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Journal of the Optical Society of America B

Dispersive optical bistability in a dielectric sphere

Md. Mohiuddin Mazumder, Steven C. Hill, Dipak Q. Chowdhury, Richard K. Chang

Published Feb 1, 1995• 21 citations

Abstract

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.

DOI: 10.1364/josab.12.000297

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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.

We analyze instabilities in mixed absorptive and dispersive optical bistability in the rate-equation approximation and the mean-field and good-cavity limits. Our starting point is a set of multimode equations derived from the Maxwell-Bloch equations for ring-cavity boundary conditions. We obtain analytic expressions for the instability conditions. In a plane-wave analysis, we find that a portion of the lower transmission branch can be unstable in addition to the upper-branch instability found in purely absorptive bistability. Also, a new disconnected region of instability can exist on the upper branch. Our analysis becomes particularly simple for equal and opposite cavity detunings and we explore this case in detail. We extend our treatment to include a Gaussian transverse intensity profile and show that the instabilities remain in the presence of Gaussian averaging. We also show that many of the results obtained in the rate-equation approximation hold when the atomic linewidth and atomic decay rate are of the same order.

Based on Fabry-Perot cavity's theories and efficiency refractive index,the optical bistability of a nonlinear microcavity is studied,and the corresponding mathematical formula are deduced.The theoretical curves are well fitted with those of numerical simulation in other papers.The investigation shows that appropriate frequency-shifting should be preset on the incident light in order to produce bistability for a nonlinear system.If the system is composed of focusing nonlinear medium,the frequency must be redshifted, otherwise it must be blue-shifted.The magnitude of critical shifting is 0.866 times of the width of microcavity resonance mode.

A general theory of optical bistability for a homogeneously broadened two-level system in a Fabry-Perot interferometer is presented. Both absorptive and dispersive mechanisms are included, and in the mean-field approximation a cubic state equation is derived relating transmitted intensity to all physical parameters. From the perspective of catastrophe theory, this equation describes an elementary cusp catastrophe. We show that bistable switching may follow not only from sweeping the incident laser intensity, but also with continuous variation of atomic or cavity detuning, or atomic density, with the laser intensity fixed. For the case having incident intensity as the variable control, the domain of bistability is studied in some detail as a function of the remaining fixed parameters. Stability criteria are considered for the general case including both absorption and dispersion.

Intrinsic optical bistability in the scattering and absorption of laser radiation from microparticles having an intensity-dependent refractive index is investigated.1 We work only with particles whose radius is small compared with the wavelength of the incident radiation. Our calculation is based on the assumption that the electric field inside the particle is in fact uniform (as is the case in the linear regime). For particles with fairly sharp surface piasmon resonances, optical bistability can occur if the frequency detuning is above a certain critical value. The threshold intensity is found to be reduced by several orders of magnitude compared with the non-resonant case. Optical switching can also occur at fixed intensity above the threshold by sweeping the frequency across the resonant frequency. Right at the critical detuning frequency, the particle can act as an optical transistor with a very sizable differential gain. Spherical1 as well as elongated microparticles2 are studied. In the latter case, optical tristability can also be achieved, and there are, in addition, interesting shape dependence and orientational effects.

Intrinsic optical bistability in the scattering and absorption of light from Rayleigh-particle-sized microparticles having an intensity-dependent refractive index is theoretically investigated. For particles near plasmon resonances optical switching also occurs by sweeping the frequency across the resonance at fixed incident intensity above a certain threshold. Several orders of magnitudes of reduction in the switching intensities are possible near sharp resonances, and an optical transistor mode with a very sizable differential gain can be achieved.