W. Forysiak

Bifurcations of an optically pumped three-level laser model

Abstract We study the bifurcations in a sixth-order model of a resonant, homogeneously broadened, three-level, optically pumped laser. Standard analytical and numerical techniques are used to obtain a complete unfolding of the models equilibrium bifurcations in its four-dimensional parameter space. Regions of stationary, periodic and potentially chaotic behaviour are then readily identified. Turning to two specific cases, we study the principal global bifurcations in a two-parameter plane and show their origin in special degenerate bifurcation points of codimension two. The different relative dispositions of the principal homoclinic and heteroclinic connections in these two examples result in different local bifurcation behaviours and chaotic dynamics, which we illustrate in detail.

Second harmonic generation of single- and multilongitudinal-mode CO 2 laser emissions

Second harmonic generation of laser radiation from a carbon dioxide laser is significantly increased when a smooth temporal profile is not a requirement. (AIP)

Influence of competition on optical sum frequency generation

Abstract We present results of a theoretical analysis of sum-frequency generation incorporating second harmonic generation of the incident fields. It is shown that under certain conditions, a significant reduction in conversion efficiency can occur even when phase mismatch for second harmonic generation is relatively large. Experimental results on sum frequency generation in CdGeAs 2 of two CO 2 laser emission tuned to the 9 μm vibrational band are presented which are in good qualitative agreement with the theoretical predictions.

Regular and Chaotic Dynamics of Coherently Pumped 3-Level Lasers

Optically pumped lasers (OPL’s) have emerged as highly attractive systems for experimental investigation of nonlinear laser dynamics [1–4]. They have attracted particular attention as perhaps providing systems most closely resembling that of the Haken-Lorenz model for a single-mode, resonant two-level laser with a homogeneously broadened gain [3]. For the two-level system the onset of dynamical instabilities and chaos in the laser output requires a cavity with high transmission such that the cavity field decay rate κ satisfies the so-called bad cavity condition κ ≥ Γ + ϒ (or 6 ≥ 1 + b) where Γ and ϒ are the energy and dephasing reduction rates respectively from the two levels and o = κ/ϒ and b = Γ/ϒ While conditions have been determined by which these lasers may be reduced to that of the Haken model [5] such a mode of operation provides but a limited aspect of their more general nonlinear dynamical behaviour [6–11]. The notable distinguishing feature of these systems is the two-photon coherent interaction associated with the coupled pump and lasing transitions. In this report we extend our earlier treatments of 3-level systems in the bad cavity limit to examine the good/bad cavity boundary around 6 = 1 + b.

Local and global bifurcations of optically-pumped three-level lasers

In recent years, experimental and theoretical studies of instability phenomena in active laser systems have been widely reported in the laser physics literature1. Many theoretical studies have considered the simplest physical configurations and therefore models comprising small systems of ordinary differential equations. In general, analysis of such models has concentrated on the equilibrium solutions and their bifurcations, with particular attention to the magnitudes of instability thresholds. This latter emphasis is largely a consequence of the high instability thresholds of the Haken-Lorenz two-level laser model2, which are widely considered to be physically unrealisable3. In fact, with the exception of the Haken-Lorenz model, which has been intensively studied because of its dual origin as a model of fluid flow4, the global bifurcation pictures of most laser models are unknown. Instead, laser physicists have focussed on dynamic features which are readily compared with experiments, such as properties of time series, power spectra, transitions to chaos and measures of chaotic attractor dimension. These observational descriptions of chaotic behaviour often appear partial and disjoint, whereas the direct study of model solutions and their global bifurcations can provide a clear and unfolded bifurcation diagram.

Analysis of Instability and Chaos in Optically Pumped Three Level Lasers

Chaotic behaviour in lasers may exist in even the simplest of systems; one in which population inversion is established between two discrete energy levels of the medium and where the lasing transition between these two levels is homogeneously broadened. A further simplification is that the laser cavity, a ring resonator system surrounding the gain medium, be sufficiently short so that only one resonant frequency of the cavity lies within the bandwidth of the gain medium and that this mode be resonantly tuned to the gain centre frequency.

Effect of second harmonic generation of idler wave on difference frequency generation

The effect of second harmonic generation of idler wave on the process of difference frequency generation is analyzed theoretically. It is shown that, in general, the presence of second harmonic generation has a favorable influence on the evolution of the difference frequency wave. When the two processes are exactly phase matched, the usual oscillations in the variation of generated wave intensity with the interaction length are almost completely eliminated while retaining nearly complete conversion.