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Journal of Modern Optics

Influence of Light Polarization on the Behaviour of a Resonant Cascade Laser

V. Espinosa, Germán J. de Valcárcel, Eugenio Roldán, Ramon A. Vilaseca

Published Apr 1, 1995• 5 citations
Publisher

Abstract

A cascade laser model based on a J = 0 M J = 1 M J = 0 ladder atomic-level scheme is proposed. The cases of relative parallel and orthogonal linear field polarizations are studied. The parallel configuration reduces to a three-level cascade laser model in the limit of minimal Zeeman-coherence relaxation rate. Contrarily, the absence of two-photon processes in the orthogonal configuration makes this case equivalent to a pair of incoherently coupled two-level laser models. The stability properties and dynamic behaviour of the orthogonal configuration are analysed.

DOI
10.1080/713824409

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A cascade laser model based on a J = 0 M J = 1 M J = 0 ladder atomic-level scheme is proposed. The cases of relative parallel and orthogonal linear field polarizations are studied. The parallel configuration reduces to a three-level cascade laser model in the limit of minimal Zeeman-coherence relaxation rate. Contrarily, the absence of two-photon processes in the orthogonal configuration makes this case equivalent to a pair of incoherently coupled two-level laser models. The stability properties and dynamic behaviour of the orthogonal configuration are analysed.
The emission of a resonant nondegenerate cascade laser in which up to two fields can be simultaneously amplified inside a cavity is theoretically investigated. Each field is resonantly coupled with one of the transitions of a ladder three-level atomic system, in conditions of homogeneous broadening. General analytical expressions for zero-, one-, and two-field solutions are given. Cooperative emission between both fields is found. Through the linear stability analysis of these solutions we obtain phase diagrams showing their respective domains of stability. Together with the existence of Hopf bifurcations associated with one-photon processes, which coincide with those of a Lorenz-Haken laser, a genuine Hopf bifurcation due to two-photon processes has been found. This last bifurcation does not require the ``bad cavity'' nor the ``Lorenz threshold'' conditions. The stability of the orbits that bifurcate from these critical points is analytically investigated. For this we have rewritten one of the standard criteria in a useful and straightforward way. Finally, the dynamic regimes exhibited by the system well above the instability thresholds is numerically investigated revealing transitions to chaos via quasiperiodicity.
The dynamics of an optically pumped single mode laser with pump and laser fields with either parallel or crossed linear polarizations and a homogeneously broadened four-level medium is theoretically investigated in detail. Numerical simulations reveal dramatically different dynamic behaviors for these two polarization configurations. The analysis of the model equations allows us to find the physical origin of both behaviors. In particular, the Lorenz-type dynamics exhibited by the orthogonal configuration arises from the lack of coherent effects in spite of the optical pumping.
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 longitudinal magnetic field or of modulation of the pump-field polarization orientation leads to new features and complex dynamic behaviour which includes full polarization (or vector ) chaos.
A model for a nondegenerate cascade J '' = 0→ J = 1→ J ' = 0 vector laser is presented. It takes into account the two polarization degrees of freedom associated with each of the two laser fields as well as possible constraints in the polarization states imposed by the cavity anisotropies. The cases of cavities with strong and weak anisotropy and perfect isotropy are studied. It is shown that in all cases bimode instabilities can occur independently of the `bad cavity' limit and for small pumping. Stability of the bimode solution is very sensitive to misalignment of the linear cavity anisotropies, to differences in the cavity isotropic losses, and to phase anisotropy. The time-dependent dynamics has been analysed.
We study theoretically the polarization dynamics of a new type of quantum oscillator that is based on the two-photon stimulated emission process in the presence of a magnetic field of arbitrary orientation. Both cases of cascade (small intermediate-state atomic detuning) and two-photon (large atomic detuning) lasers are considered. The primary goal of this work is to investigate the origin of recently observed polarization instabilities in a two-photon laser (Pfister et al 2001 Phys. Rev. Lett. 86 4512) using a highly simplified model. It is found that the two-photon laser can emit linearly polarized radiation with its plane of polarization orthogonal to the direction of the magnetic field at small magnetic field strengths. It can also emit elliptically polarized radiation over a large range of magnetic field strengths and orientations. When the magnetic field deviates from a direction perpendicular to the laser cavity axis periodic instabilities can appear through a Hopf bifurcation. This dynamic regime could have contributed to the polarization instabilities observed in the experiment.
The behavior of a cascade laser in which two fields are simultaneously amplified is theoretically investigated. Each field is coupled with one of the transitions of a ladder three- level atomic or molecular system in conditions of homogeneous broadening. Steady-state as well as dynamic solutions are considered. Cooperative emission of both fields is found in steady state regime. Single-field solutions can loose stability through two different types of Hopf bifurcations. One of them can appear below the Lorenz-Haken second laser threshold, and the `bad cavity' condition is not necessarily required. In the unstable regimes transitions to chaos via the quasiperiodicity road are found. The influence of cavity detuning and the passage from cascade to two-photon laser are considered.