Cold-cavity thresholds of microdisks with uniform and nonuniform gain: quasi-3-D modeling with accurate 2-D analysis

An electromagnetic analysis of thin-disk semiconductor resonators with uniform and nonuniform gain regions is presented. A "cold-cavity-with-gain" Maxwellian formulation, including accurate boundary and radiation conditions, is considered as an eigenvalue problem, for the real-valued parameters of frequency and threshold material gain. Although the well-known approximate effective-index method is used to reduce a three-dimensional (3-D) field problem to a two-dimensional (2-D) one, a rigorous formulation of the latter is retained. A quasi-3-D feature is provided through full account of the multiple-wave nature and dispersion of the effective index. Results obtained quantify the ultralow thresholds of the whispering-gallery modes and show the advantage of a ring-shaped gain region.