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Physical Review A

Polarization instability in lasers. II: Influence of the pump polarization on the dynamics

H. Zeghlache, Arnaud Boulnois

Published Nov 1, 1995• 7 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.52.4243

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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.
The aim of this paper is to provide a vectorial model which can describe the dynamics of the two transverse field polarizations presented by an optical fiber laser. These dynamics are supposed to take their origin from the interaction between the propagating field and the atoms: an assumption based on the existence of a transverse distribution of dipole moments and which leads to a vectorial atomic polarization. Also, and as we have considered a frequency for each field polarization, a longitudinal dependence of the population inversion must be taken into account. A double Fourier expansion (transverse and longitudinal) of the material variables is then needed and the resulting model is analyzed using the bifurcation theory: the existence of all stationary states is fully expressed in the parameter space. The stability of these states and the system dynamic is studied in the following paper [Phys. Rev. A 52, 4243 (1995)].
A theoretical treatment is given of the dynamical and steady-state behavior of an anisotropic laser. The model is based on a homogeneously broadened, pumped J=1/2\ensuremath{\leftrightarrows}J=1/2 atomic transition, and is solved to all orders of the electric field, in contrast to previous studies of anisotropic lasers. A survey of the system behavior is presented, and complementary analytic descriptions developed to describe the small- and large-field evolutions are given. The small-field polarization behavior is shown to be oscillatory in general, and dominated by the properties of the cavity. The large-field description allows the polarization stability of the final output states to be analyzed, and shows that stable steady states in this regime must be linearly polarized along either one or the other of the two anisotropy axes. The possible range of cavity lengths which allows bistable output between these two polarizations is characterized analytically, and a regime identified where the polarization undergoes sustained oscillation.
The influence of light polarization on the dynamics of an optically pumped single-mode laser with a homogeneously broadened four-level medium is theoretically investigated in detail. Pump and laser fields with either parallel or crossed linear polarizations are considered, as are typical in far-infrared-laser experiments. 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 crossed-polarization configuration is shown to be effective in decoupling the pump and laser fields, thus allowing for the appearance of Lorenz-type dynamics.
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.
We have carried out a series of numerical experiments on the dynamic behavior of J=0 yields J=1 yields J=0 lasers optically pumped by a linearly polarized laser field and operating either: (1) with a strongly anisotropic cavity yielding fixed linear laser field polarization at any angle (theta) with that of the pump beam, or (2) with an isotropic cavity and an axial magnetic field. In the first case (1) we show that by changing (theta) the steady-states experience a smooth monotonic variation, but the dynamic states undergo a complex sequence of bifurcations. In case (2) we find that the laser field is always linearly polarized, but for some parameter settings we report the first observation that the plane of polarization together with the laser intensity change chaotically.
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.