Second-harmonic generation in arrays of spherical particles

Abstract

We calculate the optical second harmonic (SH) radiation generated by small spheres made up of a homogeneous centrosymmetric material illuminated by inhomogeneous transverse and/or longitudinal electromagnetic fields. We obtain expressions for the hyperpolarizabilities of the particles in terms of the multipolar bulk susceptibilities and dipolar surface susceptibilities of their constitutive material. We employ the resulting response functions to obtain the nonlinear susceptibilities of a composite medium made up of an array of such particles and to calculate the radiation patterns and the efficiency of SH generation from the bulk and the edge of thin composite films illuminated by finite beams. Each sphere has comparable dipolar and quadrupolar contributions to the nonlinear radiation, and the composite has comparable bulk and edge contributions which interfere among themselves yielding nontrivial radiation and polarization patterns. We present numerical results for Si spheres and we compare our results with recent experiments.