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International Meeting on Instabilities and Dynamics of Lasers and Nonlinear Optical Systems

Resonatorless Optical Bistability

Charles M. Bowden

Published Jan 1, 1985• 0 citations

Abstract

Intrinsic (mirrorless) optical bistability (MOB) has been predicted independently by a number of authors1. Recent experiments have demonstrated at least one major aspect of this phenomenon, i.e., MOB due to increasing absorption2. Other categories of MOB which have been predicted from theoretical models are caused by: interatomic correlation in a many-body quantum model, the anharmonic contribution in a classical Duffing oscillator, the local field correction in the macroscopic Maxwell-Bloch formulation, and coherent dipole-dipole interaction in a microscopic semiclassical model of a finite number of damped, two-level atoms driven by an external field3. All of these models share a single common characteristic which causes MOB in some region of the parameter space of each model. The characteristic is simply: an interaction-dependent nonlinearity which causes a renormalization of the resonance frequency. In each case, the sign and magnitude of the incident field detuning from the unrenormalized resonance is a crucial parameter.

DOI: 10.1364/idlnos.1985.wd19

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A system of coherently driven spatially distributed two-level atoms, coupled with each other via dipole–dipole interaction, exhibits intrinsic optical bistability (IOB) at solid-state densities,1 i.e., optical bistability without optical feedback. The origin of the IOB was shown to be due to inversion-dependent renormalization of the single-atom resonance frequency caused by dipole–dipole interaction among the atoms located mainly within an atomic resonance wavelength.2 For normally incident plane waves of intensity beyond threshold, a spatially dependent discontinuity in the nonlinear refractive index was shown to exist inside the medium,1 corresponding to spatial separation of the high and low absorption phases of the IOB. We present numerical results for the time-dependent solutions of the equations of motion and dynamics of the field propagation.

We use a quantum-electrodynamical, many-body treatment to show mirrorless optical bistability in terms of the spatial properties of coherent dipole-dipole interactions among interacting two-level atoms. The general theory is applied to two special cases: (1) a thin sample of two-level atoms, with a width smaller than a resonance wavelength and (2) a long sample of two-level atoms, with dimensions very large relative to a resonance wavelength. While for the thin sample we are able to use a mean-field approximation with validity, for the long sample we are compelled to take into account retardation and propagation. In both cases bistability is found to be related to a renormalization of the frequency (or relaxation rate) that is inversion dependent. For the long sample the frequency renormalization is significant for high atomic densities and for large oscillator strengths.

We use a fully quantum, many-body treatment to show mirrorless optical bistability in terms of the spacial properties of interacting two-level systems. The bistability effects are related to the coherent dipole-dipole interactions which introduce an inversion-dependent renormalization of the frequency (or relaxation). Conditions of stability and instability are discussed for a thin sample of two-level atoms with a width smaller than a wavelength. For a long sample of two-level atoms, we find that the two phases of high transmissivity and low transmissivity may coexist spacially in the material.

Optical bistability in nonlinear media is potentially useful because of its fast transition speed for all-optical logic operation [1-3]. The dynamics of these mirrorless systems have been described by a anharmonic Duffing oscillator [1-4]. After normalization the equation of motion is described by x + k x + x - f(x) = F sinwt, where k is the damping factor, F is the driving amplitude, w is the driving frequency and f(x) is a nonlinear function of x. Such a model predicts the existence of bistability under appropriate conditions [3]. It would be particularly important for this system to be tuned to some situation in order to efficiently generate these nonlinear phenomena. In this summary we would provide a global picture of possible dynamic behaviours in Eq.(1), which can be used as a guide line in real experiment.