Multipolar nonlinear light-matter interactions with Gaussian vector beams

We show that surface second-harmonic generation (SHG) with focused Gaussian vector beams can be described in terms of effective Mie-type multipolar contributions to the SHG signal even in the electric dipole approximation of constitutive relations. Traditionally, Mie-type multipoles arise from field retardation across nanoparticles. In our case, the multipolar light-matter interaction is due to excitation with Gaussian vector beams and the tensorial properties of the SH response. As different multipoles have different radiative properties, we demonstrate the presence of multipoles 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. Secondly, we generalize the treatment beyond the electric dipole approximation and propose that analogous vector excitation-induced multipolar effects could also occur in the microscopic light-matter interaction. Our results may allow new possibilities to designing confined and thin nonlinear sources with desired radiation patterns.