Adiabatic Absorbers in Photonics Simulations with the Volume Integral Equation Method

This paper describes the implementation and performance of adiabatic absorbing layers in a fast Fourier transform (FFT)-accelerated volume integral equation (VIE) method for simulating truncated nanophotonics structures. At the truncation sites, we place absorbing regions in which the conductivity is increased gradually in order to minimize reflections. In the continuous setting, such adiabatic absorbers have been shown via coupled-mode theory to produce reflections that diminish at a rate related to the smoothness of the absorption profile function. The VIE formulation we employ relies on uniform discretizations of the geometry over which the continuously varying fields and material properties are represented by piecewise constant functions. Such a discretization enables the acceleration of the method via the FFT and, furthermore, the introduction of varying absorption can be performed in a straightforward manner without compromising this speedup. We demonstrate that, in spite of the crude discrete approximation to the smooth absorption profiles, our approach recovers the theoretically predicted reflection behavior of adiabatic absorbers. We thereby show that the FFT-accelerated VIE method is an effective and fast simulation tool for nanophotonics simulations.