Full-Wave Analytical Solution of Second-Harmonic Generation in Metal Nanospheres

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 a 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 dependence of the p- and s-components of the second-harmonic radiation on the Rudnick-Stern parameters. This approach provides a rigorous methodology to understand second-order optical processes in nanostructured metals and to design novel nanoplasmonic devices in the nonlinear regime.