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Communications in Theoretical Physics

Dynamics of Optical Bistability with Kerr-nonlinear Blackbody Radiation Reservoir

Yasser Amoun Sharaby

Published Apr 1, 2017• 4 citations
Publisher

Abstract

Abstract In this paper we investigate the nonlinear dynamics for optical bistabile (OB) model of homogeneously broadened two-level atomic medium interacting with a single mode of the ring cavity in the presence of a Kerr-nonlinear blackbody (KNB) radiation reservoir. We show the impact of the relative temperature of the reservoir on the transition between the dynamical states via bifurcation diagrams that represents the relation between maximum values of the output field and the relative temperature for fixed input field. Specifically, decreasing the relative temperature (T b ) causes the system to bifurcate from periodic to chaotic behavior and in turn reverts back to periodic behavior with further decrease of T b . Varying atomic detuning leads to a change in the nature of the dynamic transition between the system’s states from self pulsing to chaotic behavior.

DOI
10.1088/0253-6102/67/4/435

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Abstract In this paper we investigate the nonlinear dynamics for optical bistabile (OB) model of homogeneously broadened two-level atomic medium interacting with a single mode of the ring cavity in the presence of a Kerr-nonlinear blackbody (KNB) radiation reservoir. We show the impact of the relative temperature of the reservoir on the transition between the dynamical states via bifurcation diagrams that represents the relation between maximum values of the output field and the relative temperature for fixed input field. Specifically, decreasing the relative temperature (T b ) causes the system to bifurcate from periodic to chaotic behavior and in turn reverts back to periodic behavior with further decrease of T b . Varying atomic detuning leads to a change in the nature of the dynamic transition between the system’s states from self pulsing to chaotic behavior.
In this paper, we investigate the nonlinear dynamical behavior of dispersive optical bistability (OB) for a homogeneously broadened two-level atomic medium interacting with a single mode of the ring cavity without invoking the rotating wave approximation (RWA). The periodic oscillations (self-pulsing) and chaos of the unstable state of the OB curve is affected by the counter rotating terms through the appearance of spikes during its periods. Further, the bifurcation with atomic detuning, within and outside the RWA, shows that the OB system can be converted from a chaotic system to self-pulsing system and vice-versa.
We study optical bistability (OB) in a controllable giant self-Kerr nonlinear atomic gaseous medium placed in a unidirectional ring cavity. The medium is coherently excited by strong controlling field and a weak probe laser field under electromagnetically induced transparency (EIT) and Doppler broadening. In a weak field limit of the probe light, an analytic OB equation for the probe light field is derived as an analytic function of parameters of the controlling field and temperature of the medium. It is shown that OB characters can be manipulated with the parameters due to the controllable properties of the self-Kerr nonlinearity. Furthermore, enhancement of the Kerr nonlinearity reduces the switching intensity threshold and width of the OB.
The cooperative behavior of a system of atoms contained in a ring cavity is investigated under the condition that the fundamental atomic transition is a two photon transition1. Maxwell-Block equations are used to obtain the input vs. output relation by adiabatically eliminating all the atomic variables. The fundamental equation that results is a complex two dimensional map--which in the mean field limit reduces to the standard bistability equations. The characteristics of the two dimensional map are numerically investigated. Such a map is shown to lead to chaotic behavior following the Feigenbaum2 scenario. The sequence of events following first regime of chaos is a set of period halving bifurcations. The characteristics of the power spectrum in the region of chaos are presented. The effect of noise on the period doubling bifurcations in the present model, is also investigated and the connection with the theoretical predictions3 is established. The changes in the dynamical characteristics of the system when atomic inversion relaxes on the same time scale as the cavity round trip time will also be discussed in detail.
We study the propagation of electromagnetic radiation through a ring-cavity device containing a dispersive nonlinear medium. Under conditions appropriate for introducing the slowly varying envelope approximation and for adiabatically eliminating the atomic variables, we calculate analytical expressions between the steady-state-output intensity and the input-field amplitude for two models of the nonlinear susceptibility, the two-level atomic medium and the Kerr medium. The stability of these curves is determined, with special attention given to changes in the thresholds by varying the return-trip phase shift, the linear absorption, and the reflection coefficients of the mirrors. We investigate the positive-branch instabilities resulting in a pulsing output intensity and calculate the bifurcation rate for the period-doubling hierarchy and the fractal dimension of our two-dimensional maps for the Kerr medium. The convergence of the bifurcation rate to a constant is slow, and we find, as in the publications of Snapp et al. [ Opt. Commun.40, 68 ( 1981)] and Carmichael et al. [ Phys. Rev. A26, 3408 ( 1982)], that this constant is consistent with that found for the class of one-dimensional maps with a quadratic maximum. This universal constant is observed over a large range of fractal dimensions for the chaotic attractor. Discussions of pulse-output bistability, intermittency, and anomalous switching are given.