Quantum theory of the third-order nonlinear electrodynamic effects in graphene

TL;DR

This paper develops a comprehensive quantum theory for third-order nonlinear electrodynamic effects in graphene, enabling the prediction of various nonlinear phenomena relevant for terahertz and optoelectronic applications.

Contribution

It introduces a general quantum framework for third-order nonlinear conductivity in graphene, covering multiple nonlinear optical effects.

Findings

Analytical formulas for third-order nonlinear conductivity in graphene.

Prediction of phenomena like third harmonic generation and four wave mixing.

Potential applications in terahertz and optoelectronic devices.

Abstract

The linear energy dispersion of graphene electrons leads to a strongly nonlinear electromagnetic response of this material. We develop a general quantum theory of the third-order nonlinear local dynamic conductivity of graphene $\sigma_{\alpha\beta\gamma\delta}(\omega_1,\omega_2,\omega_3)$, which describes its nonlinear response to a uniform electromagnetic radiation. The derived analytical formulas describe a large number of different nonlinear phenomena such as the third harmonic generation, the four wave mixing, the saturable absorption, the second harmonic generation stimulated by a dc electric current, etc., which may be used in different terahertz and optoelectronic devices.