Third-order Nonlinear Dispersion Properties of Surface Plasmon Resonance in Gold Nanoparticles

Experimental results of degenerate four wave mixing spectroscopy in the visible spectrum for polymer semiconductor films with embedded gold nanoparticles are presented. An enlargement of third-order optical nonlinearity at the shortwave wing of the surface plasmon absorption band was experimentally registered. A theoretical model of surface plasmons as longitudinal standing waves in nanoobjects was developed in order to analyze the experimental data. As it was pointed, the amplification of the third-order nonlinear coefficients occurs in the spectral region with simultaneously large numbers of dielectric constant and refractive index. Experiments using scanning tunneling microscopy with a spatial resolution of up to 1nm allowed us to characterize in detail the morphology of the sample with embedded gold nanoparticles. Microscopy measurements results showed that nanoparticles with a size of 10-20 nanometers have a non-spherical shape and amorphous ordering of atoms. The nanoparticles were found to be coupled into clusters having a few hundred nanometers dimensions. Numerical solutions of Maxwell's equations for nanoparticles having the shape, which was previously experimentally measured by scanning tunneling microscopy, were obtained. The results of the calculations confirm a homogeneous character of the plasmon absorption band spectral broadening in samples and suitability of the developed theoretical approach where spectral properties of surface plasmons can be considered in frames of harmonic damping oscillator model. Degenerate four wave mixing interaction in an organic polymer with embedded gold nanoparticles was found to be a simultaneous manifestation of two processes – quantum mechanical originated third-order nonlinear interaction and a longitudinal standing wave of charge carriers, which can be correctly explained in frames of the classical electrodynamics.