Propagación de luz en medios turbulentos

The study of phenomena occurring in a turbulent fluid has been successively improved during the last 40 years. Speci cally, the concentration of a substance advected by the turbulence has received most of the attention, for it covers a wide range of natural and engineering settings: heat transport, dye di usion, microscopic organism movements, etc. These substances are described by scalar elds with a negligible back-e ect on the flow; thus, they are called passive scalar elds. The turbulent refractive index also belongs to this class; this is not a novelty (?). The temperature is a passive scalar eld whenever it produces buoyancy forces smaller than the inertial stresses driving the flow, and a direct calculation shows that its fluctuations are proportional to those of the index. Our interest in lightwave propagation through turbulent media must start here then. That is, we have to comprehend the media before attempt a description of the propagation itself. In the forthcoming sections we will study the dynamics and stochastic properties of passive scalars, and eventually propose models for the refractive index.Facultad de Ciencias Exacta

Beam wandering statistics of twin thin laser beam propagation under generalized atmospheric conditions

Under the Geometrics Optics approximation is possible to estimate the covariance between the displacements of two thin beams after they have propagated through a turbulent medium. Previous works have concentrated in long propagation distances to provide models for the wandering statistics. These models are useful when the separation between beams is smaller than the propagation path—regardless of the characteristics scales of the turbulence. In this work we give a complete model for these covariances, behavior introducing absolute limits to the validity of former approximations. Moreover, these generalizations are established for non-Kolmogorov atmospheric models.Fil: Pérez, Darío Gabriel. Pontificia Universidad Católica de Valparaíso; ChileFil: Funes, Gustavo Luis. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Centro de Investigaciones Ópticas. Provincia de Buenos Aires. Gobernación. Comisión de Investigaciones Científicas. Centro de Investigaciones Ópticas. Universidad Nacional de La Plata. Centro de Investigaciones Ópticas; Argentin

Propagación de luz en medios turbulentos

The study of phenomena occurring in a turbulent fluid has been successively improved during the last 40 years. Speci cally, the concentration of a substance advected by the turbulence has received most of the attention, for it covers a wide range of natural and engineering settings: heat transport, dye di usion, microscopic organism movements, etc. These substances are described by scalar elds with a negligible back-e ect on the flow; thus, they are called passive scalar elds. The turbulent refractive index also belongs to this class; this is not a novelty (?). The temperature is a passive scalar eld whenever it produces buoyancy forces smaller than the inertial stresses driving the flow, and a direct calculation shows that its fluctuations are proportional to those of the index. Our interest in lightwave propagation through turbulent media must start here then. That is, we have to comprehend the media before attempt a description of the propagation itself. In the forthcoming sections we will study the dynamics and stochastic properties of passive scalars, and eventually propose models for the refractive index.Facultad de Ciencias Exacta

Turbulence-induced persistence in laser beam wandering

We have experimentally confirmed the presence of long-memory correlations in the wandering of a thin Gaussian laser beam over a screen after propagating through a turbulent medium. A laboratory-controlled experiment was conducted in which coordinate fluctuations of the laser beam were recorded at a sufficiently high sampling rate for a wide range of turbulent conditions. Horizontal and vertical displacements of the laser beam centroid were subsequently analyzed by implementingdetrended fluctuation analysis. This is a very well-known and widely used methodology to unveil memory effects from time series. Results obtained from this experimental analysis allow us to confirm that both coordinates behave as highly persistent signals for strong turbulent intensities. This finding is relevant for a better comprehension and modeling of the turbulence effects in free-space optical communication systems and other applications related to propagation of optical signals in the atmosphere

Characterization of laser propagation through turbulent media by quantifiers based on the wavelet transform: dynamic study

We analyze, within the wavelet theory framework, the wandering over a screen of the centroid of a laser beam after it has propagated through a time-changing laboratory-generated turbulence. Following a previous work (Fractals 12 (2004) 223) two quantifiers are used, the Hurst parameter, H, and the normalized total wavelet entropy. The temporal evolution of both quantifiers, obtained from the laser spot data stream, is studied and compared. This allows us to extract information on the stochastic process associated with the turbulence dynamics.Facultad de Ciencias Exacta

Unraveling the decay of the number of unobserved ordinal patterns in noisy chaotic dynamics

In this paper, we introduce a model to describe the decay of the number of unobserved ordinal patterns as a function of the time series length in noisy chaotic dynamics. More precisely, we show that a stretched exponential model fits the decay of the number of unobserved ordinal patterns for both discrete and continuous chaotic systems contaminated with observational noise, independently of the noise level and the sampling time. Numerical simulations, obtained from the logistic map and the x coordinate of the Lorenz system, both operating in a totally chaotic dynamics were used as test beds. In addition, we contrast our results with those obtained from pure stochastic dynamics. The fitting parameters, namely, the stretching exponent and the characteristic decay rate, are used to distinguish whether the dynamical nature of the data sequence is stochastic or chaotic. Finally, the analysis of experimental records associated with the hyperchaotic pulsations of an optoelectronic oscillator allows us to illustrate the applicability of the proposed approach in a practical context.Fil: Olivares Zamora, Felipe Esteban. Pontificia Universidad Católica de Valparaíso; Chile. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Zunino, Luciano José. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Centro de Investigaciones Ópticas. Provincia de Buenos Aires. Gobernación. Comisión de Investigaciones Científicas. Centro de Investigaciones Ópticas. Universidad Nacional de La Plata. Centro de Investigaciones Ópticas; Argentina. Universidad Nacional de La Plata. Facultad de Ingeniería. Departamento de Ciencias Básicas; ArgentinaFil: Soriano, Miguel C.. Universitat de les Illes Balears; EspañaFil: Pérez, Darío Gabriel. Pontificia Universidad Católica de Valparaíso; Chil

Estimating the optimal sampling rate using wavelet transform: an application to optimal turbulence

Sampling rate and frequency content determination for optical quantities related to light propagation through turbulence are paramount experimental topics. Some papers about estimating properties of the optical turbulence seem to use ad hoc assumptions to set the sampling frequency used; this chosen sampling rate is assumed good enough to perform a proper measurement. On the other hand, other authors estimate the optimal sampling rate via fast Fourier transform of data series associated to the experiment. When possible, with the help of analytical models, cut-off frequencies, or frequency content, can be determined; yet, these approaches require prior knowledge of the optical turbulence. The aim of this paper is to propose an alternative, practical, experimental method to estimate a proper sampling rate. By means of the discrete wavelet transform, this approach can prevent any loss of information and, at the same time, avoid oversampling. Moreover, it is independent of the statistical model imposed on the turbulence.Centro de Investigaciones Óptica

Wavelet entropy of stochastic processes

We compare two different definitions for the wavelet entropy associated to stochastic processes. The first one, the normalized total wavelet entropy (NTWS) family [S. Blanco, A. Figliola, R.Q. Quiroga, O.A. Rosso, E. Serrano, Time–frequency analysis of electroencephalogram series, III. Wavelet packets and information cost function, Phys. Rev. E 57 (1998) 932–940; O.A. Rosso, S. Blanco, J. Yordanova, V. Kolev, A. Figliola, M. Schürmann, E. Başar, Wavelet entropy: a new tool for analysis of short duration brain electrical signals, J. Neurosci. Method 105 (2001) 65–75] and a second introduced by Tavares and Lucena [Physica A 357(1) (2005) 71–78]. In order to understand their advantages and disadvantages, exact results obtained for fractional Gaussian noise (-1α1) and fractional Brownian motion (1α3) are assessed. We find out that the NTWS family performs better as a characterization method for these stochastic processes.Centro de Investigaciones ÓpticasFacultad de IngenieríaFacultad de Ciencias Exacta

Characterization of laser propagation through turbulent media by quantifiers based on the wavelet transform: dynamic study

We analyze, within the wavelet theory framework, the wandering over a screen of the centroid of a laser beam after it has propagated through a time-changing laboratory-generated turbulence. Following a previous work (Fractals 12 (2004) 223) two quantifiers are used, the Hurst parameter, H, and the normalized total wavelet entropy. The temporal evolution of both quantifiers, obtained from the laser spot data stream, is studied and compared. This allows us to extract information on the stochastic process associated with the turbulence dynamics.Facultad de Ciencias Exacta

Wavelet entropy and fractional Brownian motion time series

We study the functional link between the Hurst parameter and the normalized total wavelet entropy when analyzing fractional Brownian motion (fBm) time series—these series are synthetically generated. Both quantifiers are mainly used to identify fractional Brownian motion processes [L. Zunino, D.G. Perez, M. Garavaglia, O.A. Rosso, Characterization of laser propagation through turbulent media by quantifiers based on the wavelet transform, Fractals 12(2) (2004) 223–233]. The aim of this work is to understand the differences in the information obtained from them, if any.Centro de Investigaciones ÓpticasFacultad de Ciencias Exacta