Full-wave analytical solution of second-harmonic generation in metal nanospheres

TL;DR

This paper develops an exact analytical method based on Mie theory to analyze second-harmonic generation in metal nanospheres, highlighting the significance of multipolar contributions and parameter effects for nanoplasmonic device design.

Contribution

It introduces a full-wave analytical solution for SHG in spherical nanoparticles using spherical vector wave functions, incorporating the Rudnick-Stern model.

Findings

High-order multipolar contributions significantly affect SHG power.

SH radiation components vary strongly with Rudnick-Stern parameters.

The method enables rigorous analysis of nonlinear optical processes in metal nanoparticles.

Abstract

We present a full-wave analytical solution for the problem of second-harmonic generation from spherical nanoparticles. The sources of the second-harmonic radiation are represented through an effective nonlinear polarization. The solution is derived in the framework of the Mie theory by expanding the pump field, the nonlinear sources and the second-harmonic fields in series of spherical vector wave functions. We use the proposed solution for studying the second-harmonic radiation generated from gold nanospheres as function of the pump wavelength and the particle size, in the framework of the Rudnick-Stern model. We demonstrate the importance of high-order multipolar contributions to the second-harmonic radiated power. Moreover, we investigate the p- and s- components of the SH radiation as the Rudnick-Stern parameters change, finding a strong variation. This approach provides a rigorous methodology to understand second-order optical processes in metal nanoparticles, and to design novel nanoplasmonic devices in the nonlinear regime.