Dispersive optical bistability in a dielectric sphere

Dispersive optical bistability in a dielectric sphere is modeled. The analysis is applicable to cases in which the incident frequency is near a morphology-dependent resonance of the sphere. The refractive index of the sphere is assumed to vary as m(r) = m0 + m2I(r), where I(r) is the internal intensity at position r. In general I(r) contains all the modes of the sphere. However, we first obtain a simplified analytical expression for bistability in which we assume that I(r) consists of a single near-resonant mode. We also analyze the bistability problem; in the analysis we include all the modes of the sphere in computing I(r). The agreement between the all-mode and the single-mode results is good when the incident frequency is within a few linewidths of ahigh-Q (>104) mode. We compare bistability in a dielectric sphere with that in a Fabry–Perot cavity. We use a quasi-steady-state approximation to calculate the time-dependent backscattering from a CS2 sphere near a resonance. The computed backscattered intensity has bistable characteristics.