Transparent boundary conditions for 2D Maxwell equations in Lorentz media

Transparent Boundary Conditions (TBCs) for 2D mode of Maxwell’s equations in dispersive media described by Lorentz theory are proposed. Analytical formulas of TBCs contain a non-local term with convolutions with respect to time. In order to discretize TBCs for the alternate direction implicit time-stepping algorithm (ADI) derived in [1] for extended system we reformulate convolutions using auxiliary variables.