  The lasing and coherent perfect absorption (CPA) properties of
$\mathcal{PT}$-symmetric microrings with mixed index and gain gratings,
externally coupled to a bus waveguide, are theoretically investigated. For a
complex grating at the $\mathcal{PT}$ symmetry breaking point, perfect
unidirectional (either clockwise or counterclockwise) laser emission can be
realized, however the grating does not discriminate longitudinal modes and CPA
can not be simultaneously achieved. Above the grating $\mathcal{PT}$ symmetry
breaking point, single mode emission and simultaneous CPA can be obtained, with
unbalanced and controllable excitation of clockwise and counterclockwise modes
in the ring.
