Third order nonlinearity of graphene: effects of phenomenological relaxation and finite temperature

TL;DR

This paper analytically explores how phenomenological relaxation and temperature influence third order nonlinear optical responses in doped graphene, including harmonic generation and current injection, under various conditions.

Contribution

It provides an analytic expression for the third order nonlinear conductivity of graphene at finite temperature considering relaxation effects, extending previous zero-temperature models.

Findings

Nonlinear optical effects depend on relaxation parameters, temperature, and pulse duration.

Derived formulas enable prediction of third harmonic generation, Kerr effects, and two-photon absorption in graphene.

Analysis includes dc-current induced second harmonic and difference frequency generation.

Abstract

We investigate the effect of phenomenological relaxation parameters on the third order optical nonlinearity of doped graphene by perturbatively solving the semiconductor Bloch equation around the Dirac points. An analytic expression for the nonlinear conductivity at zero temperature is obtained under the linear dispersion approximation. With this analytic formula as starting point, we construct the conductivity at finite temperature and study the optical response to a laser pulse of finite duration. We illustrate the dependence of several nonlinear optical effects, such as third harmonic generation, Kerr effects and two photon absorption, parametric frequency conversion, and two color coherent current injection, on the relaxation parameters, temperature, and pulse duration. In the special case where one of the electric fields is taken as a dc field, we investigate the dc-current and dc-field induced second order nonlinearities, including dc-current induced second harmonic generation and difference frequency generation.