Photonic crystals with a degenerate band edge: Field enhancement effects and sensitivity analysis

Abstract

Photonic crystals (PhCs) with a degenerate band edge (DBE) are dispersion-tailored materials composed of a periodic arrangement of misaligned anisotropic dielectric layers and an isotropic dielectric layer. DBE PhCs yield an (approximately) quartic dispersion relation just below the DBE frequency rather than the conventional quadratic dispersion relation present below a regular band edge (RBE). We present a sensitivity analysis of the performance of DBE PhCs under various perturbations. This analysis is made possible by means of an unconditionally stable finite-difference time-domain scheme to solve Maxwell's equations in anisotropic media based on a complex-envelope alternating-direction-implicit algorithm. Numerical simulations are performed to examine the gigantic field intensity enhancement at Fabry-Perot resonances associated with finite-stack DBE PhCs. Numerical simulations are also used to investigate the sensitivity of field enhancement effects against the bandwidth of the excitation. The effects of layer thickness perturbations, grounding, and dielectric losses on the electromagnetic response of DBE PhCs are also examined. The numerical results are used to compare Fabry-Perot RBE resonances against Fabry-Perot DBE resonances.