t a l m e a s u r e m e n t s t h e y h a v e showed t h a t t h e method was r e s t r i c t e d t o r e l a t i v e l y t h i n L i F f i l m s f o r w h i c h6
i s o n o r d e r o f 40-50A .
I n t h e p r e s e n t s t u d y we h a v e employed t h e p k o t o a c o u s t i c t e c h n i q u e r e c e n t l y d e s c r i b e d b y I r i a g a k i a n d Arakawa / 6 , 7 / , t o d e t e r m i n e t h e same p a r a m e t e r s on i d e n t i c a l
s t r u c t u r e s w i t h t h e i n t e n t i o n o f c o m p a r i n g t h e m e t h o d s . I n c o n t r a s t t o t h e c l a s s i c a l o p t i c a l method t h e p h o t o a c o u s t i c t e c h n i q u e a l l o w s t o m e a s u r e t h e t o t a l l i g h t
s c a t t e r e d f r o m t h e s y s t e m by u s i n g a c o m b i n a t i o n o f p h o t o a c o u s t i c a n d o p t i c a l m e a s u r e m e n t s a n d c a n b e e x t e n d e d t o r o u g h e r s y s t e m s .
I1 - EXPERIMENTAL TECHNIQUES
We i n v e s t i g a t e d a l a y e r s y s t e m a s is shown i n F i g . 1.
A 350 t h i c k s i l v e r f i l m a n d a 13500 A t h i c k L i F f i l m w e r e d e p o s i t e d on t h e h y p o t e n u s e s u r f a c e o f a n ATR p h o t o n - p l a s m o n c o u p l e r e q u i p p e d w i t h a p h o t o a c o u s t i c c e l l a n d mounted i n a r e f l e c t o m e t e r .
The b a s i c d e s i g n of o u r a c o u s t i c c e l l was t h e same a s o n e d e s c r i b e d i n R e f . / 6 / . The t i n y e l e c t r e t m i c r o p h o n e was p l a c e d a i r t i g h t l y on t h e p r i s m s u r f a c e a t t a c h e d t o t h e c e l l w i t h vacuum g r e a s e .
The i n c i d e n t l a s e r beam was p l a n e p o l a r i z e d a n d c h o p p e d a t 300 Hz b y a m e c h a n i c a l l i g h t c h o p p e r . The t h i c k n e s s o f t h e a i r f i l l e d c a v i t y formed was lmm a n d was s u f f i c i e n t l y l a r g e r t h a n t h e t h e r m a l d i f f u s i o n l e n g t h o f a i r a t t h e c h o p p i n g f r e q u e n c y o f t h e i n c i d e n t l i g h t t h a t t h e b a s i c t h e o r y f o r p h o t o a c o u s t i c - s i g n a l
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1983643
JOURNAL
DE
PHYSIQUEi n s o l i d s due t o Rosencwaig a n d Gcrsho / 8 / were a p p l i c a b l e t o t h e d a t a t a k e n w i t h t h e s e c e l l s . Checks were made on t h e c e l l t o e n s u r e t h a t t h e s i g n a l was p r o p o r - t i o n a l t o t h e i n c i d e n t power and i n d e p e n d e n t o f t h e p o s i t i o n where t h e l i g h t beam h i t t h e s y s t e m .
Glass cuum Grease
Prism
Gloss
Window
F i g . 1 : Schematic c r o s s - view o f t h e ATR equipped w i t h a a c o u s t i c c e l l .
- s e c t i o n a l c o u p l e r photo-
Microphone
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I11 - DETERMINATION OF THE OPTICAL PARAMETERS
The incoming l i g h t beam e x c i t e s - v i a t h e t h i n f i l m o f s i l v e r - g u i d e d modes i n t h e LiF f i l m and a s u r f a c e plasmon mode a t t h e metal-LiF i n t e r f a c e / 3 / . A s c a n o f r e f l e c t a n c e v s a n g l e o f i n c i d e n c e f o r p and s p o l a r i s a t i o n s showed t h e w e l l known s t r o n g d i p s /5/ a t a n g l e s above t h e c r i t i c a l a n g l e . F o r p p o l a r i z e d l i g h t , t h e s u r f a c e plasmon mode showed b r o a d e n i n g r e s u l t i n g mainly from t h e e n e r g y a b s o r p t i o n a s s o c i a t e d w i t h t h e non z e r o v a l u e o f t h e e x t i n c t i o n c o e f f i c i e n t o f t h e m e t a l .
S i m u l t a n e o u s l y w i t h t h e o p t i c a l measurements, t h e p h o t o a c o u s t i c s i g n a l was
measured a s a f u n c t i o n o f t h e a n g l e o f i n c i d e n c e , and c o r r e c t e d f o r t h e r e f l e c t i o n l o s s o f t h e i n c i d e n t l i g h t i n t e n s i t y a t t h e p r i s m e z t r a n c e s u r f a c e . The r e s u l t s o b t a i n e d w i t h p and s p o l a r i z e d l i g h t f o r = 5145 A a r e p r e s e n t e d i n F i g . 2 . S t r o n g l y enhanced p h o t o a c o u s t i c s i g n a l s were o b s e r v e d a t t h e a n g l e s 0 f o r which t h e g u i d e d mode d i p s i n R and R o c c u r e d .
P
An o p t i c a l l ~ g h t mode w i t h t h e wave-vector ko i s e x c i t e d i f t h e p h a s e matching c o n d i t i o n
i s f u l l f i l l e d .
.
n is t h e i n d e x of r e f r a c t i o n o f t h e g l a s s p r i s a . g. eo
i s d e r i v e d from t h e d i s p e r s i o n r e l a t i o n o f a g u i d e d mode g i v e n i n Ref. / 5 / . The g u i d e d mode r e s o n a n c e s i n t h e LiF f i l m c a n t h u s b e s t u d i e d e i t h e r u s i n g t h e s h a r p d i p s i n r e f l e c t a n c e o r u s i n g t h e s t r o n g enhanced p h o t o a c o u s t i c s i g n a l s whicho c c u r a t t h e same a n g l e o f i n c i d e n c e . The p h o t o a c o u s t i c t e c h n i q u e r e q u i r e s a r e l a t i v e l y more s i m p l e e x p e r i m e n t a l e q u i p m e n t .
p modes
smodes
F i g . 2 : P h o t o a c o u s t i c s i g n a l a s a f u n c t i o n o f t h e a n g l e o f i n c i d e n c e . The p h o t o a c o u s t i c s i g n a l v s a n g l e o f i n c i d e n c e s c a n s o b t a i n e d o n t h e s y s t e m o f f i l m s w e r e a n a l y z e d b y a method u s e d p r e v i o u s l y by (H.R), w h i c h a l l o w s f o r the p o s s i b i l i t y o f the LiF b e i n g o p t i c a l l y a n i s o t r o p i c . A l e a s t s q u a r e s f i t t i n g p r o c e d u r e was u s e d t o f i t s i m u l t a n e o u s l y t h e a n g u l a r p o s i t i o n o f a l l t h e o b s e r v e d p a n d s g u i d e d r e s o n a n c e s , f o r a g i v e n f i l m a n d w a v e l e n g t h , t o t h e o r e t i c a l
e x p r e s s i o n s t o y i e l d t h e f i l m t h i c k n e s s d a n d n , a n d n,, t h e r e f r a c t i v e i n d i c e s f o r l i g h t p o l a r i z e d p e r p e n d i c u l a r a n d p a r a l l e l r e s p e c t i v e l y , t o t h e p l a n e o f i n c i d e n c e . The t h e o r e t i c a l e x p r c s s i o n s are d e r i v e d f r o m t h e g e n e r a l F r e s n e l e q u a t i o n o f a s y s t e m o f N f i l m s d e p o s i t e d on a g l a s s s u b s t r a t e .
F o r = 5145 A.we o a t a i n e d
n,, = 1.3201 k,, = 0 . 0 0 1 d = 13500 A
n, = 1 . 3 1 8 0 k L = 0.001 d = 13497 A w i c h show t h e w e l l known s m a l l a n i s o t r o p y / 5 / .
F o r c o m p a r i s o n w i t h t h e v a l u e s o f r e f r a c t i v e i n d e x t h a t we r e p o r t h e r e , ( ~ . ~ ) / g / g a v e nL = 1.3086 n,, = 1 . 3 1 75 d = 30930 A
0
n l = 1 . 3 0 9 0 n , , = 1 . 3 1 6 0 d = 3 1 4 3 0 ~
JOURNAL DE PHYSIQUE
I V
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DETERMINATION OF THE ROUGIINESS PARAYETERSI f fjO, t h e a n g l e o f i n c i d e n c e , i s f i x e d a t t h e a n g l e which c o r r e s p o n d s t o t h e e x c i t a t i o n o f a l i g h t mode, t h e s c a t t e r e d l i a h t i n t e n s i t y i s maximum. One o r more
( d e p e n d i n g on t h e L i F f l l m t h i c k n e s s ) b r i g h t l i n e s c a n b e o b s e r v e d on t h e s c r e e n s A a n d B ( F i g . I ) , w h i c h c o r r e s p o n d t o t h e p a r t o f t h e l i g h t o f t h e main mode w h i c h i s s c a t t e r e d i n t o o t h e r n o d e s a n d which c a n p r o p a g a t e i n t h e f i l m / l o / . The s c a t t e r e d l i g h t c a n b e s t u d i e d b y u s i n g a p h o t o a c o u s t i c method a shown i n R e f . / 7 / . I n R e f . / 7 / I n a g a k i a n d Arakawa h a v e e m p l o y e d a p h o t o a c o u s t i c t e c h n i q u e t o o b s e r v e non r a d i a t i v e r e l a x a t i o n o f s u r f a c e p l a s m o n s i n t h i n s i l v e r f i l m s a n d d e t e r m i n e d t h e p r o b a b i l i t y o f r o u g h n e s s a i d e d r a d i a t i v e r e l a x a t i o n . They h a v e d e m o n s t r a t e d t h a t t h e p h o t o a c o u s t i c s i g n a l g e n e r a t e d from a n ATR s y s t e m i n t h e Kretschmann g e o m e t r y g i v e s d i r e c t i n f o r m a t i o n on p l a s m o n s w h i c h u n d e r g o no? r a d i a t i v e r e l a - x a t i o n , w h i l e t h e t o t a l number o f s u r f a c e p l a s m o n s w h i c h a r e e x c i t e d i n t h e m e t a l f i l m is known from t h e t o t a l p h o t o n e n e r g y a b s o r b e d . T h e r e f o r e , t h e t o t a l l i g h t s c a t t e r i n g may b e d e t e r m i n e d from t t i e d i f f e r e n c e o f t h e p h o t o a c o u s t i c s i g n a l from t h e o p t i c a l a b s o r p t a n c e i f t h e f o r m e r i s p r o p e r l y n o r m a l i z e d t o t h e l a t t e r u s i n g t h e r e s p o n s e c o n s t a n t o f t h e p h o t o a c o u s t i c c e l l .
The p u r p o s e o f p r e s e n t s t u d y i s t o comparc t h e r o u g h n e s s p a r a m e t e r s o b t a i n e d f r o m ttie t o t a l l i g h t s c a t t e r l r g w i t h t h o s e o b t a i n e d from t h e c l a s s i c a l o p t i c a l method d e s c r i b e d b y (H.R) / 5 / .
T h u s , we h a v e a p p l i e d t h e ~ n a g a k i ' s method t o t h e s y s t e m p r i s m / ~ g / L i F / a i r s y s t e m a n d d e t e r m i n e d t h e t o t a l l i g h t s c a t t e r i n g a t t h e l i g h t modes r e s o n a n c e a n g l e s . T h e e x p e r i m e n t a l r e s u l t s w e r e a n a l y z e d by u s i n g K r o g e r a n d K r e t s c h m a n n ' s f i r s t o r d e r l i g h t s c a t t e r i n g t h e o r y f o r a r o u g h f i l m / 1 1 / . K r o g e r and Kretschmann assume t h a t t o a f i r s t a p p r o x i m a t i o n t h e r o u g h s u r f a c e c a n b e r e p l a c e d b y a smooth o n e a n d by a n a d d i t i o n a l l a y e r o f d i p o l e c u r r e n t s whose a m p l i t u d e i s p r o p o r t i o n a l t o t h e h e i g h t o f t h e r o u g h n e s s .
For t h e s c a t t e r e d power d I p e r s o l i d a n q l c e l e m e n t d l a n d p e r i n c i d e n t power I t h e s u r f a c e s c a t t e r i n g t h e o r y y i e l d s .
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k a n d k a r e t h e c o m p o n e n t s o f t h e k v e c t o r s o f t h e i n c i d e n t a n d t h e s c a t t e r e d l i g h t a l o g g t h e s u r f a c e ..
( t s ( O o )1'
i s t h e t r a n s m i s s i o n c o e f f i c i e n t f o r s p o l a r i z a t i o n .I f we assume t h a t t h e s u r f a c e r o u g h n e s s i s g a u s s i a n c o r r e l a t e d / 1 2 / , t h e n t h e s u r f a c e r o u g n n e s s s p e c t r u m is g i v e n by
w h e r e 3. i s t h e c o r r e l a t i o n l e n g t h a n d
6
t h e r o o t mean s q u a r e r o u g h n e s s .F o r S p o l a r i z a t i o n t h e s c a t t e r e d i n t e n s i t y was c a l c u l a t e d f r o m e q u a t i o n ( 1 ) a n d i n t e g r a t e d o v e r a l l p o l a r i z a t i o n a z i m u t h s a n d t h e n i n t e g r a t e d o v e r t h e e n t i r e hemisphere. T h e i n t e g r a t e d scattering i n t e n s i t y i n t o t h e p r i s m s i d e was c a l c u l a t e d u s i n g t h e m o d i f i e d K r o g e r - K r e t s c h m a n n ' s e x p r e s s i o n g i v e n b y H . J . Simon a n d
J . K . Guha /13/. The t o t a l l i g h t s c a t t e r i n g i s o b t a i n e d b y summing up t h e s e s c a t t e r i n g i n t e n s i t i e s .
W e cornpare i n F i g . 3 t h e a b s o r p t a n c e A = 1
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R - T a n d t h e n o r m a l i z e d P A s i g n a l o f o u r s y s t e m f o r t h r e e r e s o n a n c e a n g l e s a n d s p o l a r i z a t i o n . The n o r m a l i z a t i o nc o n s t a n t was f o u n d by n o r m a l i z i n g t h e PAS a n d the a b s o r p t a n c e f o r i n c i d e n c e a n g l e s d i f f e r e n t f r o m l i g h t modes r e s o n a n c e a n g l e s a f t e r c o r r e c t i o n s f o r r e f l e c t i o n l o s s e s i n t h e c e l l wlndow. Ne h a v e i g n o r e d t h e e f f e c t s o f t h e s u r f a c e r o u g h n e s s i n o u r i n t e r p r e t a t i o n o f t h e p h o t o a c o u s t i c s i g n a l . W e w i l l s e e f u r t h e r t h a t t n e root-mean- s q u a r e r o u g h n e s s o f o u r f i l m s i s o n t h e o r d e r o f 5 0 # whlch 1 s s m a l l e r
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by a f a c t o r o f l o 5 - t h a n t h e t h e r m a l diffusion l e n g t h s i n t h e s y s t e m .I
angle of ~nc~denceI
F i g . 3 : Comparison b e t w e e n t h e p h o t o a c o u s t i c - s i g n a l a m p l i t u d e a n d t h e a b s o r p t a n c e f o r s p o l a r i z e d p h o t o n s a s f u n c t i o n of the a n g l e o f i n c i d e n c e .
V a l u e s o f t h e r o u g h n e s s p a r a m e t e r s 6 a n d CJ wich g a v e t h e b e s t simultaneous f i t o f t h e c a l c u l a t e d r e s u l t s t o t h e p r e s e n t e x p e r i m e n t a l r e s u l t s f o r t h e t h r e e modes w e r e f o u n d t o b e
6
= 5 0 a n d 0 = 5 2 0 w i t h a n e r r o r o f 10%.V - CONCLUSION
Many a t t e m p t s h a v e b e e n made t o o b t a i n q u a n t i t a t i v e i n f o r m a t i o n c o n c e r n i n g s u r f a c e r o u g h n e s s b y o b s e r v i n g t h e a n g u l a r distribution o f s c a t t e r e d l l g h t from w h i c h v a l u e s o f t h e r o u g h n e s s p a r a m e t e r s a r e e x t r a c t e d by a s s u m i n g a p a r t i c u l a r f o r m o f t h e r o u g h n e s s s p e c t r u m . (H.R) /7/ h a v e o b t a i n e d r o u g h n e s s p a r a m e t e r s
6
a n 0 o n t h e o r d e r o f 5 08
a n d 5 0 0 f( r e s p e c t i v e l y .From t h e p r e s e n t method w i c h m e a s u r e s t h e t o t a l l i g h t s c a t t e r i n g we h a v e f o u n a t h e same c h a r a c t e r i c r o u g h n e s s p a r a m e t e r s . T h i s r e s u l t i s c o n s i s t e n t w i t h t h e p r e d i c t i o n s o f H.R. / 7 / who h a v e showed t h a t t h e i r method w a s r e s t r i c t e d t o g u i d e d modes e x c i t e d u n d e r r o u g h n e s s c o n d i t i o n s o f
6
= 4 0 , 5 0 f o r w h i c h t h e c o n t r i b u t i o n o f s c a t t e r e d i n t e n s i t y w i t h a p o l a r i z a t i o n d i f f e r e n t from t h e i n c o m i n g l i g h t d u e t o m u l t i p l e s c a t t e r i n g l e a d i n g t o a t r a n s f o r m a t i o n o f p i n t o s moaes c a n b e n e g l e c t e d .The p r e s e n t p h o t o a c o u s t i c method i s now u s e d i n o u r l a b o r a t o r y t o s t u d y g u i d e d modes e x c i t e d i n r o u g h e r L i F f i l m s - t h i c k e r o r d e p o s i t e d o n a r t i c i a l l y r o u g h e n e d s u b s t r a t e s - f o r w h i c h t h e conventional o p t i c a l t e c h n i q u e f a i l s .
JOURNAL DE PHYSIQUE
REFERENCES
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/ 2 / IIENSLER D . H . , CUTHBEKT J . D . , MARTIN R . J . , T I E N A.K., A p p l . O p t i c s
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( 1 9 7 1 ) 1 0 3 7/ 3 / o T T A A . , SOHLEH W., O p t i c s Comm.
2
( 1 9 7 1 ) 2 5 4 / 4 / POCKRAND I . , RAETHER N., O p t i c s Comm. 1 7 ( 1 9 7 6 ) 3 5 3 / 5 / HOHNAUER D.L., RAETHER N . , O p t i c s ~ o m m F 4 0 - ( 1 9 8 1 ) 1 0 5/6/ INAGAKI T . , KAGAMI K., ARAKAWA E . T . , P h y s . Rev.
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( 1 ~ 8 1 ) 3 6 4 4 /7/ INAGAKI T . , NAKAGAWA Y . , AHAKAWA E . T . , P n y s . R e v . B L ~ ( 1 9 8 2 ) 6 4 2 1/8/ HOSENCWAIG A . , P h o t o a c o u s t i - a n d P h o t o a c o u s t i c spectroscopy ( W i l e y , New Y o r k , 1 9 8 0 )
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;r
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T I E N P . K . , ULRICH R., MARTIN R . J . , A p p l . P h y s . L e c t e r s91
( 1 9 b 9 ) 2 9 1 / 1 1 / KRETSCHMANN E . , O p t i c s Comm.5
( 1 3 7 2 ) 3 3 1/ 1 2 / S e e f o r e x e m p l e W E T H E R H . S u r f a c e p l a s m a o s c i l l a t i o n s p . 2 4 Y i n P h y s i c s o f t h i n f i l m s V o 1 . 9 , A c a d . P r e s s . 1 9 7 7
/ 1 3 / SIMON H . J . , GUIIA J . K . , O p t i c s Comm.
