INFLUENCE OF SURFACE CORRUGATIONS ON SURFACE ELECTROMAGNETIC WAVES

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INFLUENCE OF SURFACE CORRUGATIONS ON SURFACE ELECTROMAGNETIC WAVES

E. Koteles, Y. Chen, G. Sonek, J. Ballantyne

To cite this version:

E. Koteles, Y. Chen, G. Sonek, J. Ballantyne. INFLUENCE OF SURFACE CORRUGATIONS ON

SURFACE ELECTROMAGNETIC WAVES. Journal de Physique Colloques, 1984, 45 (C5), pp.C5-

213-C5-218. �10.1051/jphyscol:1984530�. �jpa-00224148�

JOURNAL DE PHYSIQUE

Colloque C5, supplément au n04, Tome 45, a v r i l 1984 page CS-2 13

INFLUENCE OF SURFACE CORRUGATIONS ON SURFACE ELECTROMAGNETIC WAVES

E . S . Koteleç, Y . J . Chen,C.J. sonek* and J.M. ~ a l l a n t ~ n e *

C1'E L a b o m t o r i e s I n c o m o r a t e d , 40 SyZoan iîoad, WaZi;ham, Massachusetts 0 2 2 5 4 , U.S.A.

* ~ a t i o n a ~ Resenrch and Resource F a c i Z i t y f o r Submicron S t m c t u r e s a t CorrreZZ U n i v e r s i t y , Ithaca, New York 13853, U . S . A .

RESUME

Ce p a p i e r présente l a preuve expérimentale de l ' i n f l u e n c e de l ' u n i f o r - m i t é des p r o f i l s d ' u n réseau sur l e couplage des ondes électromagnéti- ques de surface e t l e s courbes de d i s p e r s i o n de ces ondes l o r s q u ' e l l e s se propagent s u r des surfaces à échelons périodiques.

ABSTRACT

We p r e s e n t experimental evidence of t h e influence of g r a t i n g p r o f i l e u n i f o r m i t y on surface electromagnetic wave (SEWI coupling a n d dispersion c u r v e s f o r SEWs p r o p a g a t i n g on periodically c o r r u g a t e d surfaces.

Recently, considerable i n t e r e s t has developed i n t h e p r o p e r t i e s a n d electrodynamics o f surface electromagnetic waves (SEWs) on r o u g h interfaces (e.g., surface enhanced Raman scattering, l i g h t emission f r o m metal-oxide-metal junctions, e t c . ) /1-9/. A systematic method o f i n v e s t i g a t i n g these, a n d similar phenomena is t o determine t h e e f f e c t o f a well defined c o r r u g a t e d surface (a g r a t i n g ) on t h e properties o f SEWs /IO-14/. T h e presence o f a g r a t i n g on t h e surface permits coupling between radiative modes a n d SEWs, which a r e non- radiative, and also c o u p l i n g between SEWs. T h e theoretical methods developed b y Toigo e t al /5/ have been widely applied i n t h i s f i e l d a n d exact numerical calculations have been c a r r i e d o u t b y Mills, Maradudin and more r e c e n t l y b y Garcia a n d coworkers i n a number o f systems /6-9/. U p t o now, most experimental a n d theoretical w o r k has concentrated on t h e e f f e c t o f g r a t i n g amplitude a n d p e r i o d on t h e coupling between SEWs and r a d i a t i v e waves and t h e dispersion of t h e SEW. Garcia's calculations have demonstrated t h e influence of t h e g r a t i n g p r o f i l e on t h e c o u p l i n g a n d t h i s has been confirmed experimentally f o r t h e case of h i g h e r o r d e r coupling i n t h e minigap region where a degeneracy exists between counterpropagating SEWs /14/. Unfortunately, d u e t o t h e scarcity of theoretical w o r k on h i g h e r o r d e r coupling, it has n o t been possible t o compare experimental r e s u l t s w i t h theoretical predictions. T h e g r a t i n g p r o f i l e e f f e c t is more important f o r h i g h e r o r d e r coupling since h i g h e r o r d e r harmonics p r e s e n t i n a non-sinusoidal g r a t i n g p r o f i l e can lead t o complicated interference effects /15/. I n addition, g r a t i n g s fabricated i n real l i f e i n general d o n o t have optically smooth surfaces a n d precisely defined periods.

Fluctuations i n t h e g r a t i n g p e r i o d generate sidebands on t h e g r a t i n g constant which can generate s i g n i f i c a n t consequences i n SEW c o u p l i n g and dispersion c u r v e s 1 6 I n t h i s paper, we i l l u s t r a t e t h e significance o f these considerations b y comparing SEW dispersion c u r v e s i n t h e v i c i n i t y o f h i g h e r o r d e r minigaps f o r t w o g r a t i n g s o f similar p e r i o d a n d amplitude, b u t w i t h d i f f e r e n t degrees of g r a t i n g fluctuations.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1984530

C5-2 14 J O U R N A L DE PHYSIQUE

T h e g r a t i n g equation t o c o u p l i n g SEWs i s :

w h e r e k(w) = (w/c)sinO, w is t h e p h o t o n e n e r g y , c i s t h e speed of l i g h t a n d 8 t h e i n c i d e n t angle; k t o f i r s t o r d e r , is t h e wavevector o f t h e SEW i n t h e

SP'

absence o f a g r a t i n g ( e x c e p t i n t h e minigap regions); n is an i n t e g e r a n d G = 2 n / d is t h e r e c i p r o c a l " l a t t i c e " v e c t o r of t h e g r a t i n g ( d i s t h e g r a t i n g s p a c i n g ) . Degenerate States o c c u r when t h e d i s p e r s i o n c u r v e s f o r " f o r w a r d " p r o p a g a t i n g ( + k s p ) a n d " b a c k w a r d " p r o p a g a t i n g ( - k ) modes cross, as i l l u s t r a t e d i n F i g u r e

SP

1. I f t h e i n t e r a c t i o n between t h e modes i s s t r o n g , r e p u l s i o n can o c c u r a n d a gap forms i n t h e d i s p e r s i o n r e l a t i o n . T h e m a g n i t u d e of t h e repulsion, i . e . , t h e minigap size, is determined by t h e SEW-SEW c o u p l i n g s t r e n g t h . We have s t u d i e d minigaps a t t h e crossings o f t h e f o l l o w i n g modes: (-1,2) [ i . e . , k = k

s P -G a n d k = -ksp+2G,] (-2,2) a n d (-1,3).

MOMENTUM ( 2 ~ x l o 4 cm -1)

F i g u r e 1. Schematic diagrarn o f the dispersion c u r v e s of s u r f a c e plasmons o n a grating w i t h a periodicity of d=27/G (solid lines).

The dash-dotted line is the dispersion curve of a free space electro-

magnetic w a v e a n d the dotted l i n e indicates the slope of a typical

experimental scan. The m i n i g a p s discussed in this paper a r e shaded.

EXPERIMENT

T h e experiment was p e r f o r m e d b y m o n i t o r i n g t h e i n t e n s i t y o f l i g h t r e f l e c t e d f r o m a metallic g r a t i n g w h i l e t h e e n e r g y o f t h e l i g h t was v a r i e d . T h i s was accomplished b y m a k i n g constant a n g l e scans i n w h i c h t h e angle o f incidence was k e p t f i x e d a n d t h e wavelength o f t h e i n c i d e n t l i g h t was v a r i e d (see t h e d o t t e d l i n e i n F i g u r e 1 ) . When t h e e n e r g y a n d momentum of t h e i n c i d e n t l i g h t matched t h a t of a SEW, c o u p l i n g o c c u r r e d a n d t h e r e f l e c t e d l i g h t i n t e n s i t y decreased. T h e magnitude a n d w i d t h o f t h e r e f l e c t i v i t y " d i p " is determined b y t h e c o u p l i n g s t r e n g t h o f t h e SEW mode a n d t h e c o r r e s p o n d i n g d i e l e c t r i c a n d r a d i a t i v e ( s c a t t e r i n g a n d d i f f r a c t i o n ) losses. B y i n c r e m e n t i n g t h e i n c i d e n t angle, 8, a n d m o n i t o r i n g t h e p h o t o n e n e r g y a t w h i c h t h e d i p occurs, SEW d i s p e r s i o n c u r v e s w e r e mapped o u t .

T h e p e r i o d i c i t y o f t h e g r a t i n g s was set a t 21. l p m i n o r d e r t h a t several o r d e r s o f minigaps b e accessible t o Our d y e laser system. T h e y were f a b r i c a t e d o n silicon s u b s t r a t e s a t t h e National Research a n d Resource F a c i l i t y f o r Submicron S t r u c t u r e s a t C o r n e l l U n i v e r s i t y .

T h e g r a t i n g p a t t e r n was established b y f i r s t e x p o s i n g an i n t e r f e r e n c e hologram o n p h o t o r e s i s t coated silicon s u b s t r a t e s . T h e p a t t e r n was t h e n etched i n t o t h e silicon u s i n g e i t h e r a r e a c t i v e ion e t c h i n g t e c h n i q u e (RIE) o r an ion m i l l i n g t e c h n i q u e ( I M ) . T h e g r a t i n g amplitudes w e r e measured u s i n g a scanning e l e c t r o n microscope a n d w e r e f o u n d t o b e similar ( t h e t y p i c a l g r a t i n g amplitude was = 500 A ) . However, t h e p r o f i l e s o f t h e t w o g r a t i n g s w e r e q u t t e d i f f e r e n t as shown i n F i g u r e 2. T h e I M g r a t i n g h a d a clean, w e l l - d e f i n e d a n d c o n s t a n t g r a t i n g p e r i o d w h i l e t h a t o f t h e RIE g r a t i n g was q u i t e i r r e g u l a r . The w i d t h s o f i n d i v i d u a l lines o f t h e RIE g r a t i n g v a r i e d b y as much as 30%. I n addition, t h e R I E c o r r u g a t i o n p r o f i l e was approximately sinusoidal, b u t w i t h a f l a t t o p w h i l e t h e IM p r o f i l e was more t r i a n g u l a r .

S i l v e r was chosen as t h e metaflic o v e r c o a t i n g because o f i t s low d i e l e c t r i c loss t h r o u g h o u t t h e v i s i b l e . O p t i c a l l y t h i c k ( = 5000 A ) s i l v e r films w e r e t h e r m a l l y evaporated o n t 0 p r e p a r e d silicon s u b s t r a t e s i n a vacuum o f 1 x 1 0 - ~ to r r . T o minimize t a r n i s h i n g , t h e samples were f r e s h l y coated a n d were mounted i n a d r y n i t r o g e n f i l l e d enclosure d u r i n g measurement. A d y e laser purnped b y a k r y p t o n i o n laser was t h e t u n a b l e light s o u r c e w h i c h p e r m i t e d us t o p r o b e t h r e e separate minigaps i n t w o spectral ranges. P y r o e l e c t r i c d e t e c t o r s and l o c k - i n amplifiers w e r e employed t o d e t e c t t h e normalized r e f l e c t e d i n t e n s i t y . T h e data f r o m t h e experimental scans w e r e collected w i t h a microcornputer c o n t r o l l e d data acquisition system.

Figure 2. T h e scanning electron micrographs of grating profiles of the reactive ion etched (RIE) grating and t h e i o n milLed ( I M ) grating.

Note that the IM grating is a lot smoother than the RIE grating.

Details a r e discussed i n the text.

J O U R N A L DE PHYSIQUE

MOMENTUM ( 2 ~ x 103 cm-') 1.42

- ^1.38

.- _l

5

w

5 1.34

>

LU z

W 1.30

1.26

Figure 3. The experimentally measured SEW dispersion curves in the vicinity of the (-1,2) minigap for the RIE grating.

I

I

I

- 6 ( - 1,2) MlNlGAP -

* Y REACTIVE ION

- S x ETCHED GRATING -

8 _v .

/

- -

4 *5Q

. _{* .}

- . . ⁴ -

*. 4-

- -

. e V

0.

- . ^-

.

- . ^-

- w

I 1

I

I

I I

3.4 3.8 4.2 4.6 5.0 5.4

MlNlGAP LLED GRATING

Figure 4. Experimentally determined SEM dispersion curves in the

vicinity of the (-1,2) minigap for the IM grating.

RESULTS

T h e measured d i s p e r s i o n c u r v e s o f t h e k = - k +2G a n d k = k -G SEWS

SP s P

(termed +2 a n d -1 coupling processes, r e s p e c t i v e l y ) i n t h e v i c i n i t y o f t h e i r c r o s s i n g a r e g l v e n i n F i g u r e 3 f o r t h e R I E g r a t i n g a n d i n F i g u r e 4 f o r t h e I M g r a t i n g . T h e crossings o c c u r a t a b o u t t h e same e n e r g y (1.320 x 10 cm-' f o r 4 R I E a n d 1.247 x l o 4 cm-' f o r IM) since t h e g r a t i n g p e r i o d s w e r e similar (1.106 urn f o r RIE a n d 1.183 pm f o r I M ) . I n addition, t h e magnitudes o f t h e minigaps a r e almost identical ( - 100 cm-' f o r RIE and - 110 cm-' f o r I M ) . As t h e i n c i d e n t angle 6 was varied, t h e c o u p l i n g s t r e n g t h ( t h e m a g n i t u d e of t h e d i p ) o f t h e +2 mode decreased r a p i d l y t o zero a t ( k = 4 . 5 8 x h x 10 cm-') f o r t h e RIE 3 g r a t i n g a n d t h e n j u s t as q u i c k l y reappeared, b u t a t a h i g h e r e n e r g y /14/. I n e f f e c t , an additional l a r g e (185 c m - l ) "gap" opened u p i n t h e dispersion

3 - 1 4 -1

relation f o r t h e

2 mode at kZ4.58 x 2n x 10 cm , a n d ~ ~ 1 . 3 1 x 10 cm .

T h i s s t r u c t u r e is asymmetric i n t h a t n o analogous f e a t u r e i s p r e s e n t on t h e - 1 mode at t h e same e n e r g y . F o r t h e IM g r a t i n g however, while t h e i n t e n s i t y o f t h e

2 mode w e n t t h r o u g h a minimum a t about t h e same k , n o additional "gap"

was e v i d e n t . T h e w i d t h o f t h e coupling d i p f o r t h e RIE g r a t i n g was about 50%

l a r g e r t h a n t h a t f o r t h e IM g r a t i n g . T h i s cannot b e a t t r i b u t e d t o o v e r c o u p l i n g since t h e g r a t i n g amplitudes a r e t h e same. More l i k e l y , t h i s b r o a d e n i n g i s a r e s u l t of t h e f l u c t u a t i o n s i n t h e RIE g r a t i n g s p e r i o d which, i n effect, allows c o u p l i n g t o SEWs o v e r a d i s t r i b u t i o n o f i n c i d e n t angles. We suspect t h a t these f l u c t u a t i o n s , b y p r o d u c i n g i n t e r f e r e n c e between t h e sideband a n d t h e weak + 2 mode, may also b e t h e cause o f t h e additional f e a t u r e on t h e +2 b r a n c h .

Similar r e s u l t s a r e o b s e r v e d f o r t h e (-1.3) m i n i g a p . F o r t h e RIE g r a t i n g , t h e r e is a l a r g e (2290 c m - l ) a d d i t i o n a l "gap" p r e s e n t o n t h e

3 mode above t h e minigap ( w h i c h has a magnitude o f 2360 cm-') i n a r e g i o n where t h i s mode's c o u p l i n g i n t e n s i t y decreased t o zero. No such additional gap s t r u c t u r e was observable on t h e IM g r a t i n g . F u r t h e r , t h e minimum i n t h e +3 mode i n t e n s i t y o c c u r e d a t an e n e r g y below t h e minigap e n e r g y a n d t h e minigap w i d t h (1140 cm-'1 was s i g n i f i c a n t l y smaller t h a n was t h e case f o r t h e RIE g r a t i n g . These effects a r e l i k e l y d u e t o the influence o f t h e harmonic content o f t h e g r a t i n g p r o f i l e o n h i g h e r o r d e r SEW c o u p l i n g . We p l a n a systematic s t u d y o f SEW g r a t i n g c o u p l i n g a n d d i s p e r s i o n c u r v e s i n t h e v i c i n i t y o f minigaps f o r a v a r i e t y o f w e l l - d e f i n e d g r a t i n g p r o f i l e s i n o r d e r t o f u r t h e r elucidate t h e e f f e c t o f g r a t i n g p r o f i l e a n d u n i f o r m i t y on SEWs.

ACKNOWLEDGEMENT

W e would like to thank Dr. R.J. Seymour for helpful discussion and his critical reading of the manuscript.

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C 5-2 1 X J O U R N A L DE PHYSIQUE

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