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Resonant power exchange process in asynchronous microring-assisted directional couplers (MRDCs) is proposed as a new approach for achieving complete power coupling between dissimilar waveguides. Theoretical analysis based on the coupled mode theory and verified by finite difference time domain simulations shows that complete cross power transfer between the two bus waveguides of an MRDC can be obtained near the microring resonances. Moreover, this power exchange occurs over a much shorter coupling length than existing techniques such as grating-assisted couplers and adiabatic taper couplers. These asynchronous MRDC structures are also characterized by spectral responses with steep transition slopes, suggesting new device possibilities for applications such as power couplers, switches, modulators, and optical sensors.