Analysis of electromagnetic scattering from doubly-periodic structures using a hybrid current model

A novel solution is presented for the problem of threedimensional electromagnetic scattering of a time-harmonic plane wave from a piecewise homogeneous doubly-periodic structure. The reduction of the problem to a consideration of the fields over a suitably selected unit cell of the periodic structure is facilitated by the Floquet theorem. Sets of fictitious doubly-periodic and properly modulated patches of magnetic current of cross polarization are used to simulate the fields in the homogeneous regions crossed by the unit cell boundaries. The fields radiated by these patch-currents are represented in terms of Floquet modes. Sets of fictitious elemental electric dipoles of cross polarization are used to simulate the fields in the homogeneous regions completely enclosed within this cell. The complex amplitudes of the fictitious sources are adjusted to render the tangential components of the electric and magnetic fields continuous at selected sets of points on the boundaries between the regions within the unit cell. The suggested solution-procedure is simple to implement. It is applicable to doubly-periodic gratings composed of homogeneous regions of smooth, but otherwise arbitrary, shape. Perfectly conducting boundaries can also be handled by this procedure. The accuracy of the method has been verified by means of several accuracy checks. It has also been shown that in the limiting case of array of widely spaced spherical scatterers the numerical solution agrees well with an approximate analytic solution.