Applications of nonstandard finite difference models to computational electromagnetics

We introduce an exact nonstandard finite-difference model of the one-dimensional absorbing wave equation, and use it to develop a high accuracy version of the finite-difference time-domain (FDTD) algorithm to solve the absorbing wave equation and the conducting Maxwell's equations in two and three dimensions. For grid spacing h , and wavelength lambda, the solution error of the ordinary FDTD algorithm is epsilon similar to( h / lambda )(2) , because it uses second-order central finite difference approximations. By exploiting the analytical properties of decaying-harmonic solution basis functions in a nonstandard finite difference model we reduce the error to epsilon similar to( h / lambda )(6) without using higher order finite differences. We have verified the accuracy of the algorithms by comparing with analytic solutions of near-field Mie scattering, and have used them to investigate the optical properties of subwavelength conductive diffraction gratings.