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Journal of the Optical Society of America B

Influence of pump coherence on the dynamic behavior of a laser

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

Published May 1, 1988• 40 citations
Publisher

Abstract

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.

DOI
10.1364/josab.5.001004

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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.
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.
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 study numerically the effects of local-field corrections originating from near dipole—dipole interactions on the dynamics of a single mode, inhomogeneously broadened laser. Our analysis is based on a set of generalized Maxwell–Bloch equations in which the inhomogeneous nature of gain broadening is accounted for by introducing two new dynamical variables and a single parameter that governs the extent of inhomogeneous broadening. Our results show that local-field effects occurring in a dense gain medium reduce the range of continuous wave operation and lead to instabilities and chaos at much lower pumping levels.