Multipolar second-harmonic emission with focused Gaussian beams

Abstract

We show that electric-dipole-allowed surface second-harmonic (SH) generation with focused Gaussian beams can be described in terms of Mie-type multipolar contributions to the SH signal. In contrast to the traditional case, where Mie multipoles arise from field retardation across nanoparticles, the multipoles here arise from the confined source volume and the tensorial properties of the SH response. We demonstrate this by measuring strongly asymmetric SH emission into reflected and transmitted directions from a nonlinear thin film with isotropic surface symmetry, where symmetric emission is expected using traditional formalisms based on plane-wave excitation. The proposed multipole approach provides a convenient way to explain the measured asymmetric emission. Our results suggest that the separation of surface and bulk responses, which have dipolar and higher-multipolar character, respectively, may be even more difficult than thought. On the other hand, the multipolar approach may allow tailoring of focal conditions in order to design confined and thin nonlinear sources with desired radiation patterns.