TY - JOUR

T1 - Analysis of the Rigorous Coupled Wave Approach for p-polarized light in gratings

AU - Civiletti, Benjamin J.

AU - Lakhtakia, Akhlesh

AU - Monk, Peter B.

N1 - Funding Information:
Supported by the US National Science Foundation (NSF) under grant numbers DMS-1619904 and DMS-1619901 .

PY - 2021/4

Y1 - 2021/4

N2 - We study the convergence properties of the two-dimensional Rigorous Coupled Wave Approach (RCWA) for p-polarized monochromatic incident light. The RCWA is a semi-analytical numerical method that is widely used to solve the boundary-value problem of scattering by a grating. The approach requires the expansion of all electromagnetic field phasors and the relative permittivity as Fourier series in the spatial variable along the direction of the periodicity of the grating. In the direction perpendicular to the grating periodicity, the domain is discretized into thin slices and the actual relative permittivity is replaced by an approximation. The approximate relative permittivity is chosen so that the solution of the Maxwell equations in each slice can be computed without further approximation. Thus, there is error due to the approximate relative permittivity as well as the truncation of the Fourier series. We show that the RCWA embodies a Galerkin scheme for a perturbed problem, and then we use tools from the Finite Element Method to show that the method converges with increasing number of retained Fourier modes and finer approximations of the relative permittivity. Numerical examples illustrate our analysis, and suggest further work.

AB - We study the convergence properties of the two-dimensional Rigorous Coupled Wave Approach (RCWA) for p-polarized monochromatic incident light. The RCWA is a semi-analytical numerical method that is widely used to solve the boundary-value problem of scattering by a grating. The approach requires the expansion of all electromagnetic field phasors and the relative permittivity as Fourier series in the spatial variable along the direction of the periodicity of the grating. In the direction perpendicular to the grating periodicity, the domain is discretized into thin slices and the actual relative permittivity is replaced by an approximation. The approximate relative permittivity is chosen so that the solution of the Maxwell equations in each slice can be computed without further approximation. Thus, there is error due to the approximate relative permittivity as well as the truncation of the Fourier series. We show that the RCWA embodies a Galerkin scheme for a perturbed problem, and then we use tools from the Finite Element Method to show that the method converges with increasing number of retained Fourier modes and finer approximations of the relative permittivity. Numerical examples illustrate our analysis, and suggest further work.

UR - http://www.scopus.com/inward/record.url?scp=85096586620&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85096586620&partnerID=8YFLogxK

U2 - 10.1016/j.cam.2020.113235

DO - 10.1016/j.cam.2020.113235

M3 - Article

AN - SCOPUS:85096586620

VL - 386

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

SN - 0377-0427

M1 - 113235

ER -