Numerical study of photonic crystals with a split band edge: Polarization dependence and sensitivity analysis

Abstract

We examine photonic crystals (PhC) made of periodic stacks of anisotropic dielectric layers with a split band edge (SBE) on the band diagram. Just below the band edge frequency, the dispersion relation $\ensuremath{\omega}(k)$ of SBE PhCs can be approximated as a linear combination of a quadratic term and a quartic term. This is in contrast to regular (conventional) band edge PhCs, which produce a quadratic dispersion relation, and to degenerate band edge (DBE) PhCs, which produce a quartic dispersion relation. Finite-size DBE PhCs and SBE PhCs are of interest because they both can support slow-wave Fabry-Perot resonances with very good transmittance. One of the most significant differences between DBE and SBE is that the transmittance of the former depends on the incident wave polarization whereas in the latter it does not. In this work, we investigate the transmittance behavior of SBE PhCs and perform a sensitivity analysis of their responses against geometrical and/or material perturbations. Dielectric losses, thickness perturbations, and misalignment angle perturbations are considered. The analysis uses a full-wave numerical technique for transient Maxwell's equations in inhomogeneous anisotropic media based on a complex-envelope alternating-direction-implicit finite-difference time-domain. A comparison is also made between the sensitivity of the SBE PhCs response versus that of DBE PhCs.