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Annual Meeting Optical Society of America

Investigations of intensity fluctuations in the laser with a saturable absorber

Mansour Mortazavi, Surendra Singh

Published Jan 1, 1990• 0 citations
Publisher

Abstract

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.

DOI
10.1364/oam.1990.fcc4

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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.
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 question of the behaviour of the LSA when a control parameter is a slowly varying function of time, has recently been raised [1]. The investigation of the transient behaviour of a LSA is interesting not only in connection with the problem of the response time of optically bistable systems but also because in any real experiment, if one wants to explore a phase diagram, the parameters have to be changed in time. Although the relaxation times of the molecular medium and the cavity response time are of the order of 100μs or smaller, the time constants characterising the transient regime of the LSA may be much longer because of the critical slowing down which appears near the limit points of the hysteresis cycle[2]
Many quantum optical systems exhibit first-order phase transition analogy.1 Fluctuations of the optical field in such systems are due to spontaneous emission noise. The nature of these fluctuations for various systems has been discussed using various approaches. Fully quantum mechanical and Langevin equation treatments have been given for the dye laser2,3 and the laser with a saturable absorber (LSA) with homogeneously broadened media.2,4 For inhomogeneously broadened media, such treatments are either valid for low intensities or do not fully take into account the effect of quantum noise.5 In this contribution we present a fully quantum mechanical treatment for the LSA with an inhomogeneously broadened absorber using the Foch state representation of the density matrix.2,6
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.
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.