Complex Envelope PML-ADI-FDTD Method for Lossy Anisotropic Dielectrics

The complex envelope (CE) alternating-direction-implicit finite-difference time-domain (ADI-FDTD) algorithm augmented by perfectly matched layers (PML) is extended for lossy anisotropic dielectric media. The extension is based on a two-step discretization of complex envelope fields that factors out, on one hand, into modified Maxwell´s curl equations including complex stretching PML parameters and, on the other hand, into constitutive equations involving frequency-dependent nondiagonal permittivity and conductivity tensors that are implemented by auxiliary differential equations in the time-domain. The proposed method is validated against conventional FDTD results and illustrated to calculate FabryProt resonances in photonic crystals with degenerate band-edge, where very good accuracy is maintained with Courant numbers as large as 100.