Pergamon Infi'ared Phys. Technol. Vol. 36, No. I, pp. 489-512, 1995 Copyright ~? 1995 ElsevierScienceLtd 1350-4495(94)00088-3 Printed in Great Britain. All rights reserved 1350-4495/95 $9.50 + 0.00 LORENZ-LIKE CHAOS IN NH3-FIR LASERS CARL-OTTo WEISS, UDO HUBNER, NEAL BROADUS ABRAHAM* and DINGYUAN TANG Phys.-Techn. Bundesanstalt, D-38116 Braunschweig, Germany (Received 27 June 1994) Abstract--Studies of digitized recordings of periodic and chaotic intensity pulsations of an unidirectional far-infrared NH 3 ring laser at 81.5 ~m reveal common features (pulsing patterns, dimensions, entropies, and decay rates of the autocorrelation functions) to data sets numerically calculated from the Lorenz equations. The correspondence is striking. Nevertheless, there are small deviations of the experimental data to the numerical data which can, e.g. be explained as relics of counterpropagating waves in the ring laser and as influence of coherence effects from the coherently pumped three-level laser molecule. I. INTRODUCTION Spontaneous periodic and chaotic pulsations have been observed in many fields of physics. At least two of those fields, the physics of fluids and lasers, may even show exactly the same dynamics (i.e. obeying the same nonlinear differential equations) if the relevant physical parameters are chosen appropriately. A compact and minimal set of equations for convective fluid dynamics was developed by Lorenz~231 for the case of the Rayleigh-B~nard convection. Later, Haken ~81 found that the equations of a single-mode laser field interacting with a homogeneously broadened two-level medium are exactly the same as those so-called Lorenz equations. Of course, variables and parameters must be interpreted differently in the case of the laser. Far-infrared (FIR) lasers have been proposed °61 as examples of a realization of the Lorenz- Haken model. Some experiments on such lasers for certain operating conditions"8"38'3~have shown remarkable similarities with the predictions of that model, including characteristic time-dependent behavior and appropriate instability thresholds. The obvious correspondence between the dynamics observed on NHs laser transitions and the Lorenz-Haken model produced some controversy as to whether such optically pumped lasers can be properly modelled as incoherently pumped two-level lasers. ~5'2724'35~7~The principal objection is that the laser excitation leads to coherences in the three-level molecular system which cannot be adiabatically eliminated by reducing the equations to an equivalent two-level formulation. The three-level models differ from the Lorenz--Haken model in that they have lower instability thresholds, supercritical bifurcations to periodic pulsations, and (more typical) asymmetric periodic and chaotic attractors. However, the actual laser systems are more complex than simple coherently coupled three-level systems. Complications arise from: (a) detuned pumping of the Doppler-broadened pump transition to achieve unidirectional operation; ~7' (b) operation in the backward emission direction; and (c) involvement of high angular momentum states with the magnetic sublevels mixed by orthogonally polarized fields. In a theoretical model with more than 1000 equations"~) for single-mode FIR laser dynamics, factors (a) and (b) have been incorporated. That model finally recovered the experimental thresholds, detuning pump-bifurcation diagram, and intensity pulsation forms. More recent studies have separately considered the effects of factors (c) demonstrating that this contributes to Lorenz-like phenomena. *Permanent address: Department of Physics, Bryn Mawr College, Bryn Mawr, PA 19010, U.S.A. 489