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Topical Meeting on Optical Bistability (OB)

Mirrorless Optical Bistability Due to Coherent Dipole-Dipole Interactions in a Spacially Distributed Collection of Two-level Systems

Y. Ben-Aryeh, Charles M. Bowden

Published Jan 1, 1985• 1 citation
Publisher

Abstract

Atomic cooperative effects in mirrorless (intrinsic) optical bistability (MOB) have been treated, so far, either by assuming a small volume with dimensions smaller than a wavelength1,2, or by assuming a system with a small number of atoms3. In the present work we discuss MOB based upon cooperative effects among atoms in a system consisting of many two-level atoms, considering explicitly the spacial dependence of the coherent dipole-dipole interactions.

DOI
10.1364/obi.1985.wd7

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Mirrorless optical bistability in a spacially distributed collection of two-level systems

Y. Ben-Aryeh, Charles M. Bowden

Optics Communications•Sep 1, 1986•23 citations
Atomic cooperative effects in mirrorless (intrinsic) optical bistability (MOB) have been treated, so far, either by assuming a small volume with dimensions smaller than a wavelength1,2, or by assuming a system with a small number of atoms3. In the present work we discuss MOB based upon cooperative effects among atoms in a system consisting of many two-level atoms, considering explicitly the spacial dependence of the coherent dipole-dipole interactions.
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.
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.
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.
Our model, presented earlier, which predicts the circumstances under which intrinsic mirrorless optical bistability (OB) can occur due to atomic pair correlation in a small volume, is outlined and the results presented. These results, which Predict a first-order phase transition in steady state for an externally-driven collection of a large number of atoms far removed from thermodynamic equilibriun, forms the motivation for a detailed microscopic examination of the dynamical behavior of atonic pair correlation in the presence of externally-applied coherent radiation. 4 model is presented and results are discussed for the transient dynamic evolution of two, two-level atoms separated from each other by a distance r in the presence of an externally-applied coherent radiation field. The results predict collective radiation reaction, frequency shifts, relaxation in terms of the atomic seoaration r (assumed much larger than single atom dimensions), the externally-applied field intensity and spacial uniformity of the field with respect to the inter-atomic volume.
We investigate the effect of a linear host medium on the dynamics of a dense collection of resonant atoms. We find that near dipole-dipole interaction is enhanced by the presence of the host dielectric, resulting in a lower threshold density and a greater hysteresis area for intrinsic optical bistability. Cooperative decay terms appear that represent the interaction of near dipoles mediated by the absorptive component of the dielectric function of the host medium. These terms are part of the local response and correspond to local cooperative decay effects. \textcopyright{} 1996 The American Physical Society.