Optical microdisk resonators with circular boundaries support whispering gallery modes (WGMs) that travel along the boundary. Due to their extremely high Q-factors they have found many applications in, e.g., low-threshold lasing, the sensing of nanoparticles, optical filtering, and nonlinear optics. Recently, it has been demonstrated that the placement of a small scatterer within the microdisk can lead to highly directional modes in various frequency regimes while keeping the high Q-factors. The scatterer lifts the degeneracy of the pairs of clockwise and counter-clockwise propagating modes of the unperturbed circular disk and leads to two standing wave modes.
The frequency of the first mode is affected by the scatterer whereas the second mode has a nodal line at the position of the scatterer and its frequency is left unaffected. As a result, more than one scatterer is needed if one wants to change the frequencies of both modes of a degenerate pair. We apply a Green’s function method that is based on self-adjoint extension theory for point scatterers to compute the resonant modes with high efficiency and in a systematic way. We show that the placement of two or more scatterers can be used to split the emission into several chosen directions.