# Four-wave Mixing of Topological Edge Plasmons in Graphene Metasurfaces

## TL;DR

This paper demonstrates topologically protected four-wave mixing in graphene metasurfaces, achieving significant nonlinear interaction and net gain at very low pump powers, promising advances in integrated quantum photonics.

## Contribution

It introduces a novel topological plasmonic system in graphene that enables efficient four-wave mixing with ultra-low power requirements.

## Key findings

- Net gain of FWM interaction achieved with less than 10 nW pump power.
- Effective waveguide nonlinearity coefficient is about 1.1x10^13 1/(Wm).
- Potential for ultra-low-power, highly-integrated photonic systems.

## Abstract

We study topologically-protected four-wave mixing (FWM) interactions in a plasmonic metasurface consisting of a periodic array of nanoholes in a graphene sheet, which exhibits a wide topological bandgap at terahertz frequencies upon the breaking of time-reversal symmetry by a static magnetic field. We demonstrate that due to the significant nonlinearity enhancement and large lifetime of graphene plasmons in specific configurations, a net gain of FWM interaction of plasmonic edge states within the topological bandgap can be achieved with pump power of less than 10 nW. In particular, we find that the effective waveguide nonlinearity coefficient is about 1.1x10^13 1/(Wm), i.e., more than ten orders of magnitude larger than that of commonly used, highly nonlinear silicon photonic nanowires. These findings could pave a new way for developing ultra-low-power-consumption, highly-integrated and robust active photonic systems at deep-subwavelength scale for applications in quantum communications and information processing.