Modelling open nanophotonic structures using the Fourier modal method in infinite domains

摘要

Summary form only given. 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.In this work we have developed an open-geometry Fourier modal method with open boundary conditions in 3D Cartesian coordinates [5]. Our results show that a non-uniform sampling of the k-space is essential to obtain good convergence especially for the leaky modes. This is seen in Fig. 1, where the emission rates into the guided and radiating modes and the beta factor are computed using (a) a similar non-uniform discretization of the k-space as in [3] and (b) using an equidistant k-grid employing the direct rule and Li's inverse rule for Fourier factorization [4]. The emission rate into the guided modes is well described with both discretization schemes, but the radiation modes are poorly described with the equidistant grid. Additionally, we will discuss which type of geometries benefits from the open-geometry Fourier modal method.