Nonstandard finite difference models for the discrete Green´s function of the scattered field

The finite difference time domain (FDTD) method is easy to implement and can compute scattering and propagation in arbitrary structures, but it has two major drawbacks: (i) accuracy is low unless a fine grid is used - which greatly increases the computational cost, and (ii) when the structure has features that are much smaller than a wavelength, many grid points are needed just to represent the structure. Problem (i) has been addressed with the nonstandard (NS) FDTD method. In this paper we address problem (ii) by introducing a discrete Green´s function (DGF), which is evaluated using NS-FDTD. In computational photonics this approach is advantageous for computing transmission and reflection spectra of subwavelength structures. Although a DGF can be costly to compute and requires more storage than a FDTD calculation, it need be computed only once and gives solutions for arbitrary incident fields - with no further FDTD computations required.