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ON THE PROPAGATION OF s-POLARIZED SURFACE POLARITONS ON ROUGH SURFACES
W. Zierau, A. Maradudin, C. Falter
To cite this version:
W. Zierau, A. Maradudin, C. Falter. ON THE PROPAGATION OF s-POLARIZED SURFACE
POLARITONS ON ROUGH SURFACES. Journal de Physique Colloques, 1984, 45 (C5), pp.C5-225-
C5-228. �10.1051/jphyscol:1984532�. �jpa-00224150�
JOURNAL DE PHYSIQUE
Colloque C5, supplkment au n04, Tome 45, avril 1984 page C5-225
ON THE PROPAGATION OF s-POLARIZED SURFACE POLARITONS ON ROUGH SURFACES
W. Z i e r a u , A . A . ~ a r a d u d i n * and C . F a l t e r University of bfuenster, F.H. C.
* ~ n i v e r s i ty of CaZifornia, I r v i n e , U.S.A
.
Resum6 - 18a p o s s i b i l i t 6 d'une r e l a t i o n de d i s p e r s i o n pour, un p o l a r i t o n de s u r f a c e de p o l a r i s a t i o n s e s t 6 t u d i 6 e pour une s u r f a c e rugueuse. Afin de pou- v o i r L r a i t e r des r u g o s i t 6 s de s u r f a c e i m p o r t a n t e s , une modsle de rgseaux sinusoidaux a 6 t 6 c h o i s i pour l e s r u g o s i t g s . L'usage de l ' h y p o t h s s e de Rayleigh permct d ' o b t e n i r une e x p r e s s i o n s i c ~ i l a i r e au c a s de l a p o l a r i s a t i o n p . C e l l e - c i a 6 t 6 ktudi6e numgriquement dans le domaine n o n - r a d i a t i f , pour A 1 exemple type d'un rn6tal 2 6 l e c t r o n s presque l i b r e s , a i n s i que pour NaCl exemple type d'un c r i s t a l diatomique. Au vu de c e s r g s u l t a t s , nous devons c o n c l u r e que d e s p o l a r i t o n s de s u r f a c e de p o l a r i s a t i o n s ne pcuvenr pas s e propager, dans l e s l i m i t e s c o n s i d k r g e s , l e long d'un rEseau s i n u s o i d a l de r u g o s i t t s 2 l a s u r f a c e .
Abstra::t. - T h e p o s s i b i 1 i : y o f a r l i s p e l r s i o n r e l a t i o r 1 f o r a n s - p o - l a r i . z e d s u r . f a c c p o l a v i t c n a t a r o u g h s u r f a - c h a s b e e r , i n v e s t i - g a t e d . In o r d e r i,o b e a b l e t o t r e a t a l s o l a r g e v a l u e s o f Che : ; u r f a c e r o ~ g h r ~ c s s a s l n u s o i d a l g r a t i n g h a s b e e n c n o o s e r l a s a mode!. f'or t h e r o u g h s . l ? f ' a c c . [ ! s i n g Hay1 e i g h t s h y p o t h e s i s ari e x - a r e s s - i . o r i s i m i l a r t o t?!e p - p o l . a r i z e d c a s e i s d e r . i . v e d w h i c h h a s b e e n s t l i d i e d r l ~ m e r i c a l l y i n t h e n o r ) - r a d i a t i v e a r e a f'cr. 2 r l e a r l y Y r e e - e l e c t r o r ~ m e t a l , A l , a n d a d i a t o m i c c r y s t a l , PJaC1, r e p r e s e n - t a t i v e l y . Prom o u r S i n t l i r . g s wc n u s t c o r l c l urie \ h a t s - p o l e r i z e : i s u r f a c e p o ! a r i t o n s c a n n o t p r o c a g n t e a l o n g s r o u g h s u r f a c c r e p r e - s e n t e d b y E. s i . r l u s o i d a 1 f:r2atirlg w i t h i n t h e l i m i t s c o n s i d e r e d .
T h e p r o p a g a t i o n oi' s u ? f a c e p o l a r 2 i t o n s o n r o u g h s u r f a c e s h a s b e e p e x t e n - s i v e l y s t u d i e d d u r i n g t h e l a s t y e a r s (for a r e v j e w s e e / I 1'1. I t i s knowr. t h a t o n a f l a t s u r f a c e o n l y p - p c l a r i z e d s ~ i r f a c c p o l a r i t o n s c a n p r o p a g a t e . A p-polarized s u r r a c e p o l a r i t o r ; i s or!c whose e 1 e c t r . i c v e c - t o r i s i n t h e p l a n e d c f ' i n e d by t h e ciirec:i,ion o f p r o p z g a t i o r ~ ar!d t h e n o r m a l t,o t.he s u r l ' a c c , wiler,eas a n s - p c l a r i . z e d s u r f a c e p o : a r i t o n i s o n e w h o s e e l e c t r i c v e c t o r . i s p e v p c n d i . c u l a r t o t h i s pl.c?ne. I t fellows imme- d i a t e l y f r o m M a x w e l l ' s e q u a t i o n s t h a t s - p o l a r i z e d s u r f a c e p o l a r i t o n s c a n n o t p r o p a g a t e a l o r ? g a p l a r i a r s u r S a : : e .
I n c a s e o f a r o u g h s u r f a c e :he s o l i l t i o n o f ' t h e wave e q u a t i o n b e - c o m e s m o r e c o m p l e x s o t h a t a5 f i r s t s i g h t t h e p r o p a g a t i o n o f a n s - p o l a - r i z e t l s u r f a c e p o l . a r i t o r ~ n a y , ir. p r i n c i p l e , become p o s s i b l e . I t i s o u r a i m t o p r e s e n t i n t h i s p a p e r t h e r e s u l t s o r o u r i n v e s t i g a t i o r i o n t h e p o s s i b l e e x i s t e n c e o f s u c h s - p o l a r i z e d p o l a r i t o n s i n t h e r 1 3 n r B a d i a t i v e a r e a . We d i d r o t s t u d y i n f u r t h e r d e t a i l t h e c a s e o f a s o - c a l l c d l c a k y s u r f a c e p o l a n i t o n a s i t h a s b e e n d o n e e . g . f ' o r R a y l e i g h w a v e s i n /2/.
W i t h i n t h e s m a l l r o ~ ~ g h r , e s s I . l m i t f c r a s t a t i s t i c a l l y r>ol;gh s u r f ' a c e a n e x p r e s s i o n h a s a l r e a d y beer1 d e r i . v e d by i v l a r a d u d i : ~ /1/ w h o s e s o i u t i o n w o u l d p r e s e n t a d i s p e r s i o n r e l a t i o n f c r a n s - p o l a r i z e d s u r f a c e p o l a r i - L o n . T h i s s o l u t i o n h a s b e e n c a r r i e d o u t n u m e r i c a l l y . Xotvevcr, i t w a s n o t p o s s i b l e t o o b t a i n c o ~ v c r g e n t r e s : l l t s i n c a s e o f s m a l l r o u g h n e s s e s . To a l l o w > ~ l s c f o r t h e c a s e o f l a r g e r c u g h n e s s we t h e r e f o r e c h o s e a p e r i o d i c g - a t i n g a s a model f o r t h e r c u g h s u r f a c e . A s h n s b e e n p o i n t e d o u t i r . v a r i o u s c a s e s
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t h e R a y l e i g h h y p o t h e s i s ori he m a t c h i n g o f Che f i e l d s a t t h e s u r 2 f a c e h a s b e e n p r c v e d t o h e w e l l a d e q u a t e a l s o r c r l a r g e r o u g h ~ e s s , i . e . r s a t i o s u p t h e < , / a=.6.
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1984532
C5-226 J O U R N A L DE PHYSIQUE
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