Nonlinear susceptibility of composite optical materials in the Maxwell Garnett model

Within the context of the Maxwell Garnett model, we calculate the nonlinear susceptibility of a composite optical material comprised of spherical inclusion particles contained within a host material. We allow both constituents to respond nonlinearly and to exhibit linear absorption. Our treatment takes complete account of the tensor nature of the nonlinear interaction, under the assumption that each constituent is isotropic and that the composite is macroscopically isotropic. The theory predicts that there are circumstances under which the composite material can possess a nonlinear susceptibility that is larger than that of either of its constituents. It also predicts that, for the case in which the host material responds nonlinearly, the tensor properties of the nonlinear susceptibility of the composite can be very different from those of the host material.