THE TIME-HARMONIC MAXWELL EQUATIONS IN A DOUBLY PERIODIC STRUCTURE

Consider the diffraction of a beam of particles in R3 when the dielectric coefficient is a constant ε1 above a surface S and a (different) constant ε2 below S, and the magnetic permeability is constant μ throughout R3. S is assumed to be a doubly periodic surface, say z = f(x, y) with f(x + mL1, y + nL2) = f(x, y) for integers m, n. The existence and uniqueness of a solution satisfying a "radiation condition" at infinity is reduced to a system of Fredholm equations. Thus, for all but a discrete set of ε's there exists a unique solution. © 1992.