The lasing and coherent perfect absorption (CPA) properties of -symmetric microrings with mixed index and gain gratings, externally coupled to a bus waveguide, are theoretically investigated. For a complex grating at the -symmetry breaking point, perfect unidirectional (either clockwise or counterclockwise) laser emission can be realized, but the grating does not discriminate longitudinal modes and CPA can not be simultaneously achieved. Above the grating the -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.
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