Closed formulation for 3D problem on diffraction of electromagnetic pulse by gratings of dispersive materials

A closed formulation for 3D diffraction problem in a bounded domain, when an oblique incident electromagnetic pulse interacts with a double periodic grating of dispersive materials, is presented. In order to eliminate the convolution operator from the Maxwell equations for dispersive materials it is suggested to approximate with respect to time the susceptibility function by a sum of exponentials and to extend the set of unknown functions and the governing equation system accordingly. The field transformation technique is used to periodize the problem. The exact transparent boundary conditions for open boundaries are proposed. Problems of such type arise, for an example, while developing nanotechnologies.