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Efficient calculation of the free-space periodic Green's function

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2 Author(s)
Jorgenson, R.E. ; Dept. of Electr. & Comput. Eng., Illinois Univ., Urbana, IL, USA ; Mittra, R.

Electromagnetic scattering from periodic structures can be formulated in terms of an integral equation that has as its kernel a periodic Green's function. The periodic Green's function can be derived as a response to an array of line/point sources (spatial domain) or as a response to 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 weigh 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

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Antennas and Propagation, IEEE Transactions on  (Volume:38 ,  Issue: 5 )