# A study of the nonlinear optical response of the plain graphene and gapped graphene monolayers beyond the Dirac approximation

## TL;DR

This paper numerically investigates the nonlinear optical responses of both plain and gapped graphene monolayers across a broad spectrum, revealing new insights into their second and third order conductivities beyond the Dirac approximation.

## Contribution

It provides the first detailed numerical analysis of second and third order conductivities of graphene beyond the Dirac approximation, covering microwave to ultraviolet frequencies.

## Key findings

- Calculated second and third order conductivities for graphene monolayers.
- Analyzed harmonic generation, optical rectification, and Kerr effects.
- Extended the frequency range to ultraviolet, previously unexplored.

## Abstract

In this work, we present numerical results for the second and third order conductivities of the plain graphene and gapped graphene monolayers associated with the second and third harmonic generation, the optical rectification and the optical Kerr effect. The frequencies considered here range from the microwave to the ultraviolet portion of the spectrum, the latter end of which had not yet been studied. These calculations are performed in the velocity gauge and directly address the components of the conductivity tensor. In the velocity gauge, the radiation field is represented by a power series in the vector potential, and we discuss a very efficient way of calculating its coefficients in the context of tight-binding models.