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Physical Review A

Regular and chaotic dynamics of optically pumped molecular lasers

Jerome V. Moloney, W. Forysiak, J. S. Uppal, Robert G. Harrison

Published Feb 1, 1989• 34 citations
Publisher

Abstract

We present a detailed analysis of the dynamical behavior of an optically pumped molecular laser. This study combines bifurcation and power spectral analysis with numerical investigation of the global features of attractor topology under control parameter variation. The special role of the pump laser in generating physically distinct periodic and chaotic dynamics is emphasized through the complementary use of laser gain and dispersion characteristics. Our main results are the following: (i) instabilities associated with the physically distinct mechanisms of relaxation and pump-induced Rabi sideband oscillations are readily generated; (ii) the topological characteristics of both periodic and chaotic attractors reflect these physically distinct mechanisms, making it possible to discriminate between both types of behavior in heterodyne power spectra; and (iii) the ratio of deenergization to dipole-dephasing rates is central to determining the operating characteristics of the laser.

DOI
10.1103/physreva.39.1277

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We present a detailed analysis of the dynamical behavior of an optically pumped molecular laser. This study combines bifurcation and power spectral analysis with numerical investigation of the global features of attractor topology under control parameter variation. The special role of the pump laser in generating physically distinct periodic and chaotic dynamics is emphasized through the complementary use of laser gain and dispersion characteristics. Our main results are the following: (i) instabilities associated with the physically distinct mechanisms of relaxation and pump-induced Rabi sideband oscillations are readily generated; (ii) the topological characteristics of both periodic and chaotic attractors reflect these physically distinct mechanisms, making it possible to discriminate between both types of behavior in heterodyne power spectra; and (iii) the ratio of deenergization to dipole-dephasing rates is central to determining the operating characteristics of the laser.
Interaction of two coherent fields of arbitrary intensity with a general homogeneously broadened three-level molecular system for both an amplifier as well as a laser oscillator under general conditions of pumping is discussed. The amplifier solution is obtained through the time-averaged density-matrix formalism with two coherent fields treated classically. A detailed consideration of both real and imaginary parts of the electric susceptibility at pump and emission frequencies, corresponding to gain and dispersion in the active medium has been taken into account. The results obtained are used to study a number of situations for weak and strong pumping in the laser amplifier. Subsequently these are applied to a mode analysis of a unidirectional single-mode laser oscillator to determine the output characteristics of the laser and to establish conditions under which emission becomes dynamically unstable resulting in sustained oscillatory emission. The results obtained are found to be in good agreement with those of a full numerical analysis of the atomic and field coupled equations describing the system.
The dynamic behaviour of an optically pumped J = 0 ↔ J = 1 ↔ J = 0 laser for any arbitrary value of the relative orientation angle between the linear polarizations of the pump and laser fields is analysed. By changing this angle, the steady states show a smooth monotonic variation, but the dynamic states undergo a complex sequence of bifurcations, including a generalized class of type-I intermittency that leads to the glueing of attractors. Small variations in the polarization angle bring about structural attractor modifications as large as those produced by large variations in the pump intensity.
The dynamical behavior of a Raman ring laser is investigated in the plane-wave limit. Assuming that the polarizability adiabatically follows the fields and that the molecular ground state remains undepleted, we obtain a discrete mapping for the pump and Stokes field amplitudes. We find that, when the two injected fields are sufficiently detuned from the Raman transition, the transmitted fields can become chaotic. Additionally, when the injected fields are of comparable magnitudes, hyperchaos—characterized by two positive Lyapunov exponents—is observed. This system thus represents an alternative for observing "bad-cavity" optical chaos indicated for nonlinear interferometers filled with two-level atoms1, 2 but not so far observed in purely optical systems. We compare the Lyapunov and correlation dimensions in the chaotic regime. Finally, we relax the assumption of adiabatic following to show the importance of the molecular dynamics in determining the characteristics of the chaotic field oscillations.
Interaction of two coherent fields with a homogeneously broadened three-level system is discussed for both a laser amplifier and laser oscillator under weak field emission. Analytic expressions are obtained to study explicitly the dependence of the amplifier emission characteristics on various pump parameters. These results are used to examine the steady-state and sustained oscillatory emission features of a single-mode laser oscillator. Subsequently, the amplifier analysis is generalized for an arbitrary deenergization to dephasing rate for the three-level system.>
The distributions, in parameter space, of subcritical Hopf bifurcations and the various attractors of time-dependent motions of optical bistable systems are investigated systematically. The main emphasis is placed on the influence of the variations of the control parameters on the distributions. We have observed the tristability of large-amplitude regular or chaotic motions, periodic pulsations, and the stationary state for the parameters where no instability of the stationary solution exists at all over the complete range of the external field. The problem of how to find the various attractors and how to reveal chaotic motions by adjusting the control parameters is discussed according to the numerical results.
In a previous paper [Phys. Rev. A 52, 4229 (1995)] a vectorial model has been derived to describe the dynamics of an optical fiber laser output. In this semiclassical theory, the time-dependent behaviors of the two field polarizations are deduced through the interaction between the light and the active atoms which supposes the presence of a vectorial atomic polarization. This paper is devoted to the analysis of the dynamics presented by such a model using the bifurcation theory. An analytical study investigates the parameter space as far as possible and numerical simulations show the presence of various types of behaviors displayed by the two output field polarizations in the domains where the steady states have lost their stability. The influence of the pump polarization is emphasized. The results are in accordance with the experimental observations.