Abstract
The paper presents results which form a theoretical basis for solving numerically the problem of electromagnetic wave scattering by two-dimensionally periodic structures in time domain. The respective initial boundary-value problems are posed in a mathematically rigorous formulation, including in particular the exact absorbing conditions on the virtual boundaries in the transverse cross-section of the rectangular Floquet channel. Using these conditions it is possible to reduce the original initial boundary-value problem with an infinite domain of analysis to an equivalent closed problem in a bounded region which can be solved numerically using the familiar finite-difference algorithms.