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An all-optical switch based on an absorbing microring resonator laterally coupled to two waveguides is described theoretically using the coupling of modes in time formalism and numerically using the finite-difference time-domain method. The operating principle of the device is based on the recently published time-reversed laser concept. The proposed switch relies on a combination of coherent interference and absorption in the microring and does not require nonlinear refractive index changes. It has a smaller footprint than other approaches, and it is capable of converting frequency- or phase-shift-keyed digital signals to amplitude-shift-keyed signals for direct detection.