Spherical Bragg resonators for lasing applications: a theoretical approach

Abstract

This work considers a perfect 3D omnidirectional photonic crystal; Spherical Bragg Resonators (SBR), for lasing applications. We use the recursive transfer matrix method to study scattering in an Er 3+ doped SBR. We find the threshold gain factor for lasing by scanning poles and zeros of the S-matrix in the complex frequency plane. For a six Si/SiO 2 bilayer SBR, the threshold gain factor corresponds to a dopant density of Er 3+ of 5.63 × 10 20 ions / cm 3 . We believe, our work is the first theoretical demonstration of the ability to engineer optical amplification and threshold gain for lasing in SBRs.