Abstract

Three-dimensional vectorial diffraction analysis of gratings is presented based on Legendre polynomial expansion of electromagnetic fields. In contrast to conventional rigorous coupled wave analysis (RCWA) in which the solution is obtained using state variables representation of the coupled wave amplitudes, here the solution of first-order coupled Maxwell’s equations is expanded in terms of Legendre polynomials, where Maxwell’s equations are analytically projected in the Hilbert space spanned by Legendre polynomials. This approach yields well-behaved algebraic equations for deriving diffraction efficiencies and electromagnetic field profiles without facing the problem of numerical instability. The proposed approach can be applied in the analysis of two cases: first, arbitrarily oriented planar gratings with slanted yet homogeneous fringes; second, nonslanted but longitudinally inhomogeneous gratings. The method is then applied to various test cases within the above-mentioned two categories, comparison to other methods already reported in the literature is made, and the presented approach is justified. Different aspects of the proposed method such as numerical stability and convergence rate are also investigated. Special attention is given to how the resonant frequency of frequency selective structures varies with introducing tilt angles and/or longitudinal inhomogenity in the permittivity profile.

© 2007 Optical Society of America

Longitudinal Legendre polynomial expansion of electromagnetic fields for analysis of arbitrary-shaped gratings

Amin Khavasi, Ali Kazemi Jahromi, and Khashayar Mehrany
J. Opt. Soc. Am. A 25(7) 1564-1573 (2008)

Legendre polynomial expansion for analysis of linear one-dimensional inhomogeneous optical structures and photonic crystals

Maysamreza Chamanzar, Khashayar Mehrany, and Bizhan Rashidian
J. Opt. Soc. Am. B 23(5) 969-977 (2006)

Polynomial expansion method for full wave three-dimensional analysis of dielectric waveguides and periodic structures

Kamalodin Arik and Mahmood Akbari
Opt. Express 32(9) 16115-16131 (2024)

Modal analysis of diffraction by snake gratings using a tensor product of pseudo-periodic functions and Legendre polynomials

Malalatiana Rinah Rasoamilanto, Manjakavola Honoré Randriamihaja, Lala Bakonirina Andriamanampisoa, Gérard Granet, and Karyl Raniriharinosy
J. Opt. Soc. Am. A 40(8) 1628-1634 (2023)

Artifact-free analysis of highly conducting binary gratings by using the Legendre polynomial expansion method

Amin Khavasi and Khashayar Mehrany
J. Opt. Soc. Am. A 26(6) 1467-1471 (2009)