TL;DR: In this paper, the authors present a self-contained brief presentation of the scattering the-ory for periodic structures and present a theorem (the Modified Rayleigh Conjec-ture, or MRC) which gives a rigorous foundation for a numerical method for solving the direct scattering problem.
Abstract: This paper contains a self-contained brief presentation of the scattering the- ory for periodic structures. Its main result is a theorem (the Modified Rayleigh Conjec- ture, or MRC), which gives a rigorous foundation for a numerical method for solving the direct scattering problem for periodic structures. A numerical example illustrating the procedure is presented.