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Journal of the Optical Society of America B

Time-dependent behavior of a unidirectional ring laser within homogeneous broadening

Donna Kay Bandy, L. A. Lugiato, N. B. Abraham, Lorenzo M. Narducci

Published Jan 1, 1985• 22 citations
Publisher

Abstract

We solve numerically the time-dependent equations of motion for an inhomogeneously broadened single-mode ring laser. As expected from the linear stability analysis, pulsations develop in the output of the laser for appropriate values of the gain parameter. Under resonant conditions, the tendency is for the system to slip from a periodic regime into irregular oscillations; out of resonance, however, periodic oscillations and period-doubling bifurcations are more typical over a large range of gain values. We find that, as the ratio of the population-to-polarization decay rates varies from a value of two (radiative limit) to smaller values, the periodic oscillations turn into a train of well-separated pulses whose peak intensity scales approximately as the square of the atomic density.

DOI
10.1364/josab.2.000056

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We present an examination of the stability and time-dependent behavior of a semiclassical model of the ring laser with a saturable absorber, in the vicinity of multiple steady-state solutions. We consider particularly the case in which the cavity is tuned away from the resonance frequency of the gain medium. The model considers the absorbing and amplifying media to consist of two-level atoms. Only homogeneous spectral broadening and unidirectional propagation of the light are considered. We are able to treat the steady state with an approximate mean field solution and also with its exact longitudinal dependence. The latter is found numerically from an implicit function solution to the Maxwell-Bloch equations in the steady state. There may be as many as four steady-state solutions for a given set of parameter values. When there are four solutions, we find that three solutions are of one intensity class (high or low) and that one is of a second intensity class (low or high). When the absorbing and emitting atoms are in resonance and the cavity is tuned to their line-center frequency, two of the members of the three-solution class have the same intensity. This degeneracy is broken by detuning.
We propose a simple and convenient analytical model for the description of coherent passive mode locking in a two-section ring-cavity laser based on the generalized area theorem for the coherent pulse propagation in a resonant medium with inhomogeneous line broadening. This model is applied to theoretically analyze the possible regimes of the spatiotemporal dynamics of such a laser together with their stability properties. We examined the laser dynamics, when varying the energy and phase relaxation times in the media, the gain and absorption rate in the respective laser sections, as well as the ratio of the transition dipole moments of the absorber and gain media. As the result, the stability of the coherent mode locking as well as the large flexibility of the arising laser behavior were shown in wide parameter ranges.