A 2D FDTD Algorithm for Whole-Hemisphere Incidence on Periodic Media

We present a modified version of the 2D split-field finite difference time domain (FDTD) method which enables efficient simulation of periodic structures. Our algorithm allows for broadband, whole-hemisphere oblique incidence sources with structures that are inhomogeneous in permittivity, conductivity, and permeability. The structures considered are of finite extent in one dimension, periodic in a second orthogonal dimension, and uniform (or homogeneous) in a third dimension. With prior FDTD methods, this required a full 3D simulation space. In this work, we reduce the modeling space from a 3D grid to a 2D grid, while still allowing incident waves to be oblique with respect to that dimension. We derive this new algorithm beginning with a complete source definition that allows for arbitrary polarization and incidence direction. The key update equations are found, and we also give a method for finding the full vectorial far-field orders from the simulation output. We validate the method by simulating an etalon, a Bragg grating, and a photonic band gap structure.