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Physical Review Letters

Observation of Bifurcation to Chaos in an All-Optical Fabry-Perot Resonator

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

Published Jul 16, 1984• 36 citations
Publisher

Abstract

We report observation of bifurcations, higher harmonics, and chaos in an all-optical quantum system. These phenomena occur in a passive Fabry-Perot resonator, in association with deep and sustained Ikeda modulation of smooth input pulses. Results are in excellent agreement with our adaptation of optical bistability theory to the time-dependent regime.

DOI
10.1103/physrevlett.53.258

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We report observation of bifurcations, higher harmonics, and chaos in an all-optical quantum system. These phenomena occur in a passive Fabry-Perot resonator, in association with deep and sustained Ikeda modulation of smooth input pulses. Results are in excellent agreement with our adaptation of optical bistability theory to the time-dependent regime.
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.
We present a detailed analysis showing that positive-branch instabilities occur in nonlinear resonators in the Fabry-Pérot (folded) configuration. Responses in the unstable region can be unstable or chaotic, depending on parameter values. Values of the response/round-trip time ratio in excess of unity can still yield instabilities, albeit on progressively higher branches as the ratio increases. The analysis proceeds from the basic optical bistability equations through the Maxwell-Debye equations to an explicit expression for the nonlinear phase shift. Linearization leads to thresholds in good agreement with direct computation. A simple expression for the accessible domain of phase-space is derived. The fundamental oscillation is interpreted as a cavity-resonant sideband instability.