Distribution Of Intensity Fluctuations Research Articles

Randomness of optical turbulence generated by Rayleigh–Bénard convection using intensity statistics

The experimental study of optical turbulence proves difficult due to challenges in generating controllable conditions in a laboratory environment. Confined water tanks that produce Rayleigh–Bénard (RB) convection are one method to generate optical turbulence using a controllable temperature gradient. It is of utmost concern to quantify the properties of the optical turbulence generated for characterization of other optical applications such as imaging, sensing, or communications. In this experimental study a Gaussian beam is propagated through a RB water tank where two intensity measurements are made at the receiver’s pupil and focal plane. The pupil and focal plane results include quantification of the intensity fluctuation distribution, scintillation distribution, and refractive index structure constant at various values of the temperature gradient. The angle of arrival fluctuations is also calculated at the focal plane to obtain a second estimate of C n 2. The pupil plane estimate for C n 2 using scintillation index and focal plane angle of arrival fluctuations is compared to preliminary predictions of C n 2 as a function of RB temperature gradient showing C n 2∼ΔT4/3. The outcomes of the study confirm that the RB process produces intensity fluctuations that follow gamma–gamma and log-normal probability density functions. Estimates of the refractive index structure constant C n 2 produce the same trends with different magnitudes when measured from the pupil and focal plane.

Study of Bright Compact Radio Sources of the Northern Hemisphere at 111 MHz

The search for compact components of strong ($S_{int} \ge 5$ Jy at 102.5 MHz) discrete radio sources from the Pushchino catalogue was carried out using the method of interplanetary scintillation. A total of 3620 sources were examined, and 812 of them were found to compact (scintillating) components. Estimates of fluctuations of the flux density of these compact components were derived from the scintillation index ($m_{max}$) corresponding to an elongation of $25^o$. The angular size and compactness of 178 sources with compact components were estimated. Scintillation indices of sources corresponding to the compact component ($m_{max}$) and flux densities of compact components were determined. It was demonstrated that slow variations of the spatial distribution of interplanetary plasma, which are related to the 11-year cycle of solar activity, may exert a systematic influence on the estimates of angular sizes of sources. Coefficients compensating the deviation from the spherical symmetry of solar wind in the estimates of angular sizes were found using the coefficient of asymmetry of the statistical distribution of intensity fluctuations. The study of correlations between the parameters of sources in the sample revealed that the maximum value of the scintillation index decreases as the integrated flux increases, while the angular size has no marked dependence on the integrated flux.

Probability distribution of intensity fluctuations of arbitrary-type laser beams in the turbulent atmosphere.

Statistical characteristics of radiation intensity in the cross section of laser beams propagating in the turbulent atmosphere are analyzed by using numerical simulations. It is shown that for arbitrary values of the propagation distance, Rytov parameter, beam type, and position of the analyzed point in the beam cross section, the probability density function (PDF) of radiation intensity is fully determined by the scintillation index and the average intensity. In the case of moderate and weak intensity fluctuations characterized by the scintillation index smaller than unity, the probability density function is determined by the gamma distribution. For the case of strong fluctuations (with the scintillation index larger than unity), a new analytical expression for PDF is proposed, which well approximates PDFs obtained in numerical experiments under different conditions of propagation of different-type beams.

Turbulent Intermittency in a Random Fiber Laser

In fluid turbulence, intermittency is the emergence of non-Gaussian tails in the distribution of velocity increments in small space and/or time scales. Intermittence is thus expected to gradually disappear as one moves from small to large scales. Here we study the turbulent-like intermittency effect experimentally observed in the distribution of intensity fluctuations in a disordered continuous-wave-pumped erbium-doped-based random fiber laser with specially-designed random fiber Bragg gratings. The intermittency effect is investigated as a crossover in the distribution of intensity increments from a heavy-tailed distribution (for short time scales), to a Gaussian distribution (for large time scales). The results are theoretically supported by a hierarchical stochastic model that incorporates Kolmogorov’s theory of turbulence. In particular, the discrete version of the hierachical model allows a general direct interpretation of the number of relevant scales in the photonic hierarchy as the order of the transitions induced by the non-linearities in the medium. Our results thus provide further statistical evidence for the interpretation of the turbulence-like emission previously observed in this system.

Probability density of field and intensity fluctuations of structured light in a turbulent atmosphere

Distributions of the probability density of fluctuations of the intensity and real and imaginary parts of the complex field amplitude of the Laguerre–Gaussian laser beam propagating through a turbulent atmosphere, provided that the beam scintillation index takes values larger than unity, are studied. The calculations are performed through numerical simulation and with application of an analytical approach based on the expansion of the probability distribution density of the wave field into the Edgeworth series. The comparison of the results of numerical and analytical calculations has demonstrated that the probability density distribution of intensity fluctuations of the laser beam is resistant to small variations in parameters of the probability density distribution of fluctuations of the real and imaginary parts of the wave field. In addition, the earlier formulated statement that the normalized probability density of intensity fluctuations of a laser beam at any point of the space occupied by this beam is determined by the value of the scintillation index and does not depend directly on the turbulent propagation conditions is confirmed. It is shown that the probability density of intensity fluctuations constructed with the Edgeworth approximation of the probability density of field fluctuations is in good agreement with the results of numerical simulation and the fractional exponential distribution for the values of the scintillation index ranging from 1.0 to 1.6.

Statistical Studies of Fading in Underwater Wireless Optical Channels in the Presence of Air Bubble, Temperature, and Salinity Random Variations

Optical signal propagation through underwater channels is affected by three main degrading phenomena, namely, absorption, scattering, and fading. In this paper, we experimentally study the statistical distribution of intensity fluctuations in underwater wireless optical channels with random temperature and salinity variations, as well as the presence of air bubbles. In particular, we define different scenarios to produce random fluctuations on the water refractive index across the propagation path and, then, examine the accuracy of various statistical distributions in terms of their goodness of fit to the experimental data. We also obtain the channel coherence time to address the average period of fading temporal variations. The scenarios under consideration cover a wide range of scintillation index from weak to strong turbulence. Moreover, the effects of beam-expander-and-collimator (BEC) at the transmitter side and aperture averaging lens (AAL) at the receiver side are experimentally investigated. We show that the use of a transmitter BEC and/or a receiver AAL suits single-lobe distributions, such that the generalized Gamma and exponentiated Weibull distributions can excellently match the histograms of the acquired data. Our experimental results further reveal that the channel coherence time is on the order of 10−3 s and larger which implies to the slow fading turbulent channels.

Experimental characterization of the transition to coherence collapse in a semiconductor laser with optical feedback.

Semiconductor lasers with time-delayed optical feedback display a wide range of dynamical regimes, which have found various practical applications. They also provide excellent testbeds for data analysis tools for characterizing complex signals. Recently, several of us have analyzed experimental intensity time-traces and quantitatively identified the onset of different dynamical regimes, as the laser current increases. Specifically, we identified the onset of low-frequency fluctuations (LFFs), where the laser intensity displays abrupt dropouts, and the onset of coherence collapse (CC), where the intensity fluctuations are highly irregular. Here we map these regimes when both, the laser current and the feedback strength vary. We show that the shape of the distribution of intensity fluctuations (characterized by the standard deviation, the skewness, and the kurtosis) allows to distinguish among noise, LFFs and CC, and to quantitatively determine (in spite of the gradual nature of the transitions) the boundaries of the three regimes. Ordinal analysis of the inter-dropout time intervals consistently identifies the three regimes occurring in the same parameter regions as the analysis of the intensity distribution. Simulations of the well-known time-delayed Lang-Kobayashi model are in good qualitative agreement with the observations.

Turbulence hierarchy in a random fibre laser

Turbulence is a challenging feature common to a wide range of complex phenomena. Random fibre lasers are a special class of lasers in which the feedback arises from multiple scattering in a one-dimensional disordered cavity-less medium. Here we report on statistical signatures of turbulence in the distribution of intensity fluctuations in a continuous-wave-pumped erbium-based random fibre laser, with random Bragg grating scatterers. The distribution of intensity fluctuations in an extensive data set exhibits three qualitatively distinct behaviours: a Gaussian regime below threshold, a mixture of two distributions with exponentially decaying tails near the threshold and a mixture of distributions with stretched-exponential tails above threshold. All distributions are well described by a hierarchical stochastic model that incorporates Kolmogorov’s theory of turbulence, which includes energy cascade and the intermittence phenomenon. Our findings have implications for explaining the remarkably challenging turbulent behaviour in photonics, using a random fibre laser as the experimental platform.

WIDESPREAD NANOFLARE VARIABILITY DETECTED WITHHINODE/X-RAY TELESCOPE IN A SOLAR ACTIVE REGION

It is generally agreed that small impulsive energy bursts called nanoflares are responsible for at least some of the Sun's hot corona, but whether they are the explanation for most of the multi-million degree plasma has been a matter of ongoing debate. We here present evidence that nanoflares are widespread in an active region observed by the X-Ray Telescope on-board the Hinode mission. The distributions of intensity fluctuations have small but important asymmetries, whether taken from individual pixels, multi-pixel subregions, or the entire active region. Negative fluctuations (corresponding to reduced intensity) are greater in number but weaker in amplitude, so that the median fluctuation is negative compared to a mean of zero. Using MonteCarlo simulations, we show that only part of this asymmetry can be explained by Poisson photon statistics. The remainder is explainable with a tendency for exponentially decreasing intensity, such as would be expected from a cooling plasma produced from a nanoflare. We suggest that nanoflares are a universal heating process within active regions.

Space – Time Distribution of G-band and Ca ii H-line Intensity Oscillations in Hinode/SOT – FG Observations

We study the space-time distributions of intensity fluctuations in 2 - 3 hour sequences of multi-spectral, high-resolution, high-cadence broad-band filtergram images (BFI) made by the SOT-FG system aboard the Hinode spacecraft. In the frequency range 5.5 < f < 8.0 mHz both G-band and Ca II H-line oscillations are suppressed in the presence of magnetic fields, but the suppression disappears for f > 10 mHz. By looking at G-band frequencies above 10 mHz we find that the oscillatory power, both at these frequencies and at lower frequencies too, lies in a mesh pattern with cell scale 2 - 3 Mm, clearly larger than normal granulation, and with correlation times on the order of hours. The mesh pattern lies in the dark lanes between stable cells found in time-integrated G-band intensity images. It also underlies part of the bright pattern in time-integrated H-line emission. This discovery may reflect dynamical constraints on the sizes of rising granular convection cells together with the turbulence created in strong intercellular downflows.

Asymmetry function of interstellar scintillations of pulsars

A new method for separating intensity variations of a source’s radio emission having various physical natures is proposed. The method is based on the joint analysis of the structure function of intensity variations and the asymmetry function, which is a generalization of the asymmetry coefficient and which characterizes the asymmetry of the distribution function of intensity fluctuations on various scales for inhomogeneitiesin the diffractive scintillation pattern. Relationships for the asymmetry function in the cases of a logarithmic normal distribution of the intensity fluctuations and a normal distribution of the field fluctuations are derived. Theoretical relationships and observational data on interstellar scintillations of pulsars (refractive, diffractive, and weak scintillations) are compared. The data for PSR B0329+54, B1133+16, B1642-03, and B1933+16 pulsars were used for comparison. Pulsar scintillations match the behavior expected for a normal distribution of field fluctuations (diffractive scintillation) or logarithmic normal distribution of intensity fluctuations (refractive and weak scintillation). Analysis of the asymmetry function is a good test for distinguishing scintillations against the background of variations that have different origins.

Fluctuations in radiation scattered by small spheroids above an interface

This paper presents the results of a calculation of the low-order statistical properties of radiation which has been scattered by small spheroidal particles distributed at different heights above a surface. The results are in the form of analytical formulae for the average scattered intensity and for the normalized second moment of the intensity fluctuation distribution. The nature and magnitude of effects which can be generated by the system are discussed with particular reference to polarization phenomena at large angles of incidence. The predictions of the model are compared with the known fluctuation properties of microwave sea echo. (Some figures in this article are in colour only in the electronic version; see www.iop.org)

Dynamics and distribution of intensity fluctuations in the modes of an injection laser with strong high-frequency modulation of the pump current

The dynamical behavior and spectral density of the intensity fluctuations of optical radiation in the modes of an injection laser with strong high-frequency modulation of the pump current have been investigated by numerical methods. A method for transforming the Einstein-Fokker-Planck equation was used to analyze the effect of random fluctuations of the carrier and photon generation-recombination rate on the dynamics and spectral characteristics of an injection laser. The distribution of the time-averaged continuous and discrete components of the radiation intensity in the modes of an injection laser was studied as a function of the parameters of the laser and the characteristics of the modulation.

Amplitude fluctuations in the theory of radio-wave refraction scattering

We consider some aspects of the theory of radio-wave scattering with respect to studies of radiation intensity fluctuations behind a random phase screen. The expressions for a piecewise approximation of the function of distribution of intensity fluctuations in the near zone and in the region of random focusing behind the screen are found. The expressions obtained are used to calculate the radio-wave scintillation index in these regions. The corresponding calculations are performed with allowance for the finite dimensions of external and internal scales of turbulent inhomogeneities of the phase screen. It is shown that the radio-wave refraction scattering, as a rule, is characterized by a pronounced random focusing of the radiation intensity behind the phase screen. However, under strongly developed turbulence of the radio-wave propagation medium (phase screen) the above phenomenon may be absent.

Structure of scintillations in Neptune's occultation shadow

view Abstract Citations (16) References (16) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Structure of Scintillations in Neptune's Occultation Shadow Hubbard, W. B. ; Lellouch, Emmanuel ; Sicardy, Bruno ; Brahic, Andre ; Vilas, Faith ; Bouchet, Patrice ; McLaren, Robert A. ; Perrier, C. Abstract The intensity residuals in the stellar occultation by Neptune on 1985 August 20 are examined. These residuals (scintillations) are calculated by subtracting a best-fit oblate isothermal atmosphere model from the observed light curves at two stations in Chile and one station in Hawaii. Because of exceptionally high signal-to-noise, scintillations were observable throughout the occultation. The data are consistent with an intensity fluctuation distribution in Neptune's shadow which has extended barlike patterns lying parallel to the limb in the vicinity of the half-intensity level but which then converts to predominantly radial streaks near the center. A theoretical model of scale-free refractivity disturbances in Neptune's upper atmosphere, with considerable anisotropy, is able to account for most of the observed characteristics. Publication: The Astrophysical Journal Pub Date: February 1988 DOI: 10.1086/166019 Bibcode: 1988ApJ...325..490H Keywords: Neptune Atmosphere; Scintillation; Stellar Occultation; Atmospheric Models; Light Curve; Monte Carlo Method; Upper Atmosphere; Astronomy; OCCULTATIONS; PLANETS: ATMOSPHERES; PLANETS: NEPTUNE full text sources ADS |

The probability distribution of intensity for acoustic propagation in a randomly varying ocean

Probability distributions of intensity fluctuations from the MATE, AFAR, and S. W. Bermuda underwater acoustics experiments are compared with recently derived theoretical expressions. The limitations and strengths of these expressions are discussed. In particular, it is found that the work of Furutsu [J. Math. Phys. 17, 1252–1263 (1976)] gives a good description of the probability distribution function of intensity or log intensity, requiring only a knowledge of the second- and third-order intensity moments. Furutsu’s description is not asymptotically correct at large range, so a modified form is proposed for the moments of intensity that reduce analytically to the log-normal distribution at short range and to the exponential distribution at large range. This new form also predicts the higher moments well but cannot be inverted analytically. A numerical inversion is used, and the ensuing distribution agrees well with the analytical result of Furutsu. It is expected that the new expression will be applicable at all ranges.

Measurements of intensity fluctuations of an InGaAsP external cavity laser

We have measured the statistical distributions of intensity fluctuations in an external cavity semiconductor laser. The cavity was formed by coupling a 6.8-cm-long multimode fiber to an antireflection coated, 10-μm-wide InGaAsP ridge-waveguide laser. The fluctuations of the intensity of the laser are small when the cavity is adjusted for single-longitudinal-mode operation.

Laser beam propagation in atmospheric turbulence

The optical effects of atmospheric turbulence on the propagation of low power laser beams are reviewed in this paper. The optical effects are produced by the temperature fluctuations which result in fluctuations of the refractive index of air. The commonly-used models of index-of-refraction fluctuations are presented. Laser beams experience fluctuations of beam size, beam position, and intensity distribution within the beam due to refractive turbulence. Some of the observed effects are qualitatively explained by treating the turbulent atmosphere as a collection of moving gaseous lenses of various sizes. Analytical results and experimental verifications of the variance, covariance and probability distribution of intensity fluctuations in weak turbulence are presented. For stronger turbulence, a saturation of the optical scintillations is observed. The saturation of scintillations involves a progressive break-up of the beam into multiple patches; the beam loses some of its lateral coherence. Heterodyne systems operating in a turbulent atmosphere experience a loss of heterodyne signal due to the destruction of coherence.

Wandering laser beam in a turbulent atmosphere. I. Distribution of the probability density of the fluctuation power

Expressions are obtained for the distribution of the probability and moments of the distribution of intensity fluctuations in the case of wandering of a laser beam which itself exhibits log-normal fluctuations. The nature of the distribution and the values of the moments depend on two parameters: one represents the strength of log-normal fluctuations and the other the strength of fluctuations resulting from wandering of the beam.

Observations of Interplanetary Scintillations at 327 MHz

The properties of the interplanetary medium and the structures of9 compact radio sources have been derived from the observed interplanetary scintillations at 327 MHz using the Ooty radio telescope. The observed scale size of the electron density irregularities has a value of 100 km in the elongation range 0�3-0� 7 A. U. and shows no indication of increasing with elongation, as has been suggested by Hewish and Symonds (1969). The Bessel transforms of intensity fluctuations could seldom be used for estimating the solar wind velocity since the minima corresponding to the Fresnel filtering effect were rarely seen. The study of the skewness parameter of the probability distribution of intensity fluctuations at 327 MHz indicates that for elongations between O' 2 and O' 35 A.U. the thin screen model is satisfactory, but for larger elongations no clear conclusion can be drawn.