Spherical Bragg resonators for lasing applications: a theoretical approach.

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 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 bilayer SBR, the threshold gain factor corresponds to a dopant density of Er of 5.63 × 10ions/cm. We believe, our work is the first theoretical demonstration of the ability to engineer optical amplification and threshold gain for lasing in SBRs.