Optical coupling of whispering-gallery modes of two identical microdisks and its effect on photonic molecule lasing

The lasing characteristics of a photonic molecule in the form of two optically coupled semiconductor microdisks are investigated. Electromagnetic analysis of the lasing spectra and linear thresholds of the coupled whispering-gallery (WG) modes of four different symmetry classes is presented. Here, Maxwell\´s equations and accurate boundary and radiation conditions are considered as a specific "cold-cavity-with-gain" eigenvalue problem. Each eigenvalue is a pair of real-valued parameters -frequency and threshold material gain. In the two-dimensional (2-D) approximation, based on the introduction of an effective refractive index, this problem is reduced to a determinant equation with favorable features. A secant-type method is further used to calculate thresholds and lasing frequencies numerically. Results obtained show that optical coupling may lead to a further reduction of the ultralow thresholds of the WG modes, although the opposite, i.e., threshold spoiling, is more common.