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Оптика и спектроскопия

Relaxation and polarization oscillations in a wide-aperture bistable laser with a saturable absorber

Sergey V. Fedorov, Nikolay N. Rosanov, Nikolay A. Veretenov

Published Jan 1, 2022• 0 citations
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Abstract

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

DOI
10.21883/eos.2022.10.54862.46-22

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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
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.
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 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 dynamics of a two-mode laser is studied in the presence of a selective saturable absorber interacting only with one of the modes. The specific nature of the system is determined by the presence of the out-of-phase relaxation oscillation, which becomes undamped when a sufficiently dense saturable absorber interacts with the weaker mode. If the absorber interacts with the stronger mode, the in-phase relaxation oscillation is excited, and the situation becomes similar to that observed in a single-mode laser. In the case of a slowly relaxing absorber, the difference of populations of its working levels can be adiabatically excluded. This procedure substantially simplifies the model and does not change its dynamic characteristics.
We present an examination of the stability and time-dependent behavior of a semiclassical model of the ring laser with a saturable absorber, in the vicinity of multiple steady-state solutions. We consider particularly the case in which the cavity is tuned away from the resonance frequency of the gain medium. The model considers the absorbing and amplifying media to consist of two-level atoms. Only homogeneous spectral broadening and unidirectional propagation of the light are considered. We are able to treat the steady state with an approximate mean field solution and also with its exact longitudinal dependence. The latter is found numerically from an implicit function solution to the Maxwell-Bloch equations in the steady state. There may be as many as four steady-state solutions for a given set of parameter values. When there are four solutions, we find that three solutions are of one intensity class (high or low) and that one is of a second intensity class (low or high). When the absorbing and emitting atoms are in resonance and the cavity is tuned to their line-center frequency, two of the members of the three-solution class have the same intensity. This degeneracy is broken by detuning.
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.