Diffraction by a multilayer-coated bisinusoidal grating

Diffraction from a multilayer-coated bisinusoidal grating is analyzed by Yasuura's mode-matching method. The diffracted fields over the coating, inside the layers, and below the metal surface are represented in terms of finite modal expansions consisting of vector modal functions with unknown coefficients. Since the functions satisfy the vector wave equation and the periodicity and radiation condition, the coefficients are determined so that the representations meet the boundary condition in the least-squares sense. In the present problem where the geometry has several boundaries that are corrugated in two directions, however, the size of the least-squares problem becomes so large that we face the problem of memory deficiency in handling the problem on a computer. We, hence, employ the technique of sequential accumulation in solving the problem, a technique which considerably decreases the memory demand and enables us to solve the problem on a small-sized computer.