Multipolar second-harmonic generation by Mie-resonant dielectric nanoparticles

By combining analytical and numerical approaches, we study resonantly enhanced second-harmonic generation (SHG) by individual high-index dielectric nanoparticles made of centrosymmetric materials. Considering both bulk and surface nonlinearities, we describe second-harmonic nonlinear scattering from a silicon nanoparticle optically excited in the vicinity of the magnetic and electric dipolar resonances. We discuss the contributions of different nonlinear sources, and the effect of the low-order optical Mie modes on the characteristics of the generated far-field. We demonstrate that the multipolar expansion of the radiated field is dominated by dipolar and quadrupolar modes (two axially symmetric electric quadrupoles, an electric dipole, and a magnetic quadrupole), and the interference of these modes can ensure directivity of the nonlinear scattering. The developed multipolar analysis can be instructive for interpreting the far-field measurements of the nonlinear scattering, and it provides prospective insights into a design of CMOS-compatible nonlinear nanoantennas fully integrated with silicon-based photonic circuits, as well as new methods of nonlinear diagnostics.