Second-order nonlinear optical response of graphene

TL;DR

This paper develops a quantum-mechanical theory for the second-order nonlinear optical response of graphene, accounting for spatial dispersion and transitions beyond the electric dipole approximation, revealing strong nonlinear effects at long wavelengths.

Contribution

It introduces a comprehensive quantum theory of graphene's second-order nonlinear response that includes both intraband and interband transitions, extending previous models.

Findings

Strong second-order nonlinearity at long wavelengths

Presence of Fermi-edge resonances

Unusual polarization properties observed

Abstract

Although massless Dirac fermions in graphene constitute a centrosymmetric medium for in-plane excitations, their second-order nonlinear optical response is nonzero if the effects of spatial dispersion are taken into account. Here we present a rigorous quantum-mechanical theory of the second-order nonlinear response of graphene beyond the electric dipole approximation, which includes both intraband and interband transitions. The resulting nonlinear susceptibility tensor satisfies all symmetry and permutation properties, and can be applied to all three-wave mixing processes. We obtain useful analytic expressions in the limit of a degenerate electron distribution, which reveal quite strong second-order nonlinearity at long wavelengths, Fermi-edge resonances, and unusual polarization properties.