Analysis of Electromagnetic Wave Scattering from a Fourier Grating Multilayer-Coated Metallic Grating in Conical Mounting

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1 Sho Isttute of Techolog MEMOIRS OF SHONAN INSTITUTE OF TECHNOLOGY Vol. 37, No., 3 * Alss of Electogetc Wve Sctteg fo Foue Gtg Multle-Coted Metllc Gtg Cocl Moutg Moto OHKI* We lze the electogetc wve sctteg plole fo ultle-coted Foue gtg fo geel gle of cdece d t polzto. Ths lss s teted qus-two-desol pole the scle oud vlue. The ltcll peocedue s ppled T-tx ethod wth R-tx popgto lgoth. Ths foulto s lso useful expesso ecuse R-tx popgto lgoth s voded sgult of tx eleets fo the evescet ode. Nuecl exples e peseted fo dffcto effceces whch cdet gle d zthl gle of Fouee gtg e vle. ),) ) ) 3) 4),5) S-tx 6) R-tx 7) 8) R-tx T-tx 9),) * ) ) 3) T-tx 4),5) 6) R-tx 7) T-tx R-tx 7) T-tx 8) 8 37 NII-Electoc L Sevce

2 Sho Isttute of Techolog 37. x (Icdet edu) (Sustte) (Le) 3 e, e I, I e, (,,.., I) S (,,.., I) S S : zf (x)d (), d z x e e totl ed d, e e ( d ) totl I () z q x f E, H x z E t, H t 4) exp( j w t) E t j [ E w H ˆ ] t t (3) H t j [ H we H ˆ ] t t (3) t xz xz x x z z Ï Ô, Ì (4) Ô Ó j, z x,, z x,, z x s q cos f, s q s f, z cos q p P x x (4) 38 x, z Ê Ë x z ˆ NII-Electoc L Sevce

3 Sho Isttute of Techolog E H (5) (5) (5c) e, h q f t h h exp(j ) e cos t cos fs t s f cos q (6) (6) (6c). E, H Huges Gee E ( ) d [ G (, )ˆ E ( ) E H ( ) d [ G (, )ˆ H ( ) s t P t x xˆ ( fd)ˆ z H j h h, Ú s t P t x xˆ ( fd)ˆ z ( )ˆ G (, )] E ( ) z Ì ÓÔ z Ú E ( ) e j, H ( ) h j, exp{ j ( x z)} x h / e ( )ˆ G (, )] H ( ) z Ì ÓÔ z z (cos t s f cos qs t cos f) (7) (7) ds [ G (, )ˆ H ( ) H ds [ G (, )ˆ E ( ) E ds [ G (, )ˆ H ( ) H H ds [ G (, )ˆ E ( ) E E ( )ˆ G (, )] t ( )ˆ G (, )] t x xˆ ( fd )ˆ z ds [ G (, )ˆ H ( ) t t x xˆ ( fd )ˆ z ds [ G (, )ˆ E ( ) t ( )ˆ t G (, )] x x ˆ ( f d )ˆ z t ( )ˆ t G (, )] x x ˆ ( f d )ˆ z I I I t ( I) ( )ˆ G (, )] ( I) I t I x xˆ ( fidi )ˆ z z Ì ÓÔ E( I) ( ) z I I I t ( I) ( )ˆ G (, )] ( I) I t I x xˆ ( fidi )ˆ z z Ì ÓÔ H( I) ( ) z (8) (8) (9) (9), xz ˆ ds G (,) Gee G(, ) j P exp[ j { ( xx ) zz }] x () (8) f d f d z 39 NII-Electoc L Sevce

4 Sho Isttute of Techolog 37 S x z ˆ E t ˆ E ()t zf d () ˆ H t ˆ H ()t zf d () () ˆ( ˆ E ) ˆ t H ( ) t ( ) ˆ( ˆ ) ( ) t E( ) ˆ( ˆ H ) ˆ t E ( ) t ( ) ˆ( ˆ ) ( ) t H( ) () () (c) (d).3 (8) Gee (4) È È (5), (4N) (4N)(4N) È È, (6) ( ) ( ) e e (3) (3) (3c) (3d) E ds ˆ E ( ) j dx exp( j x ) t H ( ) ( ) Ê Á Ë ( ) exp( j x ) ( ) exp( j x ) ds ˆ H ( ) j dx exp( j x ) t ( ), ( ) ( ) ( ) Ê Á Ë ( ), ( ) ( ) ( ) ( ) ( ) ˆ we ˆ w x x x x (4) (4) (4c) (4d) È N(, f) v h (, f) ( ) v ( ) h (, f) N(, f) È N(, f) v h (, f) ( ) v ( ) h (, f) N(, f) È v ( ) D(, f ) v ( ) D(, f) È v ( ) D(, f ) v ( ) D(, f) È V N(, f) È V N(, f) È V D(, f) È V D(, f) V N(, f) V N(, f) V D(, f) V D(, f) (6) (6c) (6d) (6e) (6f) (6g) (6h) (6) 4 NII-Electoc L Sevce

5 Sho Isttute of Techolog z (5) (7) (8) (9) e R-tx T-tx (9) S S (), (), (), () S S R(), R (), R(), R() R() () R () () R (I) ÈR R () () R () () R V j z d d È () () () () exp{ ( )} È () () () () ÈR R () () R () () R È R R Z R R Z Z R Z ( ) ( ) () ( ) ( ) () () () () ( ) ( ) () () () [ ] () () ( ) Z R È È È () () (3).4 (7) (e) (h) (e) (h) zf(x) zf(x) (5) ÈR I R Ïe Ì Ó π (4) (4) (5) (e), (h), (e), (h) S I S e totl (e), (h), (e), (h) x z e totl (e) z totl (e), (h) z totl (h), (e) z totl (e), (h) z totl (h) e totl z totl z totl exp(j z e totl ) (6) È Î R R X È ÎX,,,, X È X Î È I E ( ) j, H ( ) j E ( ) j, H ( ) j Ïh Ì Ó π (7) (), È (8) 4 NII-Electoc L Sevce

6 Sho Isttute of Techolog 37 X È N f (, ) N (, f) (8) È N( I, fi) vi h ( I, fi) Y vi h ( I, fi) N( I, fi) (3d) X È D f (, ) D (, f) (8c) Y È vi D( I, fi) vi D( I, fi) (3e) (8d) (8e).5 (9) B (e) B (h) A (e) A(h) X X B j, È N (, f) È D(, f) zf(x) zf(x) (9) (9) B (e) B (h) ÈB A ÈY Y È A A A I, I, I, I,, Y I Y I È N( I, fi) I h ( I, fi) Y I h ( I, fi) N( I, fi) B N (, f) D(, f) È B B t t E ( ) A j, H ( ) A j B j (3) (3) (3).6 T-tx Dchlet D, Neu N h l, D fl (, ) dx exp jz fl ( x ) jx ( xx) P È N fl (, ) D(, fl) Î (, f ) (, f ) h l D l (3) (33) (34) h h g d Ê fl ( x) h cos p P x ˆ Ê g cos 4 p Á P x ˆ Ô Ì Á d ÓÔ Ë Ë Ô (35) (3) Bessel D fl Ê p ˆ Ô (, ) expì jsád s ÓÔ Ë Ô s ( j) J ( h) J ( hg ) (36) N, h (33), (34) D (7), (3), (3) È ÎA s z s z [ T ] ÎB [ ] (37) Y È e vi D I fi ( ) (, ) (3c) vi D( I, fi) 4 NII-Electoc L Sevce

7 Sho Isttute of Techolog È XR X XR [ T ] I Y R Y Y R ( ) ( I) ÈX R X X R YR YYR (38) (37) (6) z e totl T T- tx B A.7 TE z TM z t t h h ( ) e h (39) Dffcto effcec, Dffcto effcec, = 5 Al Sustte, (HL) = Nolzed le thcess, 5 Al Sustte (HL) 4 Lttow Icdet gle, t ( I) e I e A h A I e h h (39) totl, t totl t t, R { } I { } totl, R ( ) totl e ( I) ( I) (4) (4) 3 ( su.997j6.94, l59 ) ( L.39, M g F ) ( H =.45, T O ) 4 8 P333.3, h6, g., dp/ f t9 c ce /l{h; odd, L; eve} 6.6 () c.34 e q () f L 7) 3 ( su.7j4., l65 ) (g., dp/, P556, h5, d 6 ) t9 TM f q5 f q TM f q f q f TM TE f q f45 43 NII-Electoc L Sevce

8 Sho Isttute of Techolog R-tx T- tx Bessel T-tx 8 f q f45 ) D. Mste, M. Nevee, d R. Pett, Expeetl Vefcto d Applctos of the Theo, Electogetc Theo of Gtgs, ed. R. Pett, pp. 8, Spge-Velg, Bel, 98. ) D. Mste, M. Nevee, d R. Pett, The Hoogeeous Pole, Electogetc Theo of Gtgs, ed. R. Pett, pp. 3 57, Spge-Velg, Bel, 98. 3) D. Mste, A ew geel tegl theo fo delectc coted gtgs, J. Opt. Soc. A., vol. 68, o. 4, pp , Ap ) J. Chdezo, M. T. Dupus, G. Coet, d D. Mste, Multcoted gtg: dffeetl fols pplcle the ete optcl ego, J. Opt. Soc. A., vol. 7, o. 7, pp , Jul 98. 5) T. W. Pest, N. P. K. Cotte, d J. R. Sles, Peodc ultle gtgs of t shpe, J. Opt. Soc. A. A, vol., o. 8, pp , Aug ) N. P. K. Cotte, T. W. Pest, d J. R. Sles, Sctteg-tx ppoch to ultle dffcto, J. Opt. Soc. A. A, vol., o. 5, pp. 97 3, M ) L. F. DeSde, d J. M. Elso, Extcto-theoe lss of dffcto oles ovecoted gtgs, J. Opt. Soc. A. A, vol. 8, o. 5, pp , M 99. 8) (C-I), vol. J76-C-I, o. 6, pp. 6 4, Jul ) T-tx (C-I), vol. J8-C-I, o., pp. 4 5, J ) T-tx (C-I), vol. J8-C-I, o. 3, pp. 39 4, M ) H. Rethe, Sufce plsos d oughess: electogetc wves t sufces d tefces, Chpte 9 44 NII-Electoc L Sevce

9 Sho Isttute of Techolog Sufce poltos, Edted V. M. Agovch, d D. L. Mlls, Noth-Holld Pulshg Cop, New Yo, pp , 98. ) J. P. Plue, G. Get, d J. Chdezo, Dffeetl covt Fols fo solvg Mxwell s equtos cuvle coodtes: olque sctteg fo loss peodc sufces, IEEE Ts. o Ates d Popgt., vol. 43, o. 8, pp Aug ) TE-TM (C-I), vol. J8-C-I, o., pp. 4 49, Fe ) S. L. Chug, d J. A. Kog, Wve sctteg fo peodc delectc sufce fo geel gle of cdece, Rdo Scece, vol. 7, o. 3, pp , M Jue 98. 5) T-tx (C-I), vol. J8-C-I, o., pp , J ) S. J. Elsto, G. P. B-Bow, d J. R. Sles, Polzto coveso fo dffcto gtgs, Phs. Rev. B, vol. 44, o., pp , Sep ) L. L, Multle-coted dffcto gtgs: dffeetl ethod of Chdezo et l. evsted, J. Opt. Soc. A. A, Vol., No., pp , Nov ) M. Oh, T. Kuh, d S. Koz, Alss of electogetc wve dffcto fo etllc Foue gtg usg the T-tx ethod, J. Electogetc Wves d Applctos, Vol., No. 9, pp. 57 7, NII-Electoc L Sevce

T i t l e o f t h e w o r k : L a M a r e a Y o k o h a m a. A r t i s t : M a r i a n o P e n s o t t i ( P l a y w r i g h t, D i r e c t o r )

v e r. E N G O u t l i n e T i t l e o f t h e w o r k : L a M a r e a Y o k o h a m a A r t i s t : M a r i a n o P e n s o t t i ( P l a y w r i g h t, D i r e c t o r ) C o n t e n t s : T h i s w o