  Monochromaticity and directionality are two key characteristics of lasers.
However, the combination of directional emission and single-mode operation is
quite challenging, especially for the on-chip devices. Here we propose a
microdisk laser with single-mode operation and directional emissions by
exploiting the recent developments associated with parity-time (PT) symmetry.
This is accomplished by introducing one-dimensional periodic gain and loss into
a circular microdisk, which induces a coupling between whispering gallery modes
with different radial numbers. The lowest threshold mode is selected at the
positions with least initial wavelength difference. And the directional
emissions are formed by the introduction of additional grating vectors by the
periodic distribution of gain and loss regions. We believe this research will
impact the practical applications of on-chip microdisk lasers.
