Electromagnetic scattering from a doubly-periodic grating corrugated by cubical cavities

The author presents a rigorous theoretical formalism describing the diffraction of a plane wave by a bigrating of cubical cavities hollowed in a planar surface of perfectly conducting material. This problem is treated analytically as a coupling result of the conventional TE and TM polarization case. Based on Floquet´s theorem, the mode-matching method is used to solve the system of linear equations that have been derived by enforcing the electromagnetic boundary conditions for different sets of the scattering parameters. Diffraction efficiency curves are generated as a function of the cavity´s dimension with good numerical stability. The results not only demonstrate the dispersion characteristics, but also provide a method of computing the diffraction efficiencies for the bigrating structures