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Physical Review A

Lasers with three-level absorbers

Govind Prasad Agrawal

Published Sep 1, 1981• 10 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.24.1399

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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 \ensuremathΛ\ensuremath{\Lambda}\ensuremathΛ-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.
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.
We study the semiclassical equations for a laser with a saturable absorber in the mean-field limit, assuming homogeneously broadened two-level atoms, for a set of parameters where the system displays optical bistability and time-periodic solutions. In the first part the bifurcation diagram for stationary and periodic solutions is obtained by numerical integration. Two different classes of stable periodic solutions arise: small-amplitude solutions and passive QQQ switching. We observe hysteresis domains involving up to three solutions (stationary and/or periodic). We also discuss the validity of some standard approximations and show that even in the absence of detuning the phases play an important role. We also discuss the influence of the initial conditions whose symmetry properties induce important modifications of the bifurcation diagram. In the second part we introduce an alternative adiabatic elimination scheme which allows us to construct the small-amplitude periodic solutions over nearly their whole range of existence. We then study these solutions near the Hopf bifurcation from which they emerge and derive analytic conditions for their stability. When they are stable, $\stackrel{\mathrm{\ifmmode\acute\else\textasciiacute\fi{}}}{\mathrm{w}}$e also give the conditions under which a secondary Hopf bifurcation will occur, leading to quasiperiodic solutions.
Optical bistability in a laser with an intracavity saturable absorber is a phenomenon theoretically investigated firstly by Lugiato et al(1). The experimental observations in CO2 lasers(2,3) have provided clear evidence of the bistability phenomenon and shown that the absorber parameters could be determined from these observations. In this work a quantitative comparison between a theoretical description of optical bistability and the experimental results is presented for the first time. The parameters defining the laser cavity and the CO2 amplifying medium were measured carefully, and the bistability was observed and analyzed quantitatively as a function of the laser parameters.
In a laser with a saturable absorber (LSA), two spatially separated cells are placed in the laser cavity as shown in Figure 8.1. The roles of the two cells are quite different: one of them is pumped so that the atoms have a positive population inversion (active or amplifying medium); the other one is left with a negative population inversion (passive or absorbing medium). As these two media are in general different, they saturate at different power levels. The most interesting case corresponds to the situation where the absorber saturates more easily than the active medium, introducing nonlinear losses inside the cavity. This new nonlinearity is responsible for two phenomena. An LSA may exhibit optical bistability, i.e. two distinct stable steady states may coexist for a range of values of a parameter. It may also produce pulsating intensity oscillations which have been called “passive Q-switching” (PQS) in contrast to “active Q-switching” experiments such as the “gain switching” experiments discussed in Section 1.3.2. The interest in LSAs varied very much over time, with peaks in the late 1960s for their large intensity pulses, in the mid 1980s for their chaotic outputs, and in the late 1990s for the design of compact microlasers. Historically, physicists trying to explain the irregular intensity pulses delivered by the ruby laser suspected the possible destabilizing role of a saturable absorber. Shimoda proposed that the nonlinear losses generated by a saturable absorber could explain this phenomenon.
The regions of stability of homogeneous generation regimes in a wide-aperture laser with a saturable absorber, including a semiconductor laser with a vertical output of radiation, are determined depending on the relative relaxation rate of carriers in active and passive media and on the frequency detunings of working transitions in these media with a resonant frequency of radiation, taking into account its polarization state. The excitation thresholds for relaxation and polarization oscillations are determined within the four-level model. Keywords: wide-aperture laser, saturable absorber, relaxation and polarization oscillations
Considers phase conjugation through degenerate four-wave mixing in a Λ-type three-level system under certain simplifying assumptions, the most restrictive among them being the assumption of symmetrical detuning of the pump from the two lower lying sublevels. When compared to an absorbing resonant two-level system, it is found that significantly higher values of the phase-conjugate reflectivity are possible at pump intensities well below saturation provided the sublevel splitting is less than a homogeneous linewidth. The physical mechanism responsible for phase conjugation is coherent population trapping arising from two-photon-induced atomic coherence between the two sublevels.