Reformulation of the Fourier modal method for surface-relief gratings made with anisotropic materials

Abstract

Abstrac t.By the use of the correct Fourier factorization rules presented in an earlier paper by Li the Fourier modal method (FMM) for anisotropic surface-relief gratings is reformulated. T he newly formulated FMM converges much faster than the old formulation when the permittivity contrast in the grating groove region is large. Highly conducting lamellar gratings coated with anisotropic materials can now be analysed easily. In addition, a simple set of criteria are given for determining the energy propagation directions of the plane waves associated with the real solutions of the Booker quartic.

Detection of protein aggregation with a Bloch surface wave based sensor

“…Changes in the index of refraction near the surface produce a shift of the dip position in the spectrum. Numerically, we compute the reflection spectrum using a Transfer Matrix Method (TMM) algorithm adapted from [21].…”

Fast Converging and Widely Applicable Formulation of the Differential Theory for Anisotropic Gratings

“…The present formulation is also shown to be equivalent to the formulation in Ref. [11] when the permeability is assumed to be a constant µ 0 everywhere. These formulations proposed in Refs.…”

“…These formulations proposed in Refs. [11,15] are numerically validated by a strong improvement of the convergence speed compared with that for the conventional formulation (47).…”

“…[14,15] and Li's Fourier factorize rules are applied to derive the constitutive relations in Fourier space. As mentioned above, there have been many formulations based on Li's Fourier factorization rules [10,11,[13][14][15][16][17][18]. However, all of them have been proposed for individual types of gratings and limited their application ranges.…”

“…The origin of poor convergence was explained by Li's Fourier factorization rules [10], which gave an idea for accelerating the convergence. Li proposed RCWM formulations for isotropic [10] and anisotropic [11] gratings made of conducting materials by taking into account the rules. RCWM is well suited for lamellar profiled gratings shown as Fig.…”