Second order optical nonlinearity of graphene due to electric quadrupole and magnetic dipole effects

TL;DR

This paper develops a method to distinguish and analyze electric quadrupole and magnetic dipole contributions to graphene's second order optical nonlinearities, predicting strong effects controllable via chemical potential tuning.

Contribution

It provides analytic expressions for second order optical conductivities in graphene, accounting for electric quadrupole and magnetic dipole effects, and demonstrates their controllability.

Findings

Strong second order nonlinear effects predicted, including second harmonic generation and photon drag.

Analytic expressions derived for second order optical conductivities in graphene.

Controllability of nonlinear effects through chemical potential tuning.

Abstract

We present a practical scheme to separate the contributions of the electric quadrupole-like and the magnetic dipole-like effects to the forbidden second order optical nonlinear response of graphene, and give analytic expressions for the second order op- tical conductivities, calculated from the independent particle approximation, with relaxation described in a phenomenological way. We predict strong second order nonlinear effects, including second harmonic generation, photon drag, and difference fre- quency generation. We discuss in detail the controllability of these effects by tuning the chemical potential, taking advantage of the dominant role played by interband optical transitions in the response.