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Journal of Optics B Quantum and Semiclassical Optics

Transverse field, squeezed vacuum and inhomogeneous broadening effects on optical bistability

Mona Ali, Saad S. M. Hassan, S. M. A. Maize

Published Oct 17, 2002• 19 citations
Publisher

Abstract

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.

DOI
10.1088/1464-4266/4/6/304

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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.
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 steady-state bistability and the evolution of the field envelope of a ring-cavity optical-bistable system including the effect of the transverse radiation field and the effect of an inhomogeneously broadened atomic medium are studied by means of the mean-field approximation and dressed-mode theory in this paper. Our study shows that the bistable region enlarges with an increase of the ratio r0{\mathit{r}}_{0}r0​/w0{\mathit{w}}_{0}w0​ (r0{\mathit{r}}_{0}r0​ is the radius of the cylindrical atomic sample and w0{\mathit{w}}_{0}w0​ the beam waist of the Gaussian beam), and decreases with increasing width of the inhomogeneously broadened line. The transverse-field effect has more impact on the magnitude of the bistable region than the inhomogeneous broadening under certain conditions. In the case of two unstable modes, the evolution of the field envelope before reaching the stable oscillation regime differs remarkably from that in the case of the plane-wave approximation with a homogeneously broadened atomic medium.
Of the Lorenz-type instabilities expected in optical systems, the single-mode instability in optical bistability has been the subject of detailed theoretical and experimental work by our groups. A treatment employing the plane-wave and mean-field limits of the Maxwell-Bloch equations predicts a rich variety of higher-order bifurcations including period doublings and intermittency.1 An extension of this work to include the transverse dependence of the intracavity field reveals no significant qualitative differences between the plane-wave theory and the Gaussian beam theory as regards the stability boundaries obtained from a linearized analysis.2 The instability persists in the presence of a Gaussian transverse profile and the boundaries are not radically modified compared with those obtained from the plane-wave theory. However, numerical integration of the Maxwell-Bloch equations in the single transverse mode approximation does not show the wealth of higher-order dynamic states present in the plane-wave case. An experimental investigation of optical bistability for two-level atoms in a single transverse, single longitudinal mode cavity exhibits limit cycle oscillation with stability boundaries that agree well with the boundaries obtained from the work in Ref. 2. However, for the range of values C < 300, |Δ| < 5, |θ| < 50, X ~ 102, the experimental results do not show the diversity of higher dynamic states expected from the plane-wave theory, in agreement with our numerical results. In addition the measurements support the existence of a single transverse mode oscillation. The sum of our theoretical and experimental work provides a quantitative statement for the role of the transverse effects in optical instabilities.
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.