Integral equations for conical diffraction by coated grating (Q548793)

The author studies a scattering problem for time-harmonic electromagnetic plane waves by gratings, which are media with particular symmetry properties: they are constant with respect to a given Cartesian coordinate and periodic with respect to another Cartesian coordinate. In particular, coated gratings are given by two non-intersecting interfaces that separate different homogeneous media. For this kind of structure, oblique incident plane waves are considered. The scattering problem is formulated as a two-dimensional boundary value problem for the Helmholtz equation, and it is also formulated as a system of suitable integral equations. The analytic properties of the corresponding integral operators are analyzed, and it is shown the integral equation formulation is equivalent to the differential equation formulation. For the integral equation formulation, existence and uniqueness results are provided.