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