SPECTROSCOPY OF SURFACE POLARITON DIFFRACTION

(1)

HAL Id: jpa-00223541

https://hal.archives-ouvertes.fr/jpa-00223541

Submitted on 1 Jan 1983

HAL

is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire

HAL, est

destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

SPECTROSCOPY OF SURFACE POLARITON DIFFRACTION

V. Agranovich, V. Kravtsov, T. Leskova

To cite this version:

V. Agranovich, V. Kravtsov, T. Leskova. SPECTROSCOPY OF SURFACE POLARI- TON DIFFRACTION. Journal de Physique Colloques, 1983, 44 (C10), pp.C10-403-C10-405.

�10.1051/jphyscol:19831083�. �jpa-00223541�

(2)

JOURNAL DE PHYSIQUE

Colloque CIO, suppl6ment au n012, Tome 44, d k e m b r e 1983 page CIOY03

SPECTROSCOPY OF SURFACE POLARITON DIFFRACTION

V.M. Agranovich, V . E . Kravtsov and T.A. Leskova

I n s t i t u t e o f Spectroscopy, USSR Academy of Sc<ences, T r o i t s k , Moscou o b l . , 142092, U.S.S.R.

~&mrn6

-

On 6 t u d j e m e large, gamme d ' e f f e t s a p p a r a i s s a n t

=des ondes electrqmagnetiques de s u r f a c e ( p o l p i t o n s d e s u r f a c e ) s o n t d i f f r a ~ t e e q p a r l e b o ~ d d t u n f i l m d i e l e c t r i q u e ou semi-conducteur depose s u r un metal.

A b s t r a c t

-

^Awide range of e f f e c t s a r i s i n g a t d i f f r a c t i o n o f s m f ace electromagnetic waves ( s u r f a c e p o l a r i t o n s ) a t t h e edge of a d i e l e c t r i c o r semiconductor f i l m d e p o s i t e d on metal i s d i s c u s s e d .

Nowadays s u r f a c e electromagnetic waves ( s u r f a c e p o l a r i t o n s ) a r e f i n d i n g i n c r e a s i n g a p p l i c a t i o n f o r t h e s t u d y o f o p t i c a l p r o p e r t i e s o f s u r f a c e s and t h i n f i l m s . The r e a s o n f o r t h i s i s t h a t the s u r f a c e p o l a r i t o n d i s p e r s i o n law i s determined n o t only by the bulk d i e l e c t r i c c o n s t a n t s o f c o n t a c t i n g media, but a l s o b e a r s some information on t h e p r o p e r t i e s o f t h e t r a n s i t i o n l a y e r .

The e f f e c t o f a t r a n s i t i o n l a y e r on the s u r f a c e p o l a r i t o n d i s p e r s i o n law proves t o be most prominent a t s u r f a c e p o l a x i t o n f r e q u e n c i e s

c l o s e t o those of d i p o l e v i b r a t i o n s i n t h e t r a n s i t i o n l a y e r ( o r i n a t h i n film on a s u b s t r a t e ) . Namely, a gap i s formed i n t h e s u r f a c e p o l a r i t o n frequency spectrum a t o r and t h e width of t h i s gap i s p r o p o r t i o n n a l t o ( d / X ) 1 / 2 ( d i s the thickness of the t r a n s i t i o n layer,

A = 2 t f c / r ~ 1 ) . Such a n e f f e c t and, i n p a r t i c u l a r , t h e squaxe r o o t dependence was t h e o r e t i c a l l y p r e d i c t e d i n /I

/

and experimentally observed i n d i f f e r e n t frequency ranges / 2 , 3 /

I t w a s r e c e n t l y shown by one o f t h e a u t h o r s /4/, t h a t a t f r e q u e n c i e s j u s t below t h e gap a n a d d i t i o n a l s u r f a c e wave c a n a l s o a r i s e . This e f f e c t connected with t h e f a c t t h a t t h e long-range Coulomb i n t e r a c - t i o n of p o l a r i z a t i o n a t d i f f e r e n f i p o i n t s x and x ^t i n a t h i n f i l m l e a d s to a s t r o n g nonanalytical k

-

dependence i n t h e d i s p e r s i o n l a v i f o r v i b r a t i o n s i n t h i n f i l m s on a 2 u b s t r a t e . Namely, i n this c a s e t h e d i s p e r s i o n law i s l i n e a r i n Ikl and t h e s l o e i s n e g a t i v e , i f t h e d i e l e c t r i c c o n s t a n t o f t h e s u b s t r a t e E a ( O P i s negative. The i n t e r a c t i o n between s u r f a c e p o l a r i t o n s on a s u b s t r a t e s u r f a c e and v i b r a t i o n s i n a t h i n f i l m r e s u l t s i n a gap i n t h e frequency spectrum o f s u r f a c e p o l a z i t o n s and an a d d i t i o n a l s u r f a c e wave. The appearance o f an a d d i t i o n a l iKtave may be considered i n a c e r t a i n s e n s e a s an e f f e c t o f s p a t i a l d i s p e r s i o n due t o t h e long-range dipole-dipole i n t e r a c t i o n .

However, a l l what i s s a i d a b o v e i s v a l i d , i f w e n e l e c t t h e short-range p o l a r i z a t i o n c o m e l a t i o n s which l e a d t o t h e

#-

dependence o f t h e d i e l e c t r i c p e r m e a b i l i t y C, (a, k) i n a t h i n f i l m . The s i m p l e s t way t o allow f o r n o n l o c a l e f f e c t s i n t h e l i n e a r response i s t o i n t r o d u c e t h e

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19831083

(3)

C 10-404 30URNAL DE PHYSIQUE

dependence of t h e s'esonance frequency on t h e square wave vector k? I f -the e f f e c t i v e mass is p o s i t i v e , t h e i n i t i a l decrease i n &(k) changes i n t o a n i n c r e a s e w i t h the wave v e c t o r k. It i s c l e a r t h a t one more s u r f a c e wave appears i n such a c a s e a n d , , t h e r e f o r e , t h r e e s u r f a c e p o l a r i t o n s of the same frequency may e x i s t .

The appearance of a d d i t i o n a l naves due t o s p a t i a l , d i s p e r s i o n i s w e l l known i n bulk c r y s t a l o p t i c s ( s e e 15,'). Ln t h e frgquency r e g i o n where a d d i t i o n a l viaves e x i s t , t h e problem o f l i g h t r e f l e c t i o n from a n i n t e r f a c e becomes r a t h e r d i f f icul-l- because t h e i ~ i a m ~ e l l s boundary c o n d i t i o n s prove t o be i n s u f f i c i e n t t o s o l v e t h i s problem unambi~uo- usly. To avoid t h i s ambiguity, a d d i t i o n a l boundary c o n d i t i o n s

(ma.

a r e r e q u i r e d , which depend on the d e t a i l e d s t r u c t u r e of an i n t e r f a c e . The problem o f s u r f a c e p o l a x i t o n t r a n s f o r m a t i o n a t an i n t e r f a c e and i t s d e s c r i p t i o n by means of t h e s m f a c e analogues o f t h e f i e s n e l r e l a t i o n s c o n t a i n s a n i n h e r e n t complication connected w i t h t h e p o s s i b i l i t y o f s u r f ace p o l s i t o n t r a n s f omnation i n t o bullc r a d i a t i o n . Therefore, s u r f a c e p o l a r i t o n transformation must be regarded a s a problem o f d i f f r a c t i o n theory. Such a problem has been a n a l y t i c a l l y solved i n /6-8/.

A t h i n film ( t i c k n e s s d < < A ) w i t h d i e l e c t r i c constant

c, (O,z)

h a s been supposed t o occupy a h a l f p l a n e ( ~ 7 0 ) o n t h e metal s u r f a c e . I n t h i s c a s e a c o n s i s t e n t d e r i v a t i o n o f t h e boundary c o n d i t i o n f o r a n electromagnetic f i e l d i n s u c h a system r e s u l t s i n t h e appearance o f a l i n e a r c u r r e n t i n this c o n d i t i o n . The appearance o f t h e a d d i t i o - n a l l i n e a r c u r r e n t i s e q u i v a l e n t t o account o f ABC.

The energy t r a n s f o m a t i o n c o e f f i c i e n t s f o r s u r f ace p o l a r i t o n i n c i d e n t normal t o t h e boundary o f the f i l m x=O have been c a l c u l a t e d . A t f r e q u e n c i e s c l o s e t o the resonance w i t h v i b r a t i o n s i n t h e f i l m a l l s u r f a c e poltipiton energy t r a n s f o r m a t i o n c o e f f i c i e n t s have been shown t o i n c r e a s e . I n p a r t i c u l a r , t h e e x c i t a t i o n c o e f f i c i e n t s of a d d i t i o n a l s u r f ace p o l a x i t o n s by long-wavelength i n c i d e n t s u r f ace p o l a r i t o n show n w r o a resonance peaks a t w*

.

S i m i l a r frequency dependence has been p r e d i c t e d i n /6-8/ f o r t h e r e f l e c t i o n c o e f f i c i e n t and t h e

i n t e n s i t y of t h e bulk c y l i n d r i c a l wave, appearing due t o d i f a a c t i o n o f s u r f a c e p o l a r i t o n s . The l a t t e r e f f e c t means t h a t a t t h e i n c i d e n c e o f white ( w i t h a broad frequency spectrum) s u r f a c e r a d i a t i o n on t h e impedance step, t h e spectrum o f bulk r a d i a t i o n must c o n t a i n f r e q u e n c i e s i n t h e narrow i n t e r v a l n e a r & = d o . The above a f f e c t i s i n a c e r t a i n s e n s e analogous t o t h e formation of r e s i d u a l r a y s when w h i t e l i g h t i s r e f l e c t e d from i o n i c c r y s t a l s . Xn t h e v i c i n i t y o f t h e

maximum/

t h e p a r t of i n c i d e n t s u r f a c e p o l a r i t o n energy transformed i n t o

bulk r a d i a t i o n is as much as 9Vh f o r Eat-20 and i n c r e a s e s w i t h 141.

The a n g u l m dependence o f bulk r a d i a t i o n i n t e n s i t y has two peaks.

The more i n t e n s e peak a t s m a l l arngles corresponds t o d i f f r a c t i o n i n n e m l y forward d i r e c t i o n and the second one a t a n g l e s c l o s e t o 180°

corresponds t o back d i f f r a c t i o n .

The study o f t h e r a d i a t i o n frequencyspectrumseems t o b e o n e o f t h e p o s s i b l e methods t o determine t h e e i g e n f r e q u e n c i e s i n a t r a n s i t i o n

l a y e r o r a t h i n f i l m on a s u r f a c e . Another method may be based on t h e i n v e s t i g a t i o n o f the frequency dependence of t h e r e f l e c t i o n c o e f f i c i e n t s o f bulk r a d i a t i o n i n c i d e n t upon t h e s u r f a c e i n t h e r e g i o n o f t h e impedance s t e p . A s i t has been shown i n /7/ a t

o b s e r v a t i o n a n g l e s ( t h e a n g l e between t h e normal t o t h e s u r f a c e and t h e e r p e n d i c u l a r from t h e o b s e r v a t i o n p o i n t onto t h e impedance s tepy c l o s e t o t h e a n g l e o f m i r r o r r e f l e c t i o n , t h e frequency dependence o f t h e r e f l e c t i o n c o e f f i c i e n t R has a d i p a t t h e frequency

m a

.

The width of 'chis d i p i s very small a t almost normal and

(4)

g r a z i n g i n c i d e n c e (AO/LO-IO-~ a t y = 5 O ) and R ~

=

n^0.

A s i t has been shown i n /6,7/ t h e energy t r a n s f o r m a t i o n c o e f f i c i e n t s a r e u n i v e r s a l f u n c t i o n s o f frequency and do n o t depend on t h e shape o f t h e f i l m edge,provided t h a t t h e w i d t h of t h e t r a n s i t i o n r e g i o n a t t h e edge is much s m a l l e r t h a n t h e s u r f a c e p o l a r i t o n wavelength.

However, such a s i t u a t i o n occurs only i n t h e case when t h e k

-

^de-

pendence of t h e d i e l e c t r i c f u n c t i o n i n t h e f i l m 6, ( G O ) is ne l i g i b l e . When t h e s p a t i a l d i s p e r s i o n o f t h e d i e l e c t r i c f u n c t i o n

q

( r J

$6

^{i s}

t a k e n i n t o account, t h e l o c a l edge nodes may e x i s t /8/, whlch r e s u l t s i n a d d i t i o n a l resonance p e c u l i a r i t i e s i n t h e k-equency dependence o f energy t r a n s f o r m a t i o n c o e f f i c i e n t s . S i n c e t h e f r e q u e n c i e s o f t h e edge modes s t r o n g l y depend on t h e f i l m p r o f i l e f u n c t i o n a t t h e edge, t h e energy transTormation c o e f f i c i e n t s must a l s o depend s t r o n g l y on t h e shape of t h e f i l m edge.

References

1 . AGRANOVICII V.U., LLALSHUKOV A.G., 0pt.Commun. 11 (1974) 169.

2. YAKOVUV,V.A., NTAZIN V.G., WIZHIN G.IB.,

opt.Emmun.

1 (1975) 293 3. LOPEZ-RIOS T., ABELES B., V W G., J.de Phls.

2

(1978 645.

4.

ACRANOVlCH Y .I,l., Zh.Exp.Peo~+FIz. (1 9791 11 24.

3

5. AGRAJTOVICH V.1,;.

,

^GZL~ZBUIGV.L.

,

C r y s t a l o p t i c s w i t h S p a t i a l D i s e r - s i o n and t h e Theory of E x c i t o n s , Springer-Berlug, B e r l i n ( 1 9827.

6 . AGRATIOVICII V.I.I., I-iRAV'rSOV V.E., LES?IOVA T.A., Zh.Exp.lCeor.Fiz.

8l, (1981) 11.

7. A G W J O V I C H V-LI., XHAirTSOV O.X., LESIiOVA T.A., S o l i d S t a t e Comun.

a

(1981) 687.

8. AGIWJOVICH V.iil,, Y W T S O ' J V.E., LEWVA T.A., Zh.Exp.Teor.Fiz.

%

(1983) 103.