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

Abstract

Microdisk structures have been used to achieve low-threshold lasing. For these microcavity lasers, the spontaneous emission coupling factor β is an important parameter since it determines the threshold current of the laser. Theoretical calculation of β 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 β 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 β can still be achieved, however, in a microdisk laser.