Generation of second-harmonic surface plasmons in Al-quartz interface

We report the results of an experiment in which the linear excitation of a surface plasmon (SP) at frequency $\omega$ in an A1-quartz interface is followed by the generation of a second-harmonic surface plasmon at $2\omega$ on the same interface. The Kretschmann geometry has been used to excite the fundamental SP while the second-harmonic SP is detected by nonlinear reflection and scattering at the interface. The theory of the second-harmonic generation by surface plasmons is briefly reviewed while a roughness scattering theory including nonlinear polarization-source terms is given. The experimental results are found to be in good agreement with the theory. A best-fit analysis leads to an accurate appraisal of the linear and nonlinear optical parameters of the media involved in the interaction.