Non-reciprocal frequency conversion in a multimode nonlinear system

Nonlinear optics has become the workhorse for countless applications in classical and quantum optics, from optical bistability to single photon pair generation. However, the intrinsic weakness of optical nonlinearity has meant that large input powers and weak output powers are often a necessity in nonlinear frequency conversion. Here, motivated by recent advances in using non-Hermitian photonics and gain/loss engineering to enable non-reciprocal light transport, we explore how the interplay between non-Hermiticity and optical nonlinearity leads to a fundamentally new regime of nonlinear frequency conversion. We show how non-Hermitian coupling between discrete frequency modes can result in non-reciprocal flow of energy in the frequency dimension, closely resembling the non-Hermitian skin effect (NHSE). Applying our theory to a multimode nonlinear cavity supporting cascaded nonlinear processes, we create an asymmetric infrared (IR) comb that features a ``skin'' frequency mode populated with efficiency exceeding 85\%. Furthermore, we demonstrate how three-wave mixing processes in the non-reciprocal infrared comb we generate enables terahertz (THz) generation exceeding the Manley-Rowe limit. We then show how the non-reciprocal frequency conversion is robust against cavity defects and disorder that cause random fluctuations in the dissipation rate for different modes. Moreover, in certain regimes, the nonlinear, non-Hermitian system supports stable limit cycles that can enable multimode pulsing with picosecond pulse widths and GHz repetition rates. Finally, we explore how the system can be applied to generate simultaneous IR and THz frequency combs, potentially unlocking novel applications in spectroscopy and metrology.