Simulation of dielectric gratings using impedance boundary conditions

The two-dimensional (2D) integral equation (IE) describing dielectric gratings is reduced to a one-dimensional (1D) IE. The expression for the impedance of dielectric strips is specified. The singular part of the IE kernel is separated and analytically transformed. The collocation and Galerkin methods are applied to solve the IE of the second kind with a smooth kernel. It is shown that the introduced impedance ensures a higher accuracy of calculations than the known one. The eigenmodes of impedance-diffraction gratings (DGs) and diffraction from a finite DG are studied.