# Non-reciprocal geometric phase in nonlinear frequency conversion

## TL;DR

This paper demonstrates how a non-reciprocal geometric phase can be achieved in nonlinear frequency conversion, offering a robust and practical approach immune to dynamic reciprocity issues in photonic devices.

## Contribution

It introduces a novel method to generate non-reciprocal geometric phases via momentum-dependent nonlinear frequency conversion, with a simple implementation and high robustness.

## Key findings

- Non-reciprocal geometric phase can be realized in nonlinear frequency conversion.
- The proposed method is immune to dynamic reciprocity limitations.
- Implementation requires only a single waveguide and one pump.

## Abstract

We describe analytically and numerically the geometric phase arising from nonlinear frequency conversion and show that such a phase can be made non-reciprocal by momentum-dependent photonic transition. Such non-reciprocity is immune to the shortcomings imposed by dynamic reciprocity in Kerr and Kerr-like devices. We propose a simple and practical implementation, requiring only a single waveguide and one pump, while the geometric phase is controllable by the pump and promises robustness against fabrication errors.