Electromagnetic Scattering by Periodic Structures

This paper is devoted to the scattering of electromagnetic waves by quite general biperiodic structures which may consist of anisotropic optical materials and separate two regions with constant dielectric coefficients. The time-harmonic Maxwell equations are transformed to an equivalent $H^1$-variational problem for the magnetic field in a bounded biperiodic cell with nonlocal boundary conditions. The existence of solutions is shown for all physically relevant material parameters. The uniqueness is proved for all frequencies excluding possibly a discrete set. The results of the general problem are compared with known results for a special case, the conical diffraction.