Second harmonic generation in metal nano-spheres: full-wave analytical solution with both local-surface and nonlocal-bulk nonlinear sources

We present a full-wave analytical solution for the problem of second-harmonic generation from spherical particles made of lossy centrosymmetric materials. Both the local-surface and nonlocalbulk nonlinear sources are included in the generation process, under the undepleted-pump approximation. The solution is derived in the framework of the Mie theory by expanding the pump field, the non-linear sources and the second-harmonic fields in series of spherical vector wave functions. We apply the proposed solution to the second-harmonic generation properties of noble metal nano-spheres as function of the polarization, the pump wavelength and the particle size. 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.