Gas Laser Instabilities and their Interpretation

Abstract

Although the special interests of many laser researchers relate to instabilities and chaos in lasers and nonlinear optical systems, it is well to recall that in a mathematical sense many of the specific phenomena in which we are interested have long been recognized and studied in nonoptical systems. Maintaining this broader perspective can sometimes provide insight into the types of behavior that might or might not be expected in optics-related experiments. Thus, it may be noted that periodic oscillations in mechanical systems have been known for millennia, and this fact may be illustrated by a consideration of the ancient history of music and musical instruments. Early studies in music were directed toward such ideals as purity of tone, beauty of melody, richness of harmony, and elegance of rhythm. (Listening to a teenager’s radio, however, soon reveals that, as in optics, such ideals are sometimes now abandoned in favor of an emphasis on power, noise, and chaos.) The study of periodic instabilities in electrical systems is a somewhat more recent area of endeavor, but it still dates back centuries. The earliest electrical oscillators were electro-mechanical systems which today might simply be referred to as electric motors. These were followed in the last century by electroacoustical oscillators motivated by the problem of positive feedback in telephone repeaters. The first modern electronic oscillators used the triode vacuum tube (audion) and were reported in 1915.1 The first electronic circuit that may have produced a chaotic output was the sinusoidally-driven glow-lamp relaxation oscillator described by van der Pol and van der Mark in 1927, and those authors remark on “an irregular noise” at transitions between locking states.2,3 Van der Pol’s subsequent work with forced triode circuits inspired the forced van der Pol equation, that has been of great interest to mathematicians. The first autonomous circuits to exhibit chaotic behavior may have been glow-lamp ring oscillators. It was reported by Ives in 1958 that these circuits sometimes perform “erratically” and are hard to adjust for a specific firing order.4 Besides chaotic behavior, these circuits can also exhibit a large number of independent limit cycles.5 KeywordsChaotic BehaviorRing LaserTuning CurveRuby LaserInstability PhenomenonThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.