  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.
