2s __ _- E!B 15 January 1996 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA PHYSICS LETTERS A ELSEVIER Physics Letters A 210 (1996) 301-306 On-off intermittency in a Zeeman laser model J. Redondo, Eugenio Roldh, G.J. de Valcticel zyxwvutsrqponmlkjihgfedcbaZYXW Departament d’i)ptica, Uniuersitat de Valbcia, Dr. Moliner 50, 46100 Burjassot. Spain ’ Received 21 June 1995; revised manuscript received 29 September 1995; accepted for publication 27 October 1995 Communicated by C.R. Docring zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLK Abstract We numerically find on-off intermittency in a simple model for a Zeeman laser with large cavity anisotropy. The intermittency is observed in the field polarization component for large cavity losses and is induced by the chaotic dynamics of the other component. The statistical features of this behaviour are in good agreement with the theory for on-off intermittency. Keywords: On-off intermittency; Intermittency; Nonlinear dynamics; Laser dynamics; Zeeman laser; Chaos Although the first on-off intermittency related work began ten years ago [ 1,2], this intermittency is receiving increasing attention since the recent obtain- ing of its statistical features [3,4] and the experimen- tal observations carried out in electronic circuits [5,6]. On-off intermittency is a phenomenon in which a dynamical variable jumps from its steady state value (the off state) to an irregular behaviour (the on state) at unpredictable instants of time, the duration of the off state (laminar phase) verifying certain statistical regularities. In particular the theory pre- dicts [4] that the probability of finding a laminar phase of length n is proportional to K3/’ for small n and follows an exponential decay for large enough n. In addition there exists a power-law scaling of the mean duration of a laminar phase as a function of the coupling parameter with a critical exponent - 1 near onset. These results were analytically obtained in Ref. [4] by Heagy et al. in a parametrically driven one-dimensional map in which the parameter is ran- domly varied through a bifurcation point of the map. Although no analytical proof is available when the time dependent parameter varies chaotically they showed numerically that the same statistical features are also obtained in this last case. ’ E-mail: qoval@vm.ci.uv.es. Up to now the studies of this type of intermittency have been mainly made in maps rather than in systems of ordinary differential equations and there is a lack of predictions of such a behaviour in physical systems. In this Letter we show that on-off intermittency can be observed in lasers by studying a simple two-level Zeeman laser model. In particular we will show numerically that the intermittency statistics is in close agreement with the results ob- tained by Heagy et al. to which we will refer as on-off intermittency theory without distinguishing between random or chaotic driving. In our case the system is autonomous and there is not any time-de- pendent parameter but a chaotic dynamics in some of the system variables. Under suitable conditions this 03759601/96/$12.00 0 1996 Elsevier Science B.V. All rights reserved SSDIO375.9601(95)00879-9