Efficient Complex Envelope ADI-FDTD Method for the Analysis of Anisotropic Photonic Crystals

This letter presents a new efficient formulation of the recently proposed complex envelope alternating direction implicit finite-difference time-domain (CE-ADI-FDTD) method for anisotropic photonic crystal (PhC) analysis. The proposed CE-ADI-FDTD method is based on a concise E-H formulation that is more efficient and simpler to implement compared to the conventional method. The concise formulation includes perfectly matched layer (PML) boundary conditions and caters for nonuniform grid discretization. The efficiency of the proposed CE-ADI-FDTD method is validated through a numerical study of the field enhancement effect in a finite sized PhC composed of periodic cells of misaligned anisotropic dielectric layers with split band edge (SBE) on the band diagram. In the numerical study, we further illustrate that by properly tuning the orientation angles of the anisotropy axes of the SBE PhC layers, the field enhancement effect can be optimized for an incident wave polarization.