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Bistability and tristability of single-mode gas lasers and lasers containing a saturable absorber

John C. Englund

Published Jun 9, 1986• 0 citations
OpenAlex

Abstract

When a tuned standing-wave gas laser operates on-resonance, neighboring frequencies experience gain in accordance with the Lamb dip. Bennett1 showed that it is possible for certain of these frequencies also to satisfy the phase-matching condition required by the dispersion relation. In such cases, gas lasers possess three possible steady states—one on-resonance state and two frequency-pushed ones. Bennett suggested that this effect could give rise to bistability and hysteresis in the frequency vs detuning characteristics.

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Physical Review A•Apr 1, 1991•9 citations
When a tuned standing-wave gas laser operates on-resonance, neighboring frequencies experience gain in accordance with the Lamb dip. Bennett1 showed that it is possible for certain of these frequencies also to satisfy the phase-matching condition required by the dispersion relation. In such cases, gas lasers possess three possible steady states—one on-resonance state and two frequency-pushed ones. Bennett suggested that this effect could give rise to bistability and hysteresis in the frequency vs detuning characteristics.
The structure of the Lamb dip may permit a standing-wave gas laser containing a saturable absorber (LSA) to exhibit frequency tristability while oscillating in a single spatial mode. This is concluded from the steady-state and stability analyses of a plane-wave gas-laser model in which the atomic populations are taken as homogeneous. Conditions for this behavior are investigated, and it is concluded that very high pump excitations are needed, which is in contrast to previously reported predictions of frequency multistability for LSA’s containing homogeneously broadened media.
This paper discusses the case of a Doppler-broadened gas laser with a saturable intracavity absorber gas. The semiclassical equations governing the field intensities and the atomic density-matrix elements are set up. The latter are written as Fourier series, the components of which are shown to obey coupled difference equations. In this paper the exact steady-state solution in single-mode operation is obtained. The lowest approximation (rate-equation approximation) is used to compute detailed characteristics of the system. In particular, the influence of the pumping rates in the two cells are investigated and displayed in the figures. The regions of bistable operation are determined and conditions for the occurrence of an inverted Lamb dip are given. The effect of a slow modulation of the pumping rates is discussed. The range of validity of the lowest approximation is investigated both analytically and numerically. Finally, there is a brief discussion of the influence of pressure on the parameters of the theory.
When the strong Doppler limit is applicable, a tuned laser containing Doppler-broadened gain and absorption media may produce a steady-state standing-wave field that is both frequency pushed and isolated from the branch of on-resonance steady states. The locus of the isolated states plotted as a function of the linear gain is a pair of closed loops, called isolas. Similar running-wave modes are not found in this limit. A connection is indicated between the isolated steady states and both the mode-pushed states discovered by Bennett [ The Physics of Gas Lasers ( Gordon and Breach, New York, 1977)] and the instability found by Casperson [ Phys. Rev. A21, 911 ( 1980)].
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.
The resonance condition is used to describe theoretically the three main kinds of standing waves with E\ensuremath{\perp}B (linear) and E?B (helicoidal and circular polarizations) that can be produced by the same laser and their nonlinear interaction with an atomic medium. It is shown that the saturation behavior of a single-mode gas laser is drastically modified by the nature of the operating standing wave. The predictions are checked experimentally with a laser from which each kind of standing wave can be generated with the same losses. The anisotropic structure of the saturation and in particular of the Lamb dip is isolated in each case. Very good agreement is observed between experiments and theory.