(Work in conjunction with G. V. Morozov, M. Sieber and H. Waalkens )

A new design of dielectric microcavities supporting modes with large quality factors and highly directional light emission is presented. The key idea is to place a point scatterer inside a dielectric circular microdisk. It is shown that, depending on the position and the strength of the scatterer, this design leads to highly directional modes in various frequency regions while preserving the high $Q$-factors reminescent of the whispering gallery modes of the microdisks without scatterer. The design presented is very appealing due to its simplicity which promises a simpler experimental realisation than other microcavity designs studied earlier on the one hand and its analytic tractability based on Green's function techniques and self-adjoint extension theory on the other hand.