Theory of plasmonic effects in nonlinear optics: the case of graphene

TL;DR

This paper develops a comprehensive microscopic theory for nonlinear optical effects in graphene, accounting for electron interactions, and compares theoretical predictions with experimental observations of graphene plasmons.

Contribution

It introduces a general large-N theoretical framework for second- and third-order nonlinear responses, specifically applied to graphene's electron dynamics.

Findings

The theory reduces to the random phase approximation in linear response.

Calculated nonlinear response functions match experimental measurements.

Demonstrates the role of electron interactions in nonlinear optical phenomena in graphene.

Abstract

We develop a microscopic large-$N$ theory of electron-electron interaction corrections to multi-legged Feynman diagrams describing second- and third-order nonlinear response functions. Our theory, which reduces to the well-known random phase approximation in the linear-response limit, is completely general and is useful to understand all second- and third-order nonlinear effects, including harmonic generation, wave mixing, and photon drag. We apply our theoretical framework to the case of graphene, by carrying out microscopic calculations of the second- and third-order nonlinear response functions of an interacting two-dimensional (2D) gas of massless Dirac fermions. We compare our results with recent measurements, where all-optical launching of graphene plasmons has been achieved by virtue of the finiteness of the quasi-homogeneous second-order nonlinear response of this inversion-symmetric 2D material.