Highly accurate schemes for 3D Maxwell equations with Lorentz media on the basis of alternate direction implicit time stepping algorithms

An algorithm for computation of 3D unsteady diffraction problems for Maxwell equations in Lorentz media is suggested. The algorithm is based on the alternate direction implicit scheme and pseudospectral approximation of spatial derivatives. Order of approximation in time is equal to 2, 4 or 6. The Lorentz dispersion is taken into account by means of introducing additional auxiliary unknowns in the first order governing system. Computational cost of the algorithm is of order $O(N^3)\log N$ operations per time step, where $N$ is a number of grid points in one direction.