Nonreciprocity and zero reflection in nonlinear cavities with tailored loss

We demonstrate how to tailor the losses of nonlinear cavities in order to suppress their reflection and enhance their nonreciprocal transmission. We derive analytical expressions predicting the existence of zero-reflection channels in single and coupled nonlinear cavities, depending on the driving frequency and loss rates. While suppressing the reflection from a single cavity imposes a stringent condition on the input-output leakage rates, we demonstrate that this condition can be significantly relaxed in systems of coupled cavities. In particular, zero-reflection and nonreciprocity can be achieved across a range of driving frequencies in coupled cavities by tuning the output leakage rate alone. Numerical calculations based on the driven-dissipative Gross-Pitaevskii equation, usually employed to describe microcavity polaritons, reveal the spatial phenomenology associated with zero-reflection states and provide design guidelines for the construction of nonlinear optical isolators.