Fluctuational transitions and related phenomena in a passive all-optical bistable system

Dykman, M. I.; Golubev, G. P.; Luchinsky, D. G.; Velikovich, A. L.; Tsuprikov, S. V.

doi:10.1103/physreva.44.2439

Cited by 23 publications

(29 citation statements)

References 31 publications

(35 reference statements)

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“…It is in this parameter range (the KPT range) that a supernarrow spectral peak (17,20) arises in the SDF. It broadens dramatically with increasing noise intensity T , just like the zero-frequency spectral peak (22) that is responsible (3,4,6) for conventional SR (1,2) in systems with static attractors. The value of Q (0) (Ω) for ω close to ω F therefore rises very rapidly (approximately exponentially) with increasing T .…”

Section: Stochastic Resonance For Periodic Attractorsmentioning

confidence: 99%

“…We would emphasize that the case (a) variant of SR investigated in the present work is in no way confined to the particular system (2). Rather, it is a quite general phenomenon that is to be anticipated in all underdamped nonlinear oscillators (including, for example, those for which |B|> 0.43 in the model (2)).…”

mentioning

confidence: 94%

“…For convenience, we shall refer to the noise-induced enhancement of a weak periodic signal in systems of this kind, where the net applied force is a sum of regular and stochastic terms, as conventional SR. The overwhelming majority of earlier work on SR (1,2) has related to conventional SR. We note that the description of conventional SR in terms of a susceptibility (3,4) , i.e. within the scope of linear response theory, has not only proven to be correct (5) , but is also simple and revealing.…”

Section: Introductionmentioning

confidence: 99%

“…The remarkable diversity (1,2) of the systems in which stochastic resonance (SR) has already been found, or is being sought -ice-ages, lasers, electronic circuits, electron spin resonance (ESR), superconducting quantum interference devices (SQUIDs), sensory neurons, and passive optical systems, for example -is in a sense slightly misleading because, at a fundamental level, the underlying phenomenon in all of these apparently disparate cases is exactly the same. It arises because of the noise-induced increase in the system's generalised susceptibility χ(Ω) at some frequency Ω on the wing of the zero-frequency spectral peak corresponding to hopping between two (or more) static attractors (3,4) .…”

Section: Introductionmentioning

confidence: 99%

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Nonconventional stochastic resonance

et al. 1993

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It is argued, on the basis of linear response theory (LRT), that new types of stochastic resonance (SR) are to be anticipated in diverse systems, quite different from the one most commonly studied to date, which has a static double-well potential and is driven by a net force equal to the sum of periodic and stochastic terms. On this basis, three new nonconventional forms of SR are predicted, sought, found and investigated both theoretically and by analogue electronic experiment: (a) in monostable systems; (b) in bistable systems with periodically modulated noise; (c) in a system with coexisting periodic attractors. In each case, it is shown that LRT can provide a good quantitative description of the experimental results for sufficiently weak driving fields. It is concluded that SR is a much more general phenomenon than has hitherto been appreciated.KEY WORDS: Analogue simulation; fluctuation phenomena; resonance; noise; spectral density; linear response; periodic attractors. 1 1. INTRODUCTION The remarkable diversity (1,2) of the systems in which stochastic resonance (SR) has already been found, or is being sought -ice-ages, lasers, electronic circuits, electron spin resonance (ESR), superconducting quantum interference devices (SQUIDs), sensory neurons, and passive optical systems, for example -is in a sense slightly misleading because, at a fundamental level, the underlying phenomenon in all of these apparently disparate cases is exactly the same. It arises because of the noise-induced increase in the system's generalised susceptibility χ(Ω) at some frequency Ω on the wing of the zero-frequency spectral peak corresponding to hopping between two (or more) static attractors (3,4) . For convenience, we shall refer to the noise-induced enhancement of a weak periodic signal in systems of this kind, where the net applied force is a sum of regular and stochastic terms, as conventional SR. The overwhelming majority of earlier work on SR (1,2) has related to conventional SR. We note that the description of conventional SR in terms of a susceptibility (3,4) , i.e. within the scope of linear response theory, has not only proven to be correct (5) , but is also simple and revealing.The aim of the present paper is to return to the interesting question of whether there may be other, quite different, classes of systems also able to support SR phenomena: that is, to explore the possibility of non-conventional SR. We shall use the latter term to describe SR in systems that do not have static potentials of the usual bistable (or multistable) type, or for which the periodic and stochastic forces are not mutually additive: in other words, we describe as non-conventional those systems which cannot be mapped into conventional SR systems by a suitable change of variable.In Section 2, we consider SR phenomena in thermal equilibrium systems with static attractors, and ask whether there may be new forms of SR not related to the zerofrequency spectral peaks associated with fluctuational transitions between the stable states of bi...

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Section: Stochastic Resonance For Periodic Attractorsmentioning

confidence: 99%

mentioning

confidence: 94%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Nonconventional stochastic resonance

et al. 1993

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“…An interesting effect that may provide a new and effective tool for such control is stochastic resonance ͑SR͒ in which both the signal and the SNR at the output of a nonlinear system can be increased by adding noise. 3 Most investigations of SR to date 4 have related to low-frequency signals driving bistable systems, including active 5 and passive 6,7 optically bistable ͑OB͒ systems. In such cases, the SR mechanism can operate effectively provided ͑i͒ the stationary populations of the states are nearly equal to each other, 8 and ͑ii͒ the frequency of the force is much smaller than the reciprocal relaxation time r Ϫ1 of the system.…”

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Noise-enhanced optical heterodyning in an all-optical bistable system

Dykman

Golubev

Kaufman

et al. 1995

Applied Physics Letters

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A new form of frequency-selective all-optical heterodyning at the difference frequency of two modulated laser beams, related to stochastic resonance, is reported. A noise-induced enhancement of the heterodyne signal and of the signal-to-noise ratio has been predicted and observed in an all-optical bistable system for the beams at different wavelengths. © 1995 American Institute of Physics.Recent progress in optical signal processing and optical communication 1,2 has highlighted the problem of controlling the signal and the signal-to-noise ratio ͑SNR͒ in optical systems. An interesting effect that may provide a new and effective tool for such control is stochastic resonance ͑SR͒ in which both the signal and the SNR at the output of a nonlinear system can be increased by adding noise. 3 Most investigations of SR to date 4 have related to low-frequency signals driving bistable systems, including active 5 and passive 6,7 optically bistable ͑OB͒ systems. In such cases, the SR mechanism can operate effectively provided ͑i͒ the stationary populations of the states are nearly equal to each other, 8 and ͑ii͒ the frequency of the force is much smaller than the reciprocal relaxation time r Ϫ1 of the system. It was recently suggested, 9 however, and demonstrated in analogue simulations, that a related phenomenon can occur when a nonlinear system is driven by two high frequency signals: if the resultant heterodyne signal is of sufficiently low frequency, both it and its SNR can be enhanced by the addition of noise.In this letter we report observation and outline a theory of a new form of all-optical heterodyning, noise-enhanced optical heterodyning ͑NEOH͒. The system studied is a bistable interferometer with a dispersive mechanism of nonlinearity. The intensity of the light at the output of the interferometer I T is related to that of the incident light I in via a transmission coefficient N( ) that depends periodically on the phase gain of the light inside the interferometer,The phase gain itself depends nonlinearly on I in . A practically important example of a two-dimensional array of bistable microresonators, of 4 m diameter and threshold power below 100 W, has been demonstrated recently. 10 There are several possible schemes for noise-enhanced optical heterodyning. We consider one here for which, in addition to the resonant signal beam, the cavity is driven by a nonresonant reference beam of intensity I ref (t), which affects the phase gain for the resonant beam. The dynamics of the phase gain in such a system can often 11 be described, to a reasonable approximation, by a Debye relaxation equationwhere 0 is the phase of the interferometer in the dark (I in , I ref are assumed to be properly scaled͒. The explicit forms of the periodic absorption coefficient M ( ), and of N( ), depend on the construction of the interferometer and are well-known for simple models, such as a Fabry-Perot cavity filled with a medium with cubic nonlinearity ͑cf. Ref. 11͒.We assume that the intensity of the resonant radiation has a high-frequenc...

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Fluctuational Escape and Related Phenomena in Nonlinear Optical Systems

Khovanov

Luchinsky

Mannella

et al.

Modern Nonlinear Optics, Part III

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ii FLUCTUATIONAL ESCAPE AND RELATED PHENOMENA been selected mainly for their own intrinsic scientific interest, but also in order to provide an indication of the power and utility of the simulation approach as a means of focusing on, and reaching an understanding of, the essential physics underlying the phenomena under investigation; they also provide examples of different theoretical approaches and situations where numerical and analogue simulations have led to the development of new experimental techniques and new ideas with potential technological significance. Although the different Sections all share the same general theme -of fluctuational escape phenomena in model nonlinear optical systems -they deal with quite different aspects of the subject; each of them is therefore to a considerable extent self-contained (with Secs. 1.4 and 1.5 being exceptions, because they should be read after Sec. 1.3) and thus can be read almost independently of the others. Before considering particular systems, we review briefly the scientific context of the work and discuss in a general way the significance of escape phenomena in nonlinear optics.The investigation of fluctuations by means of analog or digital simulation is usually found most useful for those systems where the fluctuations of the quantities of immediate physical interest can be assumed to be due to noise. The latter perception of fluctuations goes back to Einstein, Smoluchowski, and Langevin [2, 3, 4] and has often been used in optics (cf. Refs. [5,6,7,8]). In nonlinear optics, the noise can be regarded as arising from two main sources. First there are internal fluctuations in the macroscopic system itself. These arise because spontaneous emission of light by individual atoms occurs at random, and because of fluctuations in the populations of atomic energy levels. The physical characteristics of such noise are usually closely related to the physical characteristics of the model that describes the "regular" dynamics of the system, i.e. in the absence of noise. In particular, the power spectrum of thermal noise and its intensity can be expressed in terms of the dissipation characteristics via the fluctuation-dissipation relations (cf. Ref. [9]) and, if the dissipation is non-retarded so that the corresponding dissipative forces (e.g. the friction force) depend only on the instantaneous values of dynamical variables, the noise power spectrum is independent of frequency, i.e. the noise is white. The model of noise as being white and Gaussian is one of the most commonly used in optics because the quantities of physical interest often vary slowly compared with the fast random processes that give rise to the noise, like emission or absorption of a photon [5,6,7,8]. The second very important source of noise is external: for example, fluctuations of the pump power in a laser. The physical characteristics of such noise naturally vary from one particular system to another; its correlation time is often much longer than that of the internal noise, and its effects can be larg...

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Fluctuational transitions and related phenomena in a passive all-optical bistable system

Cited by 23 publications

References 31 publications

Nonconventional stochastic resonance

Nonconventional stochastic resonance

Noise-enhanced optical heterodyning in an all-optical bistable system

Fluctuational Escape and Related Phenomena in Nonlinear Optical Systems

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