Efficient Computation of Periodic Green's Functions with Application to Grating Structures

摘要

It is shown that electromagnetic scattering from periodic structures may be formulated in terms of an integral equation that has as its kernel a periodic Green's function. The periodic Green's function may be derived from two points of view: as a response to an array of line/point sources (spatial domain) or as a response from a series of current sheets (spectral domain). These responses are a Fourier transform pair and are slowly convergent summations. The convergence problems in each domain arise from unavoidable singularities in the reciprocal domain. A method is discussed to overcome the slow convergence by using the Poisson summation formula and summing in a combination of spectral and spatial domains. A parameter study is performed to determine an optimum way to weight the combination of domains. Simple examples of scattering from a one-dimensional array of strips and two-dimensional array of plates are used to illustrate the concepts.