  Nonlinear effects in microresonators are efficient building blocks for
all-optical computing and telecom systems. With the latest advances in
microfabrication, coupled microresonators are used in a rapidly growing number
of applications. In this work, we investigate the coupling between
twin-resonators in the presence of Kerr-nonlinearity. We use an experimental
setup with controllable coupling between two high-Q resonators and discuss the
effects caused by the simultaneous presence of linear and non-linear coupling
between the optical fields. Linear-coupling-induced mode splitting is observed
at low input powers, with the controllable coupling leading to a tunable mode
splitting. At high input powers, the hybridized resonances show spontaneous
symmetry breaking (SSB) effects, in which the optical power is unevenly
distributed between the resonators. Our experimental results are supported by a
detailed theoretical model of nonlinear twin-resonators. With the recent
interest in coupled resonator systems for neuromorphic computing, quantum
systems, and optical frequency comb generation, our work provides important
insights into the behavior of these systems at high circulating powers.
