Scattering matrix approach to the resonant states and Q-values of microdisk lasing cavities

We have developed a scattering-matrix approach for numerical calculation of resonant states and Q-values of a nonideal optical disk cavity of an arbitrary shape and of an arbitrary varying refraction index. The developed method has been applied to study the effect of surface roughness and inhomogeneity of the refraction index on Q-values of microdisk cavities for lasing applications. We demonstrate that even small surface roughness can lead to a drastic degradation of high-Q cavity modes by many orders of magnitude. The results of numerical simulation are analyzed and explained in terms of wave reflection at a curved dielectric interface combined with the examination of Poincare surfaces of section and Husimi distributions.