High accuracy models of sources in FDTD computations for subwavelength photonics design simulations

Abstract

The simple source model used in the conventional finite difference time domain (FDTD) algorithm gives rise to large errors. Conventional second-order FDTD has large errors (order h **2/ 12), h = grid spacing), and the errors due to the source model further increase this error. Nonstandard (NS) FDTD, based on a superposition of second-order finite differences, has been demonstrated to give much higher accuracy than conventional FDTD for the sourceless wave equation and Maxwell’s equations (h**6 / 24192). Since the Green’s function for the wave equation in free space is known, we can compute the field due to a point source. This analytical solution is inserted into the NS finite difference (FD) model and the parameters of the source model are adjusted so that the FDTD solution matches the analytical one. To derive the scattered field source model, we use the NS-FD model of the total field and of the incident field to deduce the correct source model. We find that sources that generate a scattered field must be modeled differently from ones radiate into free space. We demonstrate the high accuracy of our source models by comparing with analytical solutions. This approach yields a significant improvement inaccuracy, especially for the scattered field, where we verified the results against Mie theory. The computation time and memory requirements are about the same as for conventional FDTD. We apply these developments to solve propagation problems in subwavelength structures.