Second-harmonic generation by a graphene nanoparticle

We study the second-harmonic generation by a spherical dielectric nanoparticle covered by graphene. We demonstrate that a strong nonlinear response is caused by an induced surface current in the graphene nanoparticle illuminated by an external electromagnetic wave. We obtain analytical expressions for the field multipoles characterizing the second-harmonic radiation and analyze the dependence of intensity and directivity of the nonlinear scattering on the frequency and structure of the electromagnetic field, revealing the asymmetric radiation patterns due to constructive multipole interference for the resonantly enhanced second-harmonic generation.