Estimation of the spontaneous emission factor for microdisk lasers via the approximation of whispering gallery modes

Microdisk structures have been used to achieve low-threshold lasing. For these microcavity lasers, the spontaneous emission coupling factor p is an important parameter since it determines the threshold current of the laser. Theoretical calculation of p based on the exact solution of the modes in a microdisk is complicated. A simple, approximate method for solving the waveguide modes and the density of states is developed here, using conformal transformation and the Wentzel-Kramers-Brillouin approximation and taking into account the effect of the disk thickness. We find that the p value for a microdisk laser is smaller than that of an ideal laser that has a cylindrical waveguide structure with a strong index guiding. A considerably high value of 0 can still be achieved, however, in a microdisk laser.