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Acta Optica Sinica

On catastrophe behavior of the three-level laser

Min Sun

Published Jan 1, 1988• 0 citations
OpenAlex

Abstract

The behavior of the three-level single-mode laser in the presence of an applied field and a saturable absorber is revealed near the losing -threshold. It is shown by quantitatively calculating that nonlinearity of laser field and introduction of applied field cause the correspondence of steady states of the laser with the canonical cusp catastrophe manifold. In this paper the physical meaning of the cusp catastrophe manifold is explained in more detail. The quantitative condition for optical bistability generation is given.

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The behavior of the three-level single-mode laser in the presence of an applied field and a saturable absorber is revealed near the losing -threshold. It is shown by quantitatively calculating that nonlinearity of laser field and introduction of applied field cause the correspondence of steady states of the laser with the canonical cusp catastrophe manifold. In this paper the physical meaning of the cusp catastrophe manifold is explained in more detail. The quantitative condition for optical bistability generation is given.
A general theory of optical bistability for a homogeneously broadened two-level system in a Fabry-Perot interferometer is presented. Both absorptive and dispersive mechanisms are included, and in the mean-field approximation a cubic state equation is derived relating transmitted intensity to all physical parameters. From the perspective of catastrophe theory, this equation describes an elementary cusp catastrophe. We show that bistable switching may follow not only from sweeping the incident laser intensity, but also with continuous variation of atomic or cavity detuning, or atomic density, with the laser intensity fixed. For the case having incident intensity as the variable control, the domain of bistability is studied in some detail as a function of the remaining fixed parameters. Stability criteria are considered for the general case including both absorption and dispersion.
In this paper, we generalize a previously developed model describing the behavior of optical bistability in the operation of a quasi-three-level laser by taking into account a Gaussian transverse distribution for the laser mode and including inhomogeneous line broadening for the laser medium. The results show that apart from some quantitative modifications, the primary characteristics of bistability predicted by the simplified model remain correct; in particular, the fundamental condition for the existence of bistability,fxa/(xa+1), turns out to hold universally. It is also revealed that in comparison with the results obtained in the simplified model, the intensities at the up- and down-threshold will be increased, whereas the bistability range will be reduced.
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.
Output characteristics of a traveling-wave monomode laser with an intracavity three-level absorber are investigated. The laser frequency is assumed to be symmetrically detuned from the two ground-state sublevels for a $\ensuremath{\Lambda}$-type transition scheme. It is shown that bistability and hysteresis in the laser output, characteristics of a first-order phase transition, may arise much before the absorber saturates. For this reason, bistability may be observed even if the gain medium saturates faster than the absorber, in contrast with the case of a two-level saturable absorber. The physical mechanism for bistable behavior is coherent population trapping which accumulates all absorbing atoms in the ground-state sublevels with a sharp decrease in absorption.
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.