Modified Rayleigh Conjecture for scattering by periodic structures
  This paper contains a self-contained brief presentation of the scattering theory for periodic structures. Its main result is a theorem (the Modified Rayleigh Conjecture, 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. 
A.G.Ramm, S.Gutman