Abstract

The Fourier modal method in Cartesian coordinates uses Fourier series as the expansion basis [1]. This leads to periodic boundary conditions, which is advantageous for periodic structures like photonic crystals. However, for modelling open geometries periodic boundary conditions leads to parasitic reflections from the leaky modes into the computational domain. This can be overcome by using absorbing boundaries, such as perfectly matched layers (PMLs), but convergence of these PML boundaries towards an open geometry limit is generally not obtained. [2]. To avoid the need for PMLs open boundary conditions can be used and recently this was developed for structures having cylindrical symmetry [3], where a non-uniform sampling of the k-space was shown to converge much faster than for the standard equidistant k-space discretization. The open boundaries are introduced by using Fourier integrals instead of Fourier series as the expansion basis for the eigenmodes.

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