Transverse effects in a thin slab of material with local-field induced intrinsic optical bistability

We consider a thin slab of dense material exhibiting local-field induced intrinsic optical bistability irradiated by a transversely uniform optical field (holding beam). We study the transverse effects that can arise when local excitations are created by means of a narrow optical beam (writing beam). We show that whereas diffraction effects are negligible, diffusion effects make the excitation-domain walls to move inward or outward in the transverse direction, with a speed that depends on the holding-beam intensity and the diffusion coefficient. Conditions can be found, however, for which the wall movement is counterbalanced by the field transverse gradient so that stable narrow excitation …

The dynamics of optically pumped molecular lasers. On its relation with the Lorenz - Haken model

In this paper we review the work on dynamical instabilities in optically pumped molecular lasers (OPLs) that has been carried out during the last 15 years. The main purpose of this review article is to survey and extend the authors' work on optically pumped molecular lasers and to place it in context with other research done in this area, without being a comprehensive review of all previous work done on this topic. In particular, we concentrate on the theoretical interpretation of the Lorenz dynamics observed in the far-infrared ammonia laser by reviewing the results obtained with different models of OPLs. New results corresponding to the dynamics obtained with the Doppler-broadened OPL mod…

Nonlinear dynamics of a two-photon Fabry–Pérot laser

Abstract The steady-state emission, stability and temporal dynamics of a single-mode two-photon laser with a Fabry–Perot cavity is investigated and compared with that of a ring-cavity laser. It is found that the Fabry–Perot cavity makes the laser less efficient than the ring cavity because of spatial hole burning, but the domain of stability is larger for the Fabry–Perot laser. The intensity and phase dynamics are numerically investigated and distinctive features are found in the phase dynamics as compared with one-photon lasers.

Type-II intermittency in a cascade laser model

Types I and II intermittencies in a cascade laser model

Abstract We report on types I and II intermittencies found in a cascade laser model. A continuous transition from one to another type of intermittency, which involves the coexistence of both types of laminar phases within the same time series, is found. Type II intermittency has special characteristics such as its origin at a frequency locked two-torus. When frequency unlocked this torus bifurcates to a three-torus, further giving rise to a type II intermittent like behaviour with new features during the laminar phases.

Models, predictions, and experimental measurements of far-infrared NH3-laser dynamics and comparisons with the Lorenz-Haken model

Dynamics of the intensity and optical field amplitude of a coherently pumped far-infrared NH3-laser are measured and characterized. The experimental findings in certain parameter ranges closely follow the dynamics of the Lorenz model and its generalization for laser systems. Similarities and some specific differences are found in geometrical or statistical characterizations of the attractors. The experimental results are also consistent with the results of a model of optically pumped three-level lasers which takes into account the presence of a multiplicity of velocity groups as well as three-level coherence effects. For a certain region in parameter space, this far more complex model with …

Lorenz character of the Doppler-broadened far-infrared laser

The dynamic behavior of an optically pumped Doppler-broadened single-mode far-infrared laser is theoretically investigated in detail and compared with that of the simpler Lorenz–Haken laser. Through the analysis of phase diagrams, three-dimensional attractor’s projections, intensity maps, and the different terms of the laser equations, the analogies and the differences between the two models are determined. Optical pumping and Doppler broadening, present in this far-infrared laser model, can be approximately incorporated into a Lorenz–Haken model with effective parameters. These results represent a further step toward the understanding of the Lorenz-like behavior observed in recent years in…

INSTABILITIES IN DOPPLER BROADENED OPTICALLY PUMPED FAR-INFRARED LASERS

Recently Weiss and Brock observed Lorenz-type chaos in the 81.5μm emission from an optically-pumped 14NH3 laser1. The theoretical interpretation of the experimental results is an open question, however. In fact, the Lorenz-Haken model refers to incoherently pumped lasers with homogeneously-broadened two-level active media2. Models based on (at least) a three-level system are needed to describe optically-pumped lasers, whose dynamics is known to reduce to that of the Lorez-Haken model under certain limiting conditions3. But these conditions are not met in the 14NH3 laser, and indeed theoretical predictions of a model for this laser, which considered a homogeneously-broadened three-level acti…

Theoretical gain spectrum of coherently pumped mid-infrared Fabry-Pérot lasers

Abstract We study the gain spectrum of a coherently pumped mid-infrared laser which operates in a linear-cavity (Fabry-Perot), using a three-level density matrix theory. Arbitrary pump and emission field strengths as well as pressure and Doppler broadening are considered. A new strong directional gain asymmetry is found, which is related to the presence of two counterpropagating components in the standing-wave generated field. Gain lineshapes in a wide range of operating conditions are obtained and analysed.

Steady-state emission and stability of a single-mode two-level Fabry-Perot cavity laser

Abstract An analytical steady-state solution for a single-mode homogeneously-broadened two-level Fabry-Perot laser, valid for any field intensity, cavity detuning and level-population decay rates, is obtained. A power-series expansion of this solution allows to perform a linear stability analysis which reveals the existence of two Hopf bifurcations instead of one as in unidirectional ring lasers. These bifurcations delimit the domain of unstable emission of the laser with respect to small perturbations. The instability threshold for hard-mode excitation is higher than in a ring laser, although introduction of a small definite detuning makes them similar. The time-dependent behaviour above t…

Structural similarities and differences among attractors and their intensity maps in the laser-Lorenz model

Abstract Numerical studies of the laser-Lorenz model using parameters reasonably accessible for recent experiments with a single mode homogeneously broadened laser demonstrate that the form of the return map of successive peak values of the intensity changes from a sharply cusped map in resonance to a map with a smoothly rounded maximum as the laser is detuned into the period doubling regime. This transformation appears to be related to the disappearance (with detuning) of the heteroclinic structural basis for the stable manifold which exists in resonance. This is in contrast to the evidence reported by Tang and Weiss (Phys. Rev. A 49 (1994) 1296) of a cusped map for both the period doublin…

Physical interpretation of laser phase dynamics

The basic features characterizing the dynamical evolution of the phase of a detuned-laser field under an unstable regime are physically interpreted in terms of dispersive and dynamical effects. A general method for obtaining any attractor projection containing the phase information is established, which provides evidence for the heteroclinic character of the attractor in the presence of cavity detuning for any emission regime.

Polarization-sensitive population trapping in an optically pumped laser

Influence of light polarization on the dynamics of optically pumped lasers.

The dynamic behavior of a coherently pumped ring laser with a homogeneously broadened four-level medium is analyzed theoretically, considering linearly polarized pump and generated laser beams. The laser is shown to be much more stable when these polarizations are parallel than when they are orthogonal. In the latter case the instability pump threshold can be as low as four times the first laser threshold, and the laser dynamics shows Lorenz-type features.

Addressing optical pixel bits in a slab of dense optical material via intrinsic optical bistability

It is well known that dense materials with local-field effects can show "intrinsic" optical bistability when they are directly irradiated by a light beam. This has been shown theoretically in a number of works and also experimentally in several cases, in gas media and also in doped solid-state materials where nonlinearities based on standard local-field effects can be reinforced with other ion interaction effects. Although from the point of view of applications nonlinearities stronger than those found so far would be desirable, the fact that no optical resonator is needed to achieve bistability makes these materials potentially interesting for applications in optical information storage and…

Influence of pump coherence on the dynamic behavior of a laser

The dynamic behavior of a coherently pumped single-mode unidirectional ring laser with a homogeneously broadened three-level active medium is studied. Our formulation is based on a set often real equations of the plane-wave, mean-field Maxwell–Bloch type. The instability domain in the main control parameters space is determined. Our numerical study of these equations for a parameter range of the type explored in the recent experiments by Weiss Brock [ Phys. Rev. Lett.57, 2804 ( 1986)] reveals some similarities, but striking differences between our theoretical predictions and their experimental observations are also noted.

Coexistence of single-mode and multi-longitudinal mode emission in the ring laser model

A homogeneously broadened unidirectonal ring laser can emit in several longitudinal modes for large enough pump and cavity length because of Rabi splitting induced gain. This is the so called Risken-Nummedal-Graham-Haken (RNGH) instability. We investigate numerically the properties of the multi-mode solution. We show that this solution can coexist with the single-mode one, and its stability domain can extend to pump values smaller than the critical pump of the RNGH instability. Morevoer, we show that the multi-mode solution for large pump values is affected by two different instabilities: a pitchfork bifurcation, which preserves phase-locking, and a Hopf bifurcation, which destroys it.

Progress in Modelling Coherently Pumped Far-Infrared Laser Dynamics

Coherently pumped lasers (CPL) operating in the far-infrared spectral region shown a wealth of instabilities1, including a behavior remarkably similar2,3 with the predictions of the paradigmatic Lorenz-Haken model of a single-mode homogeneously broadened laser4,5. The qualitative agreement; between theory and experiments2,3 was rather surprising, for the model4,5 refers to a two-level system whereas the CPL operate on a three-level scheme, where the pumping and lasing transitions share a common upper level. Dupertuis et al.6 have identified conditions for the mathematical reduction of the CPL equations to the Lorenz-Haken equations4, but these conditions were not all fulfilled in the experi…

Generalization of the Lorenz-Haken model to atomic systems with different relaxation rates for the two laser levels

Abstract The fundamental Lorenz-Haken laser model is generalized to the case of a two-level amplifying medium with different external relaxation rates for the two levels and with internal relaxation. This represents one further degree of freedom, and important quantitative differences in the laser dynamics. i.e., in the stationary solutions, linear stability analysis, and timedependent solutions, are found. No significant qualitative differences, however, are observed.

Polarization phenomena in a laser coherently pumped by a linearly polarized field

The field intensity and polarization behaviour of an optically pumped laser is investigated in different operating conditions. For a linearly polarized pump field, a strong gain anisotropy is induced which favours generation of light with a polarization parallel to that of the pump field. Thus gain anisotropy can be counterbalanced by cavity-loss anisotropy only at low pumping field intensities, and the interplay between both types of anisotropy leads to polarization switching phenomena. In contrast to the case of the incoherently pumped laser, the decay rate for the magnetic dipole induced on the J = 1 level plays a minor role in determining the polarization dynamics. The influence of a lo…

Two-photon laser dynamics.

Degenerate as well as nondegenerate three-level two-photon laser (TPL) models are derived. In the limit of equal cavity losses for both fields, it is shown that the nondegenerate model reduces to the degenerate one. We also demonstrate the isomorphism existing between our degenerate TPL model and that of a dressed-state TPL. All these models contain ac-Stark and population-induced shifts at difference from effective Hamiltonian models. The influence of the parameters that control these shifts on the nonlinear dynamics of a TPL is investigated. In particular, the stability of the periodic orbits that arise at the Hopf bifurcation of the system and the extension of the self-pulsing domains of…

Operation conditions and stability of a degenerate two-photon laser

Abstract The presence of a far off-resonant intermediate level in a degenerate three-level two-photon laser model manifests through a steady pump-dependent and a dynamic frequency shift on the laser equations. The steady shift strongly affects the pump threshold necessary for emission, preventing it in certain cases. The dynamic shift makes the frequency pulling/pushing to be intensity-dependent and substantially modify the domains of existence and stability of the lasing solution permitting stable operation for large cavity losses in certain cases.