Transient analysis of spectrally asymmetric magnetic photonic crystals with ferromagnetic losses

We analyze transient electromagnetic pulse propagation in spectrally asymmetric magnetic photonic crystals (MPCs) with ferromagnetic losses. MPCs are dispersion-engineered materials consisting of a periodic arrangement of misaligned anisotropic dielectric and ferromagnetic layers that exhibit a stationary inflection point in the (asymmetric) dispersion diagram and unidirectional frozen modes. The analysis is performed via a late-time stable finite-difference time-domain method (FDTD) implemented with perfectly matched layer (PML) absorbing boundary conditions, and extended to handle (simultaneously) dispersive and anisotropic media. The proposed PML-FDTD algorithm is based on a D-H and B-E combined field approach that naturally decouples the FDTD update into two steps, one involving the (anisotropic and dispersive) constitutive material tensors and the other involving Maxwell's equations in a complex coordinate space (to incorporate the PML). For ferromagnetic layers, a fully dispersive modeling of the permeability tensor is implemented to include magnetic losses in a consistent fashion. The numerical results illustrate some striking properties of MPCs, such as wave slowdown (frozen modes), amplitude increase (pulse compression), and unidirectional characteristics. The numerical model is also used to investigate the sensitivity of the MPC response against excitation (frequency and bandwidth), material (ferromagnetic losses), and geometric (layer misalignment and thickness) parameter variations.