Second order optical nonlinearity of graphene due to electric quadrupole and magnetic dipole effects

J L Cheng,J E Sipe,N Vermeulen

doi:10.1038/srep43843

J L Cheng, J E Sipe + Show 1 more

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https://doi.org/10.1038/srep43843

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Abstract

We present a practical scheme to separate the contributions of the electric quadrupole-like and the magnetic dipole-like effects to the forbidden second order optical nonlinear response of graphene, and give analytic expressions for the second order optical conductivities, calculated from the independent particle approximation, with relaxation described in a phenomenological way. We predict strong second order nonlinear effects, including second harmonic generation, photon drag, and difference frequency generation. We discuss in detail the controllability of these effects by tuning the chemical potential, taking advantage of the dominant role played by interband optical transitions in the response.

Highlights

Effects in centrosymmetric atoms or molecules arise[5,11,12,13]; (2) at an asymmetric interface between graphene and the substrate the centre-of-inversion symmetry is broken, and second order nonlinearities are allowed[14,15,16,17,18]; (3) the symmetry can be locally broken due to natural curvature fluctuations of suspended graphene[19]; (4) the application of a dc electric field can be used to generate an asymmetric steady state, and a second order nonlinear optical response can arise through the third order nonlinearity[10,16,17,18,20,21]
We have separated the contributions of the magnetic dipole-like and electric quadrupole-like effects to the second order nonlinearities of monolayer graphene
We quantitatively analyze the predictions for different second order phenomena, including second harmonic generation, one photon dc current generation, and difference frequency generation

Summary

Introduction

Effects in centrosymmetric atoms or molecules arise[5,11,12,13]; (2) at an asymmetric interface between graphene and the substrate the centre-of-inversion symmetry is broken, and second order nonlinearities are allowed[14,15,16,17,18]; (3) the symmetry can be locally broken due to natural curvature fluctuations of suspended graphene[19]; (4) the application of a dc electric field can be used to generate an asymmetric steady state, and a second order nonlinear optical response can arise through the third order nonlinearity[10,16,17,18,20,21]. We became aware of related works in preprints[27,28]. Overlapping results in these papers are in agreement in the absence of relaxation]. As with the third order optical response, the contribution of interband transitions to the second order nonlinearity can lead to a rich and tunable nonlinear optical response[23,26]. In this work we present analytic results for the second order conductivities of graphene induced by the electric quadrupole-like and magnetic dipole-like effects, within the independent particle approximation and with relaxation processes described phenomenologically

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