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
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References
E.H. Armstrong, “Some recent developments in the audion receiver,” Proc. I.R.E. 3:215 (1915).
B. van der Pol and J. van der Mark, “Frequency demultiptication,” Nature 120:363 (1927).
M.P. Kennedy and L.O. Chua, “Van der Pol and chaos,” IEEE Trans. Circuits Syst., CAS-33:974 (1986).
R.L. Ives, “Neon oscillator rings,” Electronics 31:108 (1958).
L.W. Casperson and H.J. Orchard, “Periodic and chaotic pulsations in ring oscillator networks,” unpublished (1985).
E.N. Lorenz, “Deterministic nonperiodic flow,” J. Atmos. Sci. 20:130 (1963).
See for example, C. Sparrow, The Lorenz Equations: Bifurcations, Chaos, and Strange Attractors, Applied Mathematics Series, vol. 41 (Springer-Verlag, Berlin, 1982), and references.
A.G. Gurtovnik, Izv. Vyssh. Uchebn. Zaved. Radiofiz. 1:83 (1958); “On the theory of the molecular generator,” English translation in APL Library Bulletin (Johns Hopkins University) as translation TG 230-T382, 26 August 1963.
E.R. Buley and F.W. Cummings, “Dynamics of a system of N atoms interacting with a radiation field,” Phys. Rev. 134:A1454 (1964).
L.W. Casperson, “Spontaneous pulsations in lasers,” in Third New Zealand Symposium on Laser Physics, vol. 182 of Springer Lecture Notes in Physics (Springer-Verlag, Berlin, 1983), p.88.
L.W. Casperson, “Spontaneous coherent pulsations in ring-laser oscillators,” J. Opt. Soc. Am B 2:62 (1985).
J.C. Englund, R.R. Snapp, and W.C. Schieve, “Fluctuations, instabilities and chaos in the laser-driven nonlinear ring cavity,” Progress in Optics 21:355 (1984).
N.B. Abraham, L.A. Lugiato, and L.M. Narducci, “Overview of instabilities in laser systems,” J. Opt. Soc. Am. B 2:7 (1985).
J.R. Ackerhalt, P.W. Milonni, and M.L. Shih, “Chaos in Quantum Optics,” Phys. Rep. 128:205 (1985).
R.G. Harrison and D.J. Biwas, “Pulsating instabilities and chaos in lasers,” Progress in Quantum Electron. 10:147 (1985).
N.B. Abraham, P. Mandel, and L.M. Narducci, “Dynamical instabilities and pulsations in lasers,” Progress in Optics, to be published.
G. Makhov, C. Kikuchi, J. Lambe, and R.W. Terhune, “Maser action in ruby,” Phys. Rev. 109:1399 (1958).
C. Kikuchi, J. Lambe, G. Makhov, and R.W. Terhune, “Ruby as a maser material,” J. Appl. Phys. 30:1061 (1959).
R.J. Collins, D.F. Nelson, A.L. Schawlow, W. Bond, C.G.B. Garrett, and W. Kaiser, “Coherence, narrowing, directionality, and relaxation oscillations in the light emmission from ruby,” Phys. Rev. Lett. 5:303 (1960).
A.N. Oraevskii and A.V. Uspenskii, “Power pulsation modes of lasers,” in Quantum Electronics in Lasers and Masers, vol. 31, Edited by D.V. Skobel’tsyn (Plenum, New York, 1968), p. 87.
See for example, R.W. Dixon and H.R. Beurrier, “The effect of dc current bias on sustained oscillations in (AlGa)As double-heterostructure lasers,” Appl. Phys. Lett. 34:560 (1979).
W.L. Faust, R.A. McFarlane, C.K.N. Patel, and C.G.B. Garrett, “Gas maser spectroscopy in the infrared,” Appl. Phys. Lett. 1:85 (1962).
J.W. Kluver, “Laser amplifier noise at 3.5 microns in helium-xenon,” J. Appl. Phys. 37:2987 (1966).
See for example, P.O. Clark, R.A. Hubach, and J.Y. Wada, “Investigation of the dcexcited xenon laser,” Final Report, JPL Contract No. 950803 (1965).
L.W. Casperson, “Saturation and power in a high-gain gas laser,” IEEE J. Quantum Electron. QE-9:250 (1973).
L.W. Casperson and A. Yariv, “The Gaussian mode in optical resonators with a radial gain profile,” Appl. Phys.Lett. 12:355 (1968).
L.W. Casperson and A. Yariv, “Longitudinal modes in a high-gain laser,” Appl. Phys. Lett. 17:259 (1970).
L.W. Casperson and A. Yariv, “Gain and dispersion focusing in a high-gain laser,” Appl. Opt. 11:462 (1972).
L.W. Casperson and A. Yariv, “The time behavior and spectra of relaxation oscillations in a high-gain laser, IEEE J. Quantum Electron. QE-8:69 (1972).
L.W. Casperson, “Spontaneous coherent pulsations in laser oscillators,” IEEE J. Quantum Electron. QE-14:756 (1978).
L.W. Casperson, “Spontaneous coherent pulsations in ring-laser oscillators,” J. Opt. Soc. Am. B 2:62 (1985).
J. Bently and N.B. Abraham, “Mode-pulling, mode-splitting and pulsing in a high gain He-Xe laser,” Opt. Commun. 41:52 (1982).
M. Maeda and N.B. Abraham, “Measurements of mode-splitting self-pulsing in a single-mode, Fabry-Perot laser,” Phys. Rev. A 26:3395 (1982).
N.B. Abraham, T. Chyba, M. Coleman, R.S. Gioggia, N.J. Halas, L.M. Hoffer, S.N. Liu, M. Maeda, and J.C. Wesson, “Experimental evidence for self-pulsing and chaos in cw-excited lasers,” in Third New Zealand Symposium on Laser Physics, vol. 182 of Springer Lecture Notes in Physics (Springer-Verlag, Berlin, 1983), p. 107.
R.S. Gioggia and N.B. Abraham, “Routes to chaotic output from a single-mode, dcexcited laser,” Phys. Rev. Lett. 51:650 (1983).
R.S. Gioggia and N.B. Abraham, “Self-pulsing instabilities in a single-mode inhomo-geneously broadened, Fabry-Perot laser,” in Coherence and Quantum Optics V, edited by L. Mandel and E. Wolf (Plenum Press, New York, 1984), p. 563.
L.E. Urbach, S.N. Liu, and N.B. Abraham, “Instabilities and routes to chaos in a unidirectional, inhomogeneously-broadened ring laser,” in Coherence and Quantum Optics V, edited by L. Mandel and E. Wolf (Plenum Press, New York, 1984), p. 593.
L.M. Hoffer, T.H. Chyba, and N.B. Abraham, “Spontaneous pulsing, period doubling, and quasi-periodicity in a unidirectional, single-mode, inhomogeneously broadened ring laser,” J. Opt. Soc. Am. B 2:102 (1985).
M.F.H. Tarroja, N.B. Abraham, D.K. Bandy, T. Isaacs, R.S. Gioggia, S.P. Adams, L.M. Narducci, and L.A. Lugiato, “Comparison of the experimental and the theoretical results on an inhomogeneously broadened single mode laser,” in Optical Instabilities, edited by R.W. Boyd, M.G. Raymer, and L.M. Narducci, (Cambridge Univeristy Press, Cambridge, 1986), p. 246.
M.F.H. Tarroja, N.B. Abraham, D.K. Bandy, and L.M. Narducci, “Periodic and chaotic output pulsations in a single-mode inhomogeneously broadened laser,” Phys. Rev. A 34:3148 (1986).
P. Mandel, “Influence of Doppler broadening on the stability of monomode ring lasers,” Opt. Commun. 44:400 (1983).
L.W. Casperson, “Spontaneous coherent pulsations in ring-laser oscillators: stability criteria,” J. Opt. Soc. Am. B 2:993 (1985).
L.W. Casperson, “Stability criteria for lasers with mixed line broadening,” Opt. and Quantum Electron. 19:29 (1987).
L.W. Casperson, “Spontaneous coherent pulsations in ring-laser oscillators: simplified models,” J. Opt. Soc. Am. B 2:73 (1985).
L.W. Casperson, “Stability criteria for high-intensity lasers,” Phys. Rev. A 21:911 (1980).
L.W. Casperson, “Stability criteria for non-Doppler lasers,” Phys. Rev. A 23:248 (1981).
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Casperson, L.W. (1988). Gas Laser Instabilities and their Interpretation. In: Abraham, N.B., Arecchi, F.T., Lugiato, L.A. (eds) Instabilities and Chaos in Quantum Optics II. NATO ASI Series, vol 177. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-2548-0_6
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