A spectral integral method for periodic and nonperiodic structures

For a homogeneous scatterer with arbitrary geometry in free space, the surface integral equation method is a powerful tool to calculate the scattered electromagnetic fields. The method of moments (MoM) is a classical method for solving such integral equations, and has recently been accelerated by the fast multipole method (FMM). We propose a spectral integral method as an alternative way of solving the surface integral equation efficiently. We apply it to both periodic and nonperiodic electromagnetic problems involving PEC and dielectric objects. The main ingredients of the method are the use of a fast Fourier transform (FFT) algorithm and the subtraction of singularities in Green's functions to achieve a spectral accuracy in the integral. The accuracy and efficiency of the method is markedly improved from the method of moments as the sampling density can be reduced to less than three points per wavelength. The method can be further extended to three dimensions.