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Journal of the Egyptian Mathematical Society

Optical bistability outside the rotating wave approximation in mixed species

Mona Ali

Published Sep 2, 2012• 2 citations
Publisher

Abstract

Optical bistable behavior for a system of inhomogeneously broadened two sorts of two-level atoms in a ring cavity is investigated outside the rotating wave approximation (RWA). The model Maxwell–Bloch equations are treated with Fourier decomposition up to first harmonic. The first harmonic output field component exhibits reversed or mushroom bistability simultaneously with bi- and double-bistability in the fundamental field component. Inhomogeneous broadening and transverse field effects are also considered.

DOI
10.1016/j.joems.2012.05.002

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Optical bistable behavior for a system of inhomogeneously broadened two sorts of two-level atoms in a ring cavity is investigated outside the rotating wave approximation (RWA). The model Maxwell–Bloch equations are treated with Fourier decomposition up to first harmonic. The first harmonic output field component exhibits reversed or mushroom bistability simultaneously with bi- and double-bistability in the fundamental field component. Inhomogeneous broadening and transverse field effects are also considered.
Optical bistability (OB) for a homogeneously broadened two-level atomic system in a ring cavity is investigated within and without the rotating wave approximation (RWA) using nonautonomous Maxwell–Bloch equations subject to a time delay. It is shown that the dynamics both within and without the RWA are susceptible to the introduction of time delays in the differential equations. A range of instability scenarios are found as certain parameters are ramped up and down and these can affect the bistable operation of the physical devices. However, the introduction of a time delay can also result in an important positive application; for the first time, as far as the authors are aware, it is shown that a type of butterfly hysteresis can occur in the fundamental component, which is a relatively strong output signal, and may be desired in optical signal processing.
This paper is concerned with non-autonomous Maxwell–Bloch equations when subject to a time delay. We investigate the dynamical behavior of an optical bistable system for inhomogeneous Lorentzian broadening and transverse Gaussian field effects interacting with a single mode ring cavity both inside and outside the rotating wave approximation. Results show that the known bistable behavior of the device can be affected by instabilities. However, in some cases, for instance, when the incident Gaussian laser beam waist is less than that of cylindrical atomic sample, a large butterfly hysteresis is demonstrated in the fundamental field component. As far as the authors are aware, this is the first time that such behavior has been demonstrated.
The steady state behavior of a bistable system of a homogeneously or inhomogeneously broadened two sorts of two-level atoms placed in a ring cavity and driven by a coherent field is analyzed within the mean field limit where the transverse effect of the radiation field is taken into account within the single-transverse-mode model. Effects on the input–output relation, due to the transverse parameter and the Lorentzian and the Gaussian line widths which measure the inhomogeneous broadening of the atoms, are examined. The enlargement of the optical bistable (tristable) region according to the previously mentioned parameters is explained.
The interaction of a mesoscopic system of two-level Rydberg atoms with a coherently driven single cavity mode is treated outside the rotating wave approximation (RWA). This yields a system of non-autonomous Maxwell–Bloch equations that can be solved using Fourier decomposition of both field and atomic variables up to first harmonics and to O ( Q −1 ), where Q is the cavity quality factor. For the absorber and amplifier regimes, the first harmonic component of the output field (outside the RWA) exhibits closed hysteresis loops compared with hysteresis cycles for the non-oscillatory (fundamental) component within the RWA. A cooperative switching diagram (output field versus cooperative atomic parameter) outside the RWA shows overlapping branches in the resonant case and closed loops in the non-resonant case.
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.
The steady state behaviour of a bistable system of a homogeneously/inhomogeneously broadened two-level atomic medium in contact with a squeezed vacuum field and placed in a ring cavity driven by a coherent field is analysed within the mean field limit where the transverse effect of the radiation field is taken into account within the single-transverse-mode model. Effects on the input–output relation and the critical value of the cooperative parameter C crit are examined and compared with these results in the plane wave approximation. The 'cooperative switching effect' between the output states of the system due to variation of the cooperative parameter C is also investigated. Linear stability analysis for the model Maxwell–Bloch equations is presented in the homogeneously broadened case.