Time-domain matched interface and boundary (MIB) modeling of Debye dispersive media with curved interfaces

A new finite-difference time-domain (FDTD) method is introduced for solving transverse magnetic Maxwell's equations in Debye dispersive media with complex interfaces and discontinuous wave solutions. Based on the auxiliary differential equation approach, a hybrid Maxwell-Debye system is constructed, which couples the wave equation for the electric component with Maxwell's equations for the magnetic components. This hybrid formulation enables the calculation of the time dependent parts of the interface jump conditions, so that one can track the transient changes in the regularities of the electromagnetic fields across a dispersive interface. Effective matched interface and boundary (MIB) treatments are proposed to rigorously impose the physical jump conditions which are not only time dependent, but also couple both Cartesian directions and both magnetic field components. Based on a staggered Yee lattice, the proposed MIB scheme can deal with arbitrarily curved interfaces and nonsmooth interfaces with sharped edges. Second order convergences are numerically achieved in solving dispersive interface problems with constant curvatures, general curvatures, and nonsmooth corners.