Fourier modal methods for modeling optical dielectric waveguides

Abstract

This work contains new materials relative to the use of Fourier expansion techniques, also called plane-wave expansion techniques, for modelling normal modes of optical waveguides. Two rigorous fully vectorial methods are presented and benchmarked for a classical rib waveguide geometry well studied in the literature. The first method relies on a pole extraction and on a one-dimensional expansion scheme. A four-digit accuracy for the normalized propagation constant B is obtained for the dominant TE and TM modes of the benchmark problem and for a small number of retained Fourier harmonics. Better accuracy is anticipated for larger truncation ranks. The second method relies on a two-dimensional expansion scheme in Fourier space and provides a three-digit accuracy for the normalized propagation constant.

Modal properties of a strip-loaded horizontal slot waveguide

“…Both Fourier Modal Method (FMM) [16][17][18] and Finite Difference based mode solver, OptiMode by OptiWave [19,20], are used in this work to determine the optical mode profiles of the waveguides (slab or channels). In both cases a calculation window of 10 μm × 3.5 μm is taken into account with a mesh size of 20 nm in x-direction and 5 nm in y-direction.…”

“…The influence of the parameters, i.e., the thickness of the layers, is determined using a mode solver based on the Fourier Modal Method [16][17][18]. Accurate mode profiles and confinement factors are calculated by Finite Difference mode solver, OptiWave [19,20], in order to avoid ripples due to Gibbs phenomenon inherent to FMM.…”

Fourier Based Combined Techniques to Design Novel Sub-Wavelength Optical Integrated Devices

“…They can be classified attending different criteria. In this paper, we have chosen the F-EEM [10,11], which is a spectral method that belongs to the group of eigenmode expansion methods. It considers structures as longitudinally invariant sections joined by abrupt discontinuities.…”

“…Eigenmode Expansion Methods (EEM), used together with Floquet mode theory [8][9][10][11] allows a significantly reduction in memory requirements and computational time when compared with FDTD. The first implementations of EEM used a classical Finite Difference transversal discretization technique [8].…”

“…More recently, several implementations of the EEM based on the Fourier series expansion of the fields have been published [9][10][11]. These techniques are usually known as Fourier-EEM.…”