Third-order nonlinearity of graphene: Effects of phenomenological relaxation and finite temperature

J. L. Cheng, N. Vermeulen, and J. E. Sipe
Phys. Rev. B 91, 235320 – Published 29 June 2015; Erratum Phys. Rev. B 93, 039904 (2016)

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 a 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.

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  • Received 26 March 2015
  • Revised 8 June 2015

DOI:https://doi.org/10.1103/PhysRevB.91.235320

©2015 American Physical Society

Erratum

Authors & Affiliations

J. L. Cheng1,2, N. Vermeulen1, and J. E. Sipe2

  • 1Brussels Photonics Team (B-PHOT), Department of Applied Physics and Photonics (IR-TONA), Vrije Universiteit Brussel, Pleinlaan 2, 1050 Brussel, Belgium
  • 2Department of Physics and Institute for Optical Sciences, University of Toronto, 60 St. George Street, Toronto, Ontario, Canada M5S 1A7

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Issue

Vol. 91, Iss. 23 — 15 June 2015

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