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Le Journal de Physique Colloques

INSTABILITIES IN DOPPLER BROADENED OPTICALLY PUMPED FAR-INFRARED LASERS

Ferran Laguarta, Jaume Pujol, Ramon A. Vilaseca, R. Corbalán

Published Jun 1, 1988• 4 citations
Publisher

Abstract

We study the dynamic behaviour of a coherently pumped single-mode unidirectional ring laser with an active medium of Doppler broadened three-level atoms. Our formulation is based on a set of 9N+1 real equations of the plane-wave mean-field Maxwell-Bloch type (N is the number of velocity groups of molecules considered). This model predicts, for a parameter range of the type explored in the experiments by Weiss and Brock (Phys. Rev. Lett. 57 (1986) 2804), a behaviour that reproduces most of their main experimental features. These include the instability pump threshold and the sequence of instabilities ocurring on resonator tuning and on increasing pump strength.

DOI
10.1051/jphyscol:1988297

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We study the dynamic behaviour of a coherently pumped single-mode unidirectional ring laser with an active medium of Doppler broadened three-level atoms. Our formulation is based on a set of 9N+1 real equations of the plane-wave mean-field Maxwell-Bloch type (N is the number of velocity groups of molecules considered). This model predicts, for a parameter range of the type explored in the experiments by Weiss and Brock (Phys. Rev. Lett. 57 (1986) 2804), a behaviour that reproduces most of their main experimental features. These include the instability pump threshold and the sequence of instabilities ocurring on resonator tuning and on increasing pump strength.
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.
This paper contains a description of the behavior of a multimode unidirectional ring laser with a homogeneously broadened active medium. Our formulation is based on the conventional Maxwell-Bloch (MB) equations, but is distinguished from other treatments by the inclusion of a finite mirror reflectivity and an arbitrary value of the gain parameter. We review the steady-state behavior of the system and analyze the longitudinal profile of the field and of the atomic variables. With an appropriate transformation of variables, we transform the boundary conditions of the ring cavity into standard periodicity type, even in the presence of a finite reflectivity, and derive an infinite hierarchy of coupled mode equations. We analyze exactly the linear stability of the system, and investigate the dependence of the instability domain on the reflectivity and gain parameters. A numerical study of the full MB equations for a parameter range of the type explored in the recent experiments by Hillman et al. [Phys. Rev. Lett. 52, 1605 (1984)] reveals similarities, but also considerable differences between the results of the theory and the main experimental signatures of their instability. However, the injection of numerical noise shows the presence of numerous coexisting basins of attraction which are likely to play a significant role in the dynamics of a noisy laser.
We consider the dynamics of an inhomogeneously broadened unidirectional ring laser formulated in the traditional Maxwell-Bloch configuration of a two-level atom with transverse modes. We numerically analyze the model for a single-longitudinal mode in the paraxial approximation, using the uniform field limit with cylindrical symmetry and a Gaussian profile for inhomogeneous broadening. Several domains of solutions are found for the resonant case in the good cavity limit. The laser threshold is found to be dependent on the mode spacing as well as on the gain and scaled Doppler broadening. Hysteresis between stable and unstable solutions is obtained in realistic operating conditions for both increasing (decreasing) gain and increasing (decreasing) mode spacing (i.e., for changes in the initial conditions).
The dynamic behaviour of a coherently pumped single-mode far-infrared ring laser with a homogeneously broadened three-level medium is analysed theoretically, considering detuning between amplifying transition and cavity frequencies. Phase diagrams as a function of cavity detuning and amplitude of the resonant pump field have been obtained, which show different domains of stationary, oscillatory and chaotic output. In some conditions the laser is shown to exhibit hysteresis between different regular self-pulsing regimes, i.e. the phenomenon of generalised bistability.
We propose a new scheme for the classification of the optical instabilities that emerge within the framework of the Maxwell-Bloch model. Our scheme is based on an appropriate ex-tension of the notions of amplitude and phase instability advanced in earlier publications and generalized in this work to include the free running laser, optical bistability and the laser with an injected signal. We address our considerations to a unidirectional ring cavity model, in the plane wave approximation and with a homogeneously broadened, two-level active medium.