Nonlinear graphene plasmonics: amplitude equation

TL;DR

This paper derives an amplitude equation for nonlinear surface plasmon waves in graphene, revealing how in-plane diffraction and nonlinearity interplay, with graphene's contribution dominating in strongly localized TM plasmons.

Contribution

It introduces a novel amplitude equation for nonlinear graphene plasmonics, highlighting the dominant role of graphene in strongly localized TM modes and the influence of dielectric nonlinearity in TE modes.

Findings

Graphene significantly enhances nonlinearity in strongly localized TM plasmons.

Dielectric nonlinearity can dominate in weakly localized TE plasmons.

The derived equation captures the interplay between diffraction and nonlinearity in graphene plasmonics.

Abstract

Using perturbation expansion of Maxwell equations, the amplitude equation is derived for nonlinear TM and TE surface plasmon waves supported by graphene. The equation describes interplay between in-plane beam diffraction and nonlinerity due to light intensity induced corrections to graphene conductivity and susceptibility of dielectrics. For strongly localized TM plasmons, graphene is found to bring the superior contribution to the overall nonlinearity. In contrast, nonlinear response of the substrate and cladding dielectrics can become dominant for weakly localized TE plasmons.