Non-reciprocal frequency conversion in a non-Hermitian 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 and reciprocity of nonlinear interactions generally places stringent limits on the efficiency of nonlinear optical processes and their ability to be tailored for advanced applications in multimode systems. 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 a frequency dimension, closely resembling the non-Hermitian skin effect (NHSE). Applying our theory to a multimode nonlinear cavity supporting cascaded nonlinear processes, we demonstrate chiral energy flow in a frequency dimension, leading to long-range frequency shifts of quasi-continuous wave sources, shaped frequency combs robust to defects and disorder, terahertz (THz) generation far exceeding the Manley-Rowe limit, and nonlinear multimodal limit cycles for multi-frequency pump-probe spectroscopy.