Boundary integral equation Neumann-to-Dirichlet map method for gratings in conical diffraction.

Boundary integral equation methods for diffraction gratings are particularly suitable for gratings with complicated material interfaces but are difficult to implement due to the quasi-periodic Green's function and the singular integrals at the corners. In this paper, the boundary integral equation Neumann-to-Dirichlet map method for in-plane diffraction problems of gratings [Y. Wu and Y. Y. Lu, J. Opt. Soc. Am. A26, 2444 (2009)] is extended to conical diffraction problems. The method uses boundary integral equations to calculate the so-called Neumann-to-Dirichlet maps for homogeneous subdomains of the grating, so that the quasi-periodic Green's functions can be avoided. Since wave field components are coupled on material interfaces with the involvement of tangential derivatives, a least squares polynomial approximation technique is developed to evaluate tangential derivatives along these interfaces for conical diffraction problems. Numerical examples indicate that the method performs equally well for dielectric or metallic gratings.