Effect of percolation on the cubic susceptibility of metal nanoparticle composites

It is well known that one of the most unique and interesting properties of metal colloids arises at the surface plasmon resonance where the dipole moment of the particle becomes large and the local field is enhanced in magnitude in comparison to the applied field. Less discussed is the fact that the local field may also be shifted in phase with respect to the applied field. Previously, we demonstrated that a counterintuitive consequence of these local field effects occurs in metal colloids at the surface plasmon resonance. Remarkably, although χ((3)) is positive for each component by itself, χ((3)) may be negative for the colloid as a whole. There are thus two metal volume fill fractions where χ((3))=0. Our hypothesis is that the sign reversal in χ((3)) that at higher fill fractions is associated with the percolation threshold. We apply generalized two- and three-dimensional Maxwell Garnett and Bruggeman geometries to the case of these metal nanoparticle composites and use complex linear and nonlinear constituent susceptibilities to determine the complex composite nonlinear susceptibility. Because the nonlinear response in small metal particles arises primarily from absorptive mechanisms the sign reversal is most evident in the imaginary part of χ((3))