Describing discontinuous finite 3D scattering objects in Gabor coefficients: fast and accurate methods

In relation to the computation of electromagnetic scattering in layered media by the Gabor-frame-based spatial spectral Maxwell solver, we present two methods to compute the Gabor coefficients of the transverse cross section of three-dimensional scattering objects with high accuracy and efficiency. The first method employs the analytically obtained two-dimensional Fourier transform of the cross section of a scattering object, which we describe by two-dimensional characteristic functions, in combination with the traditional discrete Gabor transform method for computing the Gabor coefficients. The second method concerns the expansion of the so-called dual window function to compute the Gabor coefficients by employing the divergence theorem. Both methods utilize (semi)-analytical approaches to overcome the heavy oversampling requirement of the traditional discrete Gabor transform method in the case of discontinuous functions. Numerical results show significant improvement in terms of accuracy and computation time for these two methods against the traditional discrete Gabor transform method.