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Physical Review A

Instabilities and routes to chaos in passive all-optical resonators containing a molecular gas

W. J. Firth, R. G. Harrison, I. A. Al-Saidi

Published Apr 1, 1986• 12 citations
Publisher

Abstract

Dispersive optical bistability and instabilities leading to period doubling, higher harmonics, and chaos in an all-optical passive quantum system are discussed theoretically and experimentally. These phenomena have been observed for a wide range of operating conditions in ring and Fabry-Perot resonators containing ammonia molecular gas as the nonlinear medium. Laser input intensity, gas pressure, and cavity tuning are the main control parameters in observation of these effects. The experimental results are well modeled by our generalization of standard two-level system theory to include standing-wave, reservoir, and transverse effects.

DOI
10.1103/physreva.33.2449

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Dispersive optical bistability and instabilities leading to period doubling, higher harmonics, and chaos in an all-optical passive quantum system are discussed theoretically and experimentally. These phenomena have been observed for a wide range of operating conditions in ring and Fabry-Perot resonators containing ammonia molecular gas as the nonlinear medium. Laser input intensity, gas pressure, and cavity tuning are the main control parameters in observation of these effects. The experimental results are well modeled by our generalization of standard two-level system theory to include standing-wave, reservoir, and transverse effects.
There has been considerable interest over the last few years in transitions to chaos in passive optically bistable systems. Ikeda1 showed in 1979 that an optically bistable ring resonator containing the simplest of nonlinear systems, a two-level media, can show a period doubling route to chaos. This was demonstrated by us2 using NH3 gas near resonantly pumped by pulsed CO2 laser radiation. More generally we identified and demonstrated the unique advantages of molecular gases in this field, providing in particular a vast range of laser-molecular coincidences together with control of response time, and therefore switching time and modulation frequency, by varying gas pressure. Subsequent extension of this work to all optical Fabry-Perot resonators revealed huge oscillatory effects3 leading to chaos in the transmitted laser signal. Under other parameter conditions for both NH3 and SF6 a rich variety of optically bistable effects were observed obtained in systems as small as 1 mm for SF64,5.
Two-round-trip-time modulation of the cavity field has been observed in a passive ring resonator, containing an ammonia cell, pumped by smooth 100-ns CO2{\mathrm{O}}_{2}O2​ laser pulses. The results are in excellent accord with the theory of Ikeda instability instability in a two-level system, which is generalized to include reservoir kinetics.
We compare theoretical predictions and experimental data for the multimode instability of optical bistability, which arises from the coherent dynamics of a system of two-level molecules contained in an optical cavity and driven by an external stationary laser field. Considerable insight into this phenomenon is provided by two ``rules of thumb'' that govern the behavior of the self-pulsing frequency, and establish its relation with the Rabi frequency of the intracavity field. We describe in detail the experimental apparatus and the main features of the experimental findings. The theoretical results are based on the Maxwell-Bloch equations for a ring cavity in the plane-wave approximation. Despite the crudeness of this model, the numerical data display a satisfactory qualitative agreement with the experimental results. Additional period-doubling and chaotic phenomena, predicted by the theory and not observed in the experiment, are presumably washed out by the longitudinal and radial variation of the electric field in the cavity.
Passive fiber cavities are basic nonlinear optical systems that are described by simple models - however they have a rich spectrum of complex behaviors (optical bistability, period-doubling bifurcations, chaos, modulational instability). From a practical point of view their study would have direct implications in the understanding of more complex cavity-based optical devices such as fiber lasers, Fabry-Perot lasers or APM lasers. Moreover, passive fiber cavities have potential applications in telecommunications as ultra-short pulse generators and as optical memories using their bistable behavior. This work is a contribution to the study of this bistable behavior with pulsed input, so that the device studied could be used for pulsed optical memory storage.