Fourier modal method with spatial adaptive resolution for structures comprising homogeneous layers

Abstract

A numerical improvement of the Fourier modal method with adaptive spatial resolution is obtained. It is shown that the solutions of all the eigenvalue problems corresponding to homogeneous regions can be deduced straightforwardly from the solution of one of these problems. Numerical examples demonstrate that computation time saving can be substantial.

New reformulation of the Fourier modal method with spatial adaptive resolution for multilayered metallic strip grating

“…Later on, with the discovery of spatial adaptive resolution (ASR) [6], the CBCM has been substantially improved [7] in the sense that it was rid of the problems inherent to Fourier series (slow convergence and Gibbs phenomenon). In [8], the ASR has been extended to multilayered structures in the context of the Fourier modal method and very recently improved further [9]. In the present paper, we (i) extend the CBCM equipped with the ASR to multilayered strip gratings and (ii) show that the additional computational steps introduced by the ASR (time consuming eigenvlaue problems) can be drastically reduced.…”

“…In the present case and due to the z invariance, the problem reduces to the two classical cases of polarization TE (electric field parallel to the strips) and TM (magnetic field parallel to the strips). For homogeneous media, the wave equation has been shown to have the same expression for both of these polarizations [9]:…”

“…This represents a non negligible supplementary computational effort compared to the classical CBCM. But as (i) we are dealing with homogeneous layers and (ii) we use the same coordinate transformation for all the layers, it is possible to reduce drastically the computational load as has been shown recently [9]. The key idea is the link between the matrices of the input, the output region and the different layers:…”

Numerical Investigation of Vertical Cavity Lasers With High-Contrast Gratings Using the Fourier Modal Method

“…However, if there are several homogeneous layers, a simple relationship can be found between their eigenmodes, as discussed in Ref. [48] for 2D problems. Here, we derive a similar relation for 3D cases.…”

Modal Method Based on Subsectional Gegenbauer Polynomial Expansion for Lamellar Gratings: Weighting Function, Convergence and Stability

“…Except for the original Fourier Modal Method (FMM) where the solutions in the homogeneous media are given by the classical Rayleigh expansions, for the other modal approaches, it is necessary to solve numerically at least one eigenvalue problem [12]. This can lead to numerical difficulties if one is dealing with normal incidence or the Littrow configuration where some eigenvalues are degenerate which make it difficult to associate them with the appropriate orders.…”