Spectra and thresholds of the 2-D modes in a ring microcavity laser

Semiconductor microdisk and microring lasers are of interest for micron-scale low-threshold laser devices. The modes of a thin dielectric cavity are complicated solutions of the 3-D Maxwell equations. However, if the disk or ring cavity thickness is only a fraction of the wavelength the modes can be studied in 2-D formulation. In this paper we study lasing eigenvalue problem (LEP) for the H-polarised modes in a ring dielectric microcavity. The analysis revealed the following facts: the WG modes experience quasitotal reflection at the cavity rim that leads to exponentially small threshold getting down with index m. In each m-th family WG_m,1 mode has the lowest threshold. In the range k< m/α lasing modes are found. The lowest thresholds are observed if the inner radius b is small. Only the modes WGHm1 having large enough values of m can "survive" the thin ring-like cavities(b≈a).