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International Meeting on Instabilities and Dynamics of Lasers and Nonlinear Optical Systems

Analytic Studies of the Laser With a Saturable Absorber

Thomas Erneux

Published Jan 1, 1985• 0 citations
Publisher

Abstract

In the laser with a saturable absorber (LSA), the spontaneous and stimulated emissions build up in the laser cavity but are restrained by the intracavity absorber. As a result, two new modes of operation are observed: optical bistability and time-periodic intensity pulses. These two behaviors are not observed in the usual laser under normal conditions. Thus, the LSA is an example of an active system displaying optical bistability. (See Ref. 1 for a general review).

DOI
10.1364/idlnos.1985.tud1

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Soviet Journal of Quantum Electronics•Mar 31, 1986•1 citation
In the laser with a saturable absorber (LSA), the spontaneous and stimulated emissions build up in the laser cavity but are restrained by the intracavity absorber. As a result, two new modes of operation are observed: optical bistability and time-periodic intensity pulses. These two behaviors are not observed in the usual laser under normal conditions. Thus, the LSA is an example of an active system displaying optical bistability. (See Ref. 1 for a general review).
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 optical bistability (OB) behavior of single-mode Fabry- Perot lasers containing saturable absorber (LSA) is presented on the basis of the rate equations with allowance for spontaneous emission and spatial hole-burning. Special attention is paid to the case of dominant inhomogeneous broadening in both Lorentzian and Gaussian models. The OB occurrence conditions are clearly displayed in phase diagrams. The influence of the main LSA parameters on OB characteristics as well as on OB curves' stability are investigated in detail. Some practical suggestions for optimizing the bistable operation in LSA are also given.
The equation of motion for the slowly varying field amplitude of the laser containing an intracavity saturable absorber (LSA) is where a is the net gain (pump parameter) and b is a saturation parameter of the laser. In our experiment the absorber saturates faster than the amplifier and the parameter b is positive. q(t) is a complex Gaussian white noise random process representing spontaneous emission noise. From Eq. (1) we obtain for the steady-state probability density of light intensity I = | E |2. From this equation various moments of light intensity can be calculated and compared with experimentally measured quantities. For b > 0 the LSA exhibits bistability and a first order phase transition occurs at a = -3b2/16. For negative values of b there is a continuous transition at a = 0. Experiments were carried out on a He—Ne laser with an intracavity Ne absorber cell. The laser was operated close to the center of the absorption line. Slow drifts of light intensity were controlled by an electronic feedback loop. The parameter b was varied by changing the current in the absorber tube. Pump parameter a was then varied by changing passive losses in the cavity by means of an adjustable knife edge. The main beam from the LSA was allowed to fall on a detector/am- plifier combination. The voltage output from the detector was digitized by a multichannel analyzer and a histogram of voltage amplitudes was built up. Since the voltage output from the detector is directly proportional to the light intensity incident on the detector, voltage histogram is a direct representative of the intensity probability distribution. From the measured histogram moments of light intensity were calculated. These results are compared with the theoretical predictions.
A simple mathematical model to describe the action of a saturable absorber in a laser cavity (LSA) was developed. The approach considered here takes in a phenomenological way into account the essential physical processes which makes it possible to determine the principal parameters in a LSA and their influences on the optical bistability. We will study theoretically optical bistability in a trimodale laser containing a saturable absorber in the case that the active medium and absorber show a homogeneous broadening. We determine the densities of photons as function of the pumping of the active medium and analyze the linear stability of the solutions obtained.
In this paper, we develop a theoretical model that accurately describes the nonlinear phenomenon of optical bistability in Fabry-Perot laser containing a saturable absorber "LSA". We present an analytical model for optical bistability in a LSA. The physics of optical bistability in a classical optical resonant system such as Fabry-Perot etalon has been well-established, and can be described by simple analytical models. The photon intensities were determined as a function of the pumping rate of the active medium, and we analyzed the linear stability of the stationary solutions 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.