Linear and nonlinear optical response of spherical anisotropic semiconductor microcrystallites

We present a phenomenological theory of the linear and nonlinear optical properties associated with the Fr\"ohlich resonances of an optically anisotropic, spherical semiconductor crystallite. Using the Maxwell-Garnett approach, we calculate the effective dielectric function of a composite medium containing such crystallites. To study the effect of anisotropy, we take CdS and CdSe quantum dots as examples for the inclusions, and use a two-resonance model for the dielectric function. Even for randomly oriented inclusions, the Fr\"ohlich resonances split as a result of anisotropic local-field corrections. At higher laser intensities, absorption saturation leads to bistability or tristability in the optical response of individual crystallites, while the response of the composite medium with randomly oriented inclusions shows multistability, with many intermediate branches. The nonlinear response of such a composite medium also exhibits a new kind of orientation-induced broadening of resonances. We also find that tristability is possible in another kind of inhomogeneous material, viz., a composite medium containing two types of isotropic spherical crystallites.