Efficient electromagnetic analysis of a doubly infinite array of rectangular apertures

An accurate and rapid method is presented for solving the magnetic field integral equation for the equivalent magnetic currents representing a doubly periodic array of rectangular apertures. Ewald´s method is used to accelerate the summations associated with periodic Green´s function, allowing the Green´s function to be determined to nearly machine precision. Galerkin´s method is used to discretize the integral equation with Chebyshev polynomials used as the basis and testing functions. Efficient treatment of the “self-term” singularity is emphasized