Third-order optical nonlinearity enhancement through composite microstructures

Abstract

Formulas for the evaluation of third-order optical susceptibility of nonlinear composites are derived in the mean-field approximation for four different microstructures corresponding to those described by the Maxwell–Garnett theory, the Bruggeman self-consistent theory, the Sheng theory, and the differential effective medium theory. A commonly encountered error in the literature is pointed out, with the correct formulation given. Anomalous dispersion, i.e., surface plasmon resonance of coated spheres, is identified as the source of large optical nonlinear susceptibility enhancement. Examples are given that demonstrate this microstructural enhancement effect. Comparison with experimental data on ${\mathrm{AuSiO}}_2$ granular films shows that large enhancement in the third-order Kerr-type nonlinear susceptibility can indeed be realized at compositions below the percolation threshold, with prediction of even larger enhancement possible.