Multistable states of light in two coupled silica microresonators with dominating thermo-optical nonlinearity

We present a comprehensive theoretical analysis of thermo-optical multistability in two coupled silica microresonators with identical and slightly different partial eigenfrequencies. We consider a unidirectionally pumped system with a relatively low total Q-factor, where thermo-optical nonlinearity dominates. To analyze the system behavior, we employ a dynamical system approach that takes into account the hierarchy of the timescales associated with optical and thermal processes. We show that up to nine stationary states are possible for the same system parameters and that no more than four of them can be stable. Additionally, self-oscillation regimes are observed within specific parameter ranges. Bifurcations are discussed and nontrivial hysteretic switchings between light states under smooth pump frequency sweeping for different pump powers are demonstrated. It is also shown that even small intermode detuning can affect the dynamics of the system dramatically. This intriguing phenomenon is of fundamental interest and may potentially be used in the development of ultrasensitive sensors when operating near a bifurcation point, which is also discussed.