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Journal of Baotou University of Iron and Steel Technology

Effect of spectral line with Doppler broadening on optical bistability in a multi mode ring laser

Zhang Zhan, Uist Baotou

Published Jan 1, 1999• 0 citations
OpenAlex

Abstract

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.

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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.
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.
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.
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.
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.