Modeling of unidirectional radiation of microdisk resonators with small piercing holes by Galerkin method with accurately computed matrix elements

Using the integral-equation-based in-house guaranteed-convergence numerical code, we study the effect of a circular air hole on the frequency, threshold gain and directionality of emission of the whispering-gallery modes of a two-dimensional model of circular-disk microcavity laser. It is shown that a small hole can enhance the directionality greatly and leave the threshold gain intact, if the disk‘s refractive index is large enough and the hole‘s location is chosen properly. This location should be close to the area, in which the same uniform disk, if illuminated with a plane wave, would display a broadband focusing in the form of a hot spot called a photonic jet.