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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 Fabry-Perot resonances in photonic crystals with degenerate band-edge, where very good accuracy is maintained with Courant numbers as large as 100.