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Physical Review A

Inhomogeneously broadened ring-cavity optical-bistability system with a Gaussian transverse intensity profile

Fan Xijun, Tan Baoguo, Yuan Zhifang, Wang Xiangtai

Published Aug 1, 1991• 5 citations
Publisher

Abstract

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 ${\mathit{r}}_{0}$/${\mathit{w}}_{0}$ (${\mathit{r}}_{0}$ is the radius of the cylindrical atomic sample and ${\mathit{w}}_{0}$ 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.

DOI
10.1103/physreva.44.2048

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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.
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 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.
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.
Beams of homogeneously broadened two-state sodium atoms in a confocal ring resonator have been employed to investigate the steady-state characteristics of absorptive [1] and dispersive optical bistability. Also studied in the same system is the dynamical behavior due to the intrinsic single-longitudinal-mode instability [2] originating in the alteration of the atomic absorption profile by a strong field as in the Lorenz-type instability in the homogeneously broadened laser. All experimental parameters are carefully measured and corrected for transit broadening, finite absorption, and residual Doppler broadening in order to be able to make an absolute comparison with the single-Gaussian-transverse-mode theory [3-6]. Despite the frequency degeneracy of the transverse modes of the resonator, the agreement with this theory for absorptive bistability is remarkably good. The dispersive bistability data are more difficult to interpret, but they seem to be in reasonable agreement with the theory; the same can be said of the results for the domain and oscillation frequency of the instability, at least within a certain region of parameter space. Outside this region, multiple unstable states appear for various intracavity intensities; recent observations suggest that these may be due in part to instabilities involving higher-order transverse modes of the resonator.
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.
We consider the dynamics of an inhomogeneously broadened unidirectional ring laser formulated in the traditional Maxwell-Bloch configuration of a two-level atom with transverse modes. We numerically analyze the model for a single-longitudinal mode in the paraxial approximation, using the uniform field limit with cylindrical symmetry and a Gaussian profile for inhomogeneous broadening. Several domains of solutions are found for the resonant case in the good cavity limit. The laser threshold is found to be dependent on the mode spacing as well as on the gain and scaled Doppler broadening. Hysteresis between stable and unstable solutions is obtained in realistic operating conditions for both increasing (decreasing) gain and increasing (decreasing) mode spacing (i.e., for changes in the initial conditions).