An improved perfectly matched layer for the eigenmode expansion technique

Abstract

When performing optical simulations for rotationally symmetric geometries using the eigenmode expansion technique, it is necessary to place the geometry under investigation inside a cylinder with perfectly conducting walls. The parasitic reflections at the boundary of the computational domain can be suppressed by introducing a perfectly matched layer (PML) using e.g. complex coordinate stretching of the cylinder radius. However, the traditional PML suffers from an artificial field divergence limiting its usefulness. We show that the choice of a constant cylinder radius leads to mode profiles with exponentially increasing field amplitudes resulting in numerical instability. As a remedy we propose an improved PML based on a mode-dependent cylinder radius and mode profiles with stable field amplitudes. The new PML formulation eliminates the artificial field divergence and ensures numerical stability.

The role of phonon scattering in the indistinguishability of photons emitted from semiconductor cavity QED systems

“…We vary the number of layer pairs N top in the top distributed Bragg reflector while keeping a fixed number N bottom = 28 in the bottom mirror. The computations are performed using the eigenmode expansion technique [88] with improved perfectly matched layers [89].…”

Dimensionality reduction in computational photonics

“…VEIM calculations with a larger number of basis modes yield converged results, just as the established BEP schemes. Contrary to the BEP method with PMLs, however, our solutions are continuous everywhere; no discontinuities appear on the interfaces between slices, which is a problem for BEP especially when using a low number of modes, and the peaks near the PML boundaries that can appear in standard BEP [29] have not been observed in the current results.…”

Modeling open nanophotonic systems using the Fourier modal method: generalization to 3D Cartesian coordinates

“…Here the notation f (x, y Si ) means that the function is evaluated within section S i and is only dependent on the x coordinate within that section. With this separation, it is possible to factorize ε using the correct factorization rules provided that the discretized basis set features separable k x and k y dependency as in (11). If this is the case, we can index the k x and k y contributions to the basis mode k vector as (k m x , k l y ) using separate indices m and l. It is then possible to apply the inverse rule to the product ε x E x factorized along the x direction by first preparing the Fourier transform along the x axis of the inverse permittivity as…”