Correlation Functions of a Dye Laser: Comparison between Theory and Experiment

Short, R.; Mandeļ, L.; Roy, Rajarshi

doi:10.1103/physrevlett.49.647

Cited by 99 publications

(21 citation statements)

References 13 publications

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“…This concept was applied in the systems where, compared with its own time scale, the outside forces are under much shorter correlation times. Similar approximations can be found in physics and electronics [11], [32], etc.…”

Section: White and Coloured Noisesupporting

confidence: 59%

Characterization of Received Signal Strength Perturbations Using Allan Variance

Luo

Casaseca‐de‐la‐Higuera

McClean

et al. 2018

IEEE Trans. Aerosp. Electron. Syst.

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Abstract-The received signal strength (RSS) of wireless signals conveys important information that has been widely used in wireless communications, localisation and tracking. Traditional RSS-based research and applications model the RSS signal using a deterministic component plus a white noise term. This paper investigates the assumption of white noise to have a further understanding of the RSS signal and proposes a methodology based on the Allan Variance (AVAR) to characterise it. Using AVAR, we model the RSS unknown perturbations as correlated random terms. These terms can account for both coloured noise or other effects such as shadowing or smallscale fading. Our results confirm that AVAR can be used to obtain a flexible model of the RSS perturbations, as expressed by coloured noise components . The study is complemented by introducing two straightforward applications of the proposed methodology: 1) The modelling and simulation of RSS noise using Wiener processes, and 2) RSS localisation using the extended Kalman filter.

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Section: White and Coloured Noisesupporting

confidence: 59%

Characterization of Received Signal Strength Perturbations Using Allan Variance

Luo

Casaseca‐de‐la‐Higuera

McClean

et al. 2018

IEEE Trans. Aerosp. Electron. Syst.

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“…10 In conclusion, through numerical simulation of the dye-laser output in the presence of pump fluctuations characterized by a colored noise, we have been able to explain consistently the experimental results of Short, Mandel, and Roy. 4 Along with the usefulness of the numerical simulation, the results of the present paper also demonstrate the importance of the correlation time of the fluctuations on the dynamics of nonlinear stochastic processes. Effects such as the ones discussed here should be of importance in other nonlinear processes, for example, optical bistability, and are currently under investigation.…”

Section: <7ft)p "supporting

confidence: 55%

“…The theory proposed by Graham,Hohnerbach,and Schenzle,5 where the noise was modeled as a Gaussian 6-correlated (white-noise) process, although successful in explaining some of the experimental results of Ref. 4, fails to explain results in another parameter regime as has been demonstrated by Short, Mandel, and Roy 4 in a recent publication.…”

mentioning

confidence: 94%

Nonlinear Stochastic Processes Driven by Colored Noise: Application to Dye-Laser Statistics

1983

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The role of multiplicative colored noise on the photon statistics of the dye-laser output is investigated. This model explains consistently the recent experimental results by Short, Mandel, and Roy. PACS numbers: 42.55.Mv, 42.50. + q The physics of macroscopic systems can often be described in terms of a few collective variables whose equations of motion are obtained by the elimination of microscopic variables and are, in general, highly nonlinear. If the system is in stable equilibrium, the statistical nature of the processes arising due to the microscopic dynamics can be neglected. However, in the case where the system approaches the limit of stability, the fluctuations due to microscopic variables play a very crucial role in governing the evolution of the system and hence must be incorporated into the equation of motion for macroscopic variables. The fundamental importance of fluctuations has been realized in a large number of systems, e.g., the laser, autocatalytic reactions, hydrodynamic and current instabilities, and equilibrium phase transitions for which the deterministic macroscopic description is found to be inadequate, especially near the threshold regime.There is currently intense activity in analyzing the effect of fluctuations on the dynamics of nonlinear processes. 1 These fluctuations, appearing as additive and/or multiplicative 2 noise terms in the equations of motion, are usually modeled at 6-correlated Gaussian processes (or white noise). This assumption, although convenient for mathematical analysis, is somewhat unrealistic as the fluctuations arising due to the microscopic dynamics would have a finite (nonzero) correlation time, (Such fluctuations are commonly referred to as colored noise.) Only in certain regions of parameter space, where all other retevent times in the problem are much longer than the correlation time of the fluctuations, would the whitenoise approximation be valid while in other regions discrepancies between white-noise theory and experiment would become noticeably large.The problem of photon statistics of the dyelaser output falls into this category as the equation of motion for the electric field e(t) is nonlinear and the colored noise is important. Re-cent experiments 3 * 4 have demonstrated some very interesting statistical properties of e(t); e.g., the relative intensity fluctuations, defined as ((A/) 2 )/(/) 2 , tend to increase indefinitely as the laser is weakly excited (

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“…Recently the importance of colored noise in nonequilibrium quantum optical systems like dye lasers [3], laser gyros [-4] and bistable optical devices [5] was emphasized in a large number of papers. The majority of these papers assumes a situation where one relevant variable obeying an overdamped equation of motion is coupled to a colored noise force.…”

Section: Introductionmentioning

confidence: 99%

Colored noise driven systems with inertia

H'walisz

Jung

Hänggi

et al. 1989

Z. Physik B - Condensed Matter

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We present a novel approximation scheme, termed unified colored noise approximation (UCNA), for colored Gaussian noise driven nonlinear systems with inertia. This approximation allows one to evaluate static (stationary distributions, moments) as well as dynamical quantities (correlation functions) for small-to-moderate-to-large values of the correlation time. The approximation replaces a three-dimensional Markovian process by a reduced, two-dimensional Markovian dynamics with new drift and diffusion coefficients. For a harmonic potential the stationary moments are reproduced exactly. Most importantly, we present a criterion involving the noise strength D, the friction strength 7 and the noise color % which describes the region of validity of UCNA in the parameter space given by (D, z, 7). At small z-values we contrast the UCNA with the well-known small ~ approximation. In order to have a comparison on analytical grounds, we test the static and dynamical predictions of UCNA versus the well-known analytical results obtained from a three-dimensional Ornstein-Uhlenbeck process.

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Correlation Functions of a Dye Laser: Comparison between Theory and Experiment

Cited by 99 publications

References 13 publications

Characterization of Received Signal Strength Perturbations Using Allan Variance

Characterization of Received Signal Strength Perturbations Using Allan Variance

Nonlinear Stochastic Processes Driven by Colored Noise: Application to Dye-Laser Statistics

Colored noise driven systems with inertia

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