Graphene and few-layer graphite probed by second-harmonic generation: Theory and experiment

Abstract

We have measured second-harmonic generation (SHG) from graphene and other graphitic films, from two layers to bulk graphite, at room temperature; all samples are mounted on a 300 nm oxide layer of a Si(001) substrate. With 800 nm, 150 fs fundamental pulses, the anisotropic response was recorded for combinations of $p$-, $s$-, and diagonally polarized fundamental and second-harmonic beams as the samples were rotated about their normal. Graphene samples display SHG signatures only slightly different from that of the bare substrate which shows SHG with fourfold rotational symmetry. All other layered systems show threefold symmetry, although the ratio of isotropic to anisotropic response varies with the number of layers. A model based on linear light propagation in layered media with interface dipole and bulk quadrupole SHG sources is presented for the analysis. We show that data from all layered samples can be understood in terms of well-known linear optical properties, the SHG response of the bare substrate and four independent, complex nonlinear dipole susceptibility tensor elements of the graphene/air interface.