Optical nonlinearities of small metal particles: Surface-mediated resonance and quantum size effects

Time- and frequency-dependent measurements of optical phase conjugation in gold colloids are reported. It is shown that the nonlinear response is fast on a 5-psec time scale and can be assigned to the electrons of the small metal spheres. The frequency-dependent measurements were performed in the neighborhood of the surface-plasma resonance and give experimental evidence of the validity of our resonant enhancement model. We also report the first model calculation of the third-order Kerr susceptibility of small metal particles. The dominant terms of this electric-dipole contribution are emphasized and lead to an expression for x(3) that varies roughly as the inverse third power of the radius of the particles. This model accounts for the observed anisotropy of this susceptibility and provides an estimate of its magnitude, in agreement with the measured values. The limited size effect on the linear susceptibility is also discussed.