Effective-medium theory of sinusoidally modulated volume holograms

On the effective medium theory of subwavelength periodic structures

“…( 1 8 We look for a wave with the z-dependence of equation (3)) which satisfies equations (19). T h e x and y components of the wave electric field are since only Ex has a non-null dc component.…”

“…In this appendix, we derive equations (19). For the sake of generality, the exp (iq'/2kz) dependence of equation (3) is first not assumed, and we derive a set of second-order differential equations using the Floquet theorem.…”

“…Bouchitte and Petit [17] provided a rigorous demonstration of the equivalence of 1-D gratings and thin films in the long wavelength limit. Haggans et al [18] studied the EMT of 1-D lamellar periodic structures in conical mountings, and Campbell and Kostuk [19] modelled sinusoidally modulated and slanted gratings for conical and non-conical mountings.…”

“…Substituting S, , and SL, with sImn and -k2qslmn ( I holds for x and y ) into equations(19), we .Inl3nJls a!po!iad a-j 103 p a~p a p h[sno!~aid (&I) pue(9) suo!lenba 01 puodsauo:, (zz) suo!ianbx *sanIea u pue EU aap!sod 103 suo!ianba asayi~ap!suo:, o i d~u o paau aM 'A~iaurwbs aqi 30 asnmaq inq '(0 ' 0 ) # (u ' w ) AUE 103 p1oq (3 ZZ) pUE (q ZZ) suo!ienba aS.InO3 $0 'IE!A!Ji SaUlO3aq (4 61) uo!it?nba 1Eyl WON (4 zz) Downloaded by [North Carolina State University] at 06:03 14 October 2012 orders both in the x and y directions, equation (25) can be read as a system of M E M T ( M E M T + 1) equations (Vm 2 0, V n > 0 ) , which can be set in the compact form where A is a M E M T ( M E M T + 1) by M E M T ( M E M T + 1) matrix, SIP) is a M E M T ( M E M T + 1) vector composed of ~$ 7~ elements, and b is a M E M T ( M E M T + 1) vector with nc,,, elements. We suppose that A can be inverted (we have no demonstration of that point).…”

Effective medium approximation of anisotropic lamellar nanogratings based on Fourier factorization

“…In this subsection the zero-mode approximation algorithm is used to get analytic EMA formulas describing sub-wavelength grating [23,24,25]. The idea is based on simple assumption that for the sub-wavelength gratings the only propagating mode is the zero diffraction order (this holds for the most cases if the period is small enough).…”