Cubic nonlinearities in small-particle composites: local-field induced giant enhancements

We discuss methods for enhancing the cubic nonlinear susceptibility χe of a composite material, starting from an exact relation between χe and the fourth moment of the electric field in the related linear composite. At zero frequencies, in a random metal-insulator composite, χe can be greatly enhanced near a percolation threshold. Similar enhancement is obtained when a linear fractal is embedded in a nonlinear host. In a random Drude metal-insulator composite χe is greatly enhanced near surface-plasmon resonances; the enhancement shows very strong structure which is nearly undetectable in the linear response. In a suspension of spheres coated with a nonlinear material, χe/χcoat ⪢ 1 near the surface-plasmon resonance frequency of the core particle.