A Theoretical Model for an Optical Diode Built With Nonlinear Silicon Microrings

The optical diode effect, which is useful for on-chip optical information processing, has been recently demonstrated in cascaded nonlinear silicon microrings. In this paper, a semianalytical model for the diode is described in details, which extends the scope of the coupled-mode theory for linear microresonators to nonlinear regime through perturbation theory. The nonlinear effects addressed include the Kerr effect, two-photon absorption, free-carrier effect, and thermo-optic effect (TOE). Nonlinear effective mode volumes that characterize nonlinearities in the lumped element model are expressed using fields in vector forms. Simulations of the optical diode based on our model show good agreement with the measured spectra, where a forward-backward transmission ratio of ~ 28 dB is observed at an input power of ~ 1 mW. Moreover, TOE is discerned as the dominant nonlinearity in determining the diode functionality with this model. Being capable of dealing with photon-photon, photon-electron, and photon-phonon interactions, the methodology used here can be generalized and applied to model other microresonator-based opto-electronic devices.