Describes a solution for the scattered fields due to a plane wave incident on an infinite grating of rectangular conducting patches on a multilayer substrate. The novelty of our solution lies in including the multilayer substrate by using the G1DMULT algorithm. Thereby the solution process has been considerably simplified. G1DMULT calculates the Green's functions of planar multilayer structures (Kildal et al., 1997). G1DMULT exists both as Fortran and Matlab subroutines. The present work is based on the Matlab version. G1DMULT can handle any number of layers of any permittivity and permeability. The results have been verified against previously published results in Chen (1970) and in Mittra et al. (1988). The patches form a grid in the x- and y-directions, and they can be positioned anywhere in the multilayer substrate. With the exception of the patch array, this problem is 1D with structure variation in one coordinate only (Kildal and Sanford, 1996). The metal patches, which are assumed to be thin and perfectly conducting, are replaced by equivalent surface currents. These currents are then expanded in sinusoidal basis functions over the patches with a phase shift between the different patches corresponding to the angle of incidence of the plane wave. The expansion coefficients are found by a moment method approach by enforcing the boundary condition of zero tangential electrical field on the patches. This field is a sum of the contributions from the equivalent current sheets representing the incident field and the unknown patch currents, both in the multilayer environment.
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