Theoretical determination of lasing resonances in a microring

We present a theoretical development for the lasing frequencies of a microring laser. Such a microring is typically made from an optically active polymer, which is fabricated on a metallic wire or glass optical fiber in order to provide a substrate of well-defined geometry. Lasing resonances of the microring are computed as zeros of characteristic equations, which can be arranged such that a whispering gallery term appears explicitly together with a residual term associated with waveguide modes. It is found that the residual term recedes as the thickness of the microring increases, leaving a characteristic equation associated with a pure whispering gallery mode (WGM). The resonant condition is examined to compute the lasing frequencies and the thickness of the microring that supports WGM. Computed data are compared with published experimental data on polymer microring lasers, and computed results match well with experiments.