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Physical Review A

Effect of a spectral line with Doppler broadening on optical bistability in a ring cavity

Qiyuan Feng, Liu Ya-jie, Yang Xing-yu

Published Oct 1, 1988• 2 citations
Publisher

Abstract

We discuss the effect of a spectral line with Doppler broadening on optical bistability in a ring cavity which contains a saturable absorber of two-level atoms. In this paper, we first derive a generalized equation that is satisfied by the output light intensity of this system from the Langevin equations in H. Haken's Laser Theory (Springer, Heidelberg, 1970). Then, we simplify the generalized equation for a single mode. We study the single-mode equation for both nonexisting and existing spontaneous emission and obtain the result that the square of the bistability loop increases with the increase of Doppler broadening of the spectral line.

DOI
10.1103/physreva.38.4098

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Soviet Journal of Quantum Electronics•Sep 30, 1987•2 citations
We discuss the effect of a spectral line with Doppler broadening on optical bistability in a ring cavity which contains a saturable absorber of two-level atoms. In this paper, we first derive a generalized equation that is satisfied by the output light intensity of this system from the Langevin equations in H. Haken's Laser Theory (Springer, Heidelberg, 1970). Then, we simplify the generalized equation for a single mode. We study the single-mode equation for both nonexisting and existing spontaneous emission and obtain the result that the square of the bistability loop increases with the increase of Doppler broadening of the spectral line.
A generalized equation that is satisfied by the output light intensity of this system from the Langiven equation in H.Haken’s Laser theory is first derived Then, the effect of a spectral line with Doppler broadening on optical bistability in a multi mode ring laser which contains a saturable absorber of two level atoms is discussed,and the square of bistability loop is defined.The result that the square of the bistability loop increases with the increase of Doppler broadening as e2|ω 0-Ω j| ,and the square of the loop decreases with the increase of broadening as e2|ω 0-Ω j| is obtained.
The characteristics of the mode intensity and conditions for occurrence of optical bistability in a ring laser with a saturable absorber are considered. The rate equation approximation method is used to find analytic expressions for these characteristics. It is shown that changes in such physical parameters as the homogeneous and inhomogeneous broadening, coefficients of relaxation of amplifying and absorbing cells, etc. cause changes in the range of existence of optical bistability or a hysteresis cycle. The influence of inhomogeneous broadening and of spontaneous emission near the lasing threshold on the appearance of optical bistability is demonstrated for the single-mode regime.
This paper presents new results for the steady states of a detuned ring laser with a saturable absorber. We employ a semiclassical model which assumes homogeneously broadened two-level atoms. We proceed by solving the Maxwell-Bloch equations for the longitudinal dependence of the steady states of this system, and then simplify our solution by use of the uniform-field approximation. We present uniform-field results for squared electric field versus operating frequency, and for each of these versus cavity tuning and laser excitation. Various cavity linewidths and both resonant and nonresonant amplifier and absorber line-center frequencies are considered. The most notable finding is that cavity detuning breaks the degeneracies found in the steady-state solutions of the fully tuned case. This leads to the prediction that an actual system will bifurcate from the zero-intensity solution to a steady-state solution as laser excitation increases from zero, rather than to the small-amplitude pulsations found for the model with exactly resonant tuning of the cavity and the media line centers. Other phenomena suggested by the steady-state results include tuning-dependent hysteresis and bistability, and instability in both intensity and frequency due to the appearance of one or more new steady-state solutions as tuning is varied. These effects of detuning are being tested by a linearized stability analysis whose results will be reported separately.
We review and extend the theory of instabilities in absorptive optical bistability for ring cavities containing homogeneously broadened two-level media. The instabilities occur in the high-transmission branch and result in either a precipitation to the low-transmission branch or in pulsed multimode operation. Two numerical approaches are used to predict operation away from the simple mean-field limit. First, an iterative method is used to solve the general field eigenvalue equation for cavity modes with frequencies displaced from the input frequency. This work shows that the instability region decreases in size as the mirror transmission increases. These calculations are confirmed by the second numerical technique, consisting of direct integrations of the coupled Maxwell-Bloch equations. This second approach also provides time histories of the instability evolutions, and divides the instability range into a precipitation regime and a self-pulsing regime. The results are discussed in terms of first- and second-order phase transitions, and agree with the analytical results obtained within the dressed-mode description of optical bistability. They show that when the incident field is adiabatically decreased along the high-transmission branch, the spiking behavior always appears abruptly. By further decreasing the incident intensity, the self-pulsing disappears either continuously if the system remains in the high-transmission branch, or discontinuously if the system precipitates to the low-transmission branch. Connection is made with induced probe gain known in the saturation spectroscopy of absorbers (uninverted media), in which population pulsations transfer energy from a saturating wave to the probe waves. The very close relationship with multimode operation in homogeneously broadened unidirectional ring lasers is also established.
An analysis is made of the operation of a laser with a saturable absorber and dominant inhomogeneous line broadening. A four-level model is used to determine the characteristics of mode intensities and conditions for the appearance of an optical bistability. By analogy with a two-level model, the results obtained demonstrate that in single-mode operation this bistability appears only if the relaxation coefficients of the upper levels of atomic or molecular systems are different in the amplifying and absorbing parts of a laser. Moreover, a change in the inhomogeneous broadening alters greatly the optical bistability interval. The calculation method used in the present study can be readily extended to analyze a multimode laser.