Perturbation theory for graphene integrated waveguides: cubic nonlinearity and third harmonic generation

TL;DR

This paper develops a perturbation theory framework for analyzing third-order nonlinear optical processes in graphene integrated waveguides, specifically focusing on third harmonic generation and its efficiency.

Contribution

It introduces a novel perturbation theory approach that models graphene's nonlinear response as a boundary condition in Maxwell's equations for photonic structures.

Findings

Predicted third harmonic generation efficiency of a few percent.

Achieved high efficiency using sub-picosecond pulses with low energy.

Demonstrated resonance conditions for optimal nonlinear response.

Abstract

We present perturbation theory for analysis of generic third-order nonlinear processes in graphene integrated photonic structures. Optical response of graphene is treated as the nonlinear boundary condition in Maxwell equations. The derived models are applied for analysis of third harmonic generation in a graphene coated dielectric micro-fibre. The efficiency of up to few percent is predicted when using sub-picosecond pump pulses with energies of the order of $0.1$nJ in a sub-millimeter long fibre, when operating near the resonance of the graphene nonlinear conductivity $\hbar\omega=(2/3)E_F$.