Scattering theory for diffraction gratings / Calvin H. Wilcox

This very interesting and nicely written monograph develops a theory of the scattering of transient electromagnetic and acoustic fields by diffraction gratings. The theory is based on an eigenfunction expansion for gratings in which the eigenfunctions are Rayleigh-Bloch waves. The theory of scattering by gratings developed in the monograph is restricted to two-dimensional wave propagation. In particular waves are assumed to be solutions of the wave equation in a two-dimensional grating domain and to satisfy Dirichlet or Neumann boundary conditions on the grating profile. These problems provide models for the scattering of sound waves by acoustically soft or rigid gratings and of TE or TM electromagnetic waves by perfectly conducting gratings. The methods employed are applicable to the scattering of scalar waves by three-dimensional gratings and to systems such as Maxwell's equations and the equation of elasticity. (Zentralblatt)