EFFICIENT CALCULATION OF THE FREE-SPACE PERIODIC GREEN-FUNCTION

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 to 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. © 1990 IEEE