Numerical study of the optical nonlinearity of doped and gapped graphene: From weak to strong field excitation

TL;DR

This study numerically investigates the linear and nonlinear optical responses of doped and gapped graphene under various excitation strengths, revealing how doping, gaps, and electric field amplitude influence harmonic generation and Kerr effects.

Contribution

It provides a comprehensive numerical analysis of optical nonlinearities in doped and gapped graphene, including strong field effects and saturation phenomena, extending previous analytic perturbation results.

Findings

Weak field results agree with analytic formulas.

Strong fields induce saturation effects in nonlinear responses.

Nonlinear coefficients depend strongly on electric field amplitude.

Abstract

Numerically solving the semiconductor Bloch equations within a phenomenological relaxation time approximation, we extract both the linear and nonlinear optical conductivities of doped graphene and gapped graphene under excitation by a laser pulse. We discuss in detail the dependence of second harmonic generation, third harmonic generation, and the Kerr effects on the doping level, the gap, and the electric field amplitude. The numerical results for weak electric fields agree with those calculated from available analytic perturbation formulas. For strong electric fields when saturation effects are important, all the effective third order nonlinear response coefficients show a strong field dependence.