Multipolar second-harmonic generation by Mie-resonant dielectric nanoparticles

TL;DR

This paper investigates how high-index dielectric nanoparticles, especially silicon, can be used to enhance and control second-harmonic generation through multipolar resonances, aiding the design of integrated nonlinear nanoantennas.

Contribution

It provides a combined analytical and numerical multipolar analysis of SHG in dielectric nanoparticles, highlighting the role of dipolar and quadrupolar modes in nonlinear scattering.

Findings

Multipolar expansion shows dominance of dipolar and quadrupolar modes.

Interference of modes can direct nonlinear scattering.

Insights for designing CMOS-compatible nonlinear nanoantennas.

Abstract

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.