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International Journal of Modern Physics B

TRANSVERSE FIELD AND INHOMOGENEOUS BROADENING EFFECTS ON OPTICAL BISTABILITY IN MIXED SPECIES

Mona Ali, S. M. A. Maize, M. A. El-Deberky

Published Aug 20, 2008• 1 citation
Publisher

Abstract

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.

DOI
10.1142/s0217979208039939

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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.
In this paper we analyze the steady-state and stability properties of bistable optical systems, lasers with an injected signal, and ordinary free-running lasers. The starting point of our study is a unified model of a ring cavity containing a finite-size cylindrical sample of homogeneously broadened two-level atoms, and capable of supporting a single field mode with a Gaussian transverse profile. After solving the equations of motion in the steady state, we carry out a linear stability analysis of the stationary solutions, identify the domains of unstable operation of each of the three systems, and compare in detail the results of this work with those of earlier plane-wave uniform-field calculations. In the case of the laser with an injected signal, we find a significant enhancement of the instability domain relative to the plane-wave limit. A similar conclusion holds for mixed absorptive and dispersive optical bistability, although the enhancement of the domain of instability is less pronounced. Unstable behavior is predicted to occur for experimentally accessible values of the bistability parameter, and to be favored by the absence of bistability and by the selection of atomic and cavity detunings having opposite signs. This configuration ensures that the instability will be responsible for the emergence of undamped output pulsations of the type that will make the bistable system behave as an optical clock.