Thin-slot formalism for the FDTD analysis of narrow apertures having depth

Abstract

A new thin-slot formalism is presented for the finite-difference time-domain (FDTD) analysis of the coupling of narrow apertures having depth. To derive the formalism, the equivalence principle is used to divide the slot coupling problem into three decoupled parts. The field distribution near the aperture is gained from the equivalent magnetic current together with a constant field distribution assumption. By incorporating the field distribution into the Ampere's law and Faraday's Law, the updated equations are derived to modify the electromagnetic field components near the apertures. Two numerical examples are adopted to verify the validity of the proposed formalism, and both the high-resolution standard FDTD results and FEKO (FEldberechnung Bei Körpern mit beliebiger Oberfläche) result are presented as references. The proposed formalism is verified to be a stable and accurate model for thin-slot coupling.

A Fast Simulation Method of Silicon Nanophotonic Echelle Gratings and Its Applications in the Design of on-Chip Spectrometers

“…(7) and (8) as a simple model to analyze the numerical results. In the following simulations, we will give a more accurate calculation of the GH shift d TE or d TM by using the finite difference time domain (FDTD) method [26,27] in terms of different incidence angles. As shown in Figure 2(c), when an incident wavefront of the linearly polarized light makes a given angle θ d with the surface between silicon and air, we can simulate the total reflection phenomenon by using the FDTD method.…”