Weak Fluctuation Regime Research Articles

Analytic solution of the resolvent equations for heterogeneous random graphs: spectral and localization properties

The spectral and localization properties of heterogeneous random graphs are determined by the resolvent distributional equations, which have so far resisted an analytic treatment. We solve analytically the resolvent equations of random graphs with an arbitrary degree distribution in the high-connectivity limit, from which we perform a thorough analysis of the impact of degree fluctuations on the spectral density, the inverse participation ratio, and the distribution of the local density of states (LDOSs). For random graphs with a negative binomial degree distribution, we show that all eigenvectors are extended and that the spectral density exhibits a logarithmic or a power-law divergence when the variance of the degree distribution is large enough. We elucidate this singular behaviour by showing that the distribution of the LDOSs at the centre of the spectrum displays a power-law tail controlled by the variance of the degree distribution. In the regime of weak degree fluctuations the spectral density has a finite support, which promotes the stability of large complex systems on random graphs.

Peculiarities of adaptive phase correction of optical wave distortions under conditions of ‘strong’ intensity fluctuations

The reason for the loss of efficiency of adaptive phase correction in the propagation of optical waves in a turbulent atmosphere under conditions of ‘strong’ intensity fluctuations is experimentally explained for the first time. Based on the data from experiments conducted on both horizontal and vertical atmospheric paths, we have found that intensity fluctuations begin to significantly affect phase measurements when the coherence radius of the optical wave becomes less than the radius of the first Fresnel zone. Under these conditions, the main meter of adaptive optics systems, i. e. the Hartmann sensor, no longer provides correct measurements of the phase distribution in the presence of deep amplitude modulation. Based on the study of the behaviour of the mode components of the phase fluctuations reconstructed from the results of measurements in various operating regimes, we have found that, first of all, the amplitudes of the lowest modes of phase fluctuation expansion (tilts, defocusing, and astigmatism) are distorted, which, as the analysis shows, is very different from the regime of weak fluctuations.

Semiclassical dynamics of a dark soliton in a one-dimensional bosonic superfluid in an optical lattice

We study quantum dynamics of a dark soliton in a one-dimensional Bose gas in an optical lattice within the truncated Wigner approximation. A previous work has revealed that in the absence of quantum fluctuations, dynamical stability of the dark soliton significantly depends on whether its phase kink is located at a lattice site or a link of two neighboring sites. It has also shown that the dark soliton is unstable in a regime of strong quantum fluctuations regardless of the phase-kink position. To bridge the gap between the classical and strongly quantum regimes, we investigate the dynamical stability of the dark soliton in a regime of weak quantum fluctuations. We find that the position dependence of the dynamical stability gradually diminishes and eventually vanishes as the strength of quantum fluctuations increases. This classical-to-quantum crossover of the soliton stability remains even in the presence of a parabolic trapping potential. We suggest that the crossover behavior can be used for experimentally diagnosing whether the instability of a dark soliton is due to quantum fluctuations or classical dynamical instability.

Light scintillation in soft biological tissues

ABSTRACT The applicability limits of the small complex phase perturbation (Rytov) theory for laser light propagation in soft biological tissues have been tackled. We have found that for typical coherent optical waves and for several types of optically soft biological tissues with known spatial power spectra, the weak regime of light-field fluctuations is limited to propagation distances of tens of microns. This result is in striking difference with oceanic or atmospheric propagation of light for which weak fluctuation regime may hold for tens of meters in the former case and kilometers in the latter. Furthermore, the scintillation indexes of plane, spherical, and Gaussian-beam waves are investigated in depth. Our results are envisioned to find applications in optical/infrared techniques for soft tissue diagnostics.

Restriction on orbital angular momentum distribution: a role of media in vortex beams propagation.

The vortex beam carrying single orbital angular momentum (OAM) propagating through a medium with a certain transmission function is investigated. We show that the OAM mode weights in the output OAM spectrum involve two factors: the radial distribution of output beam power and the proposed restriction-characterized function. Based on the restriction-characterized function, we show that the OAM mode weights can only vary in a limited range. We analyze the relationship between the radial distribution of the output beam power and the OAM mode weights in the output OAM spectrum. Finally, our theoretical analysis is illustrated numerically with the cases of eccentric circular aperture and atmospheric turbulence in a weak fluctuation regime. These results provide new insights into the characterization of the OAM spectrum and may find applications for fields involving OAM, such as an OAM-based optical communication link and object detection.

Scintillation analysis of pseudo-Bessel-Gaussian Schell-mode beams propagating through atmospheric turbulence with wave optics simulation

The scintillation index of pseudo-Bessel-Gaussian Schell-mode (PBGSM) beams propagating through atmospheric turbulence is analyzed with the help of wave optics simulation due to the analytic difficulties. It is found that in the strong fluctuation regime, the PBGSM beams are more resistant to the turbulence with the appropriate parameters β and δ. However, the case is contrary in the weak fluctuation regime. Our simulation results indicate that the PBGSM beams may be applied to free-space optical (FSO) communication systems only when the turbulence is strong or the propagation distance is long.

Synergy Effect of Dually Superposed Orbital Angular Momentum States in Atmospheric Turbulence

We corroborate that a synergy effect may emerge when the dually superposed orbital angular momentum (OAM) states with two adjacent OAM numbers pass through a weak fluctuation regime of the atmospheric turbulence. We show that this novel effect closely depends on the transition probabilities between this two OAM eigenstates for superposition. While such probabilities become larger, the synergy effect becomes more obvious. Our examples show that the synergy effect enables OAM states to better resist phase fluctuation caused by the atmospheric turbulence.

Fiber-coupling efficiency for a Gaussian-beam wave passing through weak fluctuation regimes

The efficiency of Gaussian-wave light propagating in weak atmospheric turbulence coupled into a single model fiber is studied, and an approximation to the original mutual coherence function (MCF) in the coupling-efficiency expression is given to simplify the complexity of the efficiency calculation. The influence of the transmitting beam and turbulence parameters on the Gaussian-beam coupling-efficiency has also been evaluated. The numerical results show that the relative error of the expression with the approximate MCF referenced to the original Gaussian-wave fiber coupling efficiency representation is not more than 3.69%. It is anticipated that this work will be helpful in estimating the receiving performance and optimizing effective beam parameters at the transmitter in the design of a free-space laser communication system.

Effects of critical fluctuations and dimensionality on the jump in specific heat at the superconducting transition temperature: Application to YBa_{2}Cu_{3}O_{7-δ},Bi_{2}Sr_{2}CaCu_{2}O_{8+δ}, and KOs_{2}O_{6} compounds.

We report on a study of the superconducting order parameter thermodynamic fluctuations in YBa_{2}Cu_{3}O_{7-δ},Bi_{2}Sr_{2}CaCu_{2}O_{8+δ}, and KOs_{2}O_{6} compounds. A nonperturbative technique within the framework of the renormalized Gaussian approach is proposed. The essential features are reported (analytically and numerically) through Ginzburg-Landau (GL) model-based calculations which take into account both the dimension and the microscopic parameters of the system. By presenting a self-consistent approach improvement on the GL theory, a technique for obtaining corrections to the asymptotic critical behavior in terms of nonuniversal parameters is developed. Therefore, corrections to the specific heat and the critical transition temperature for one-, two-, and three-dimensional samples are found taking into account the fact that fluctuations occur at all length scales as the critical point of a system is approached. The GL model in the free-field approximation and the 3D-XY model are suitable for describing the weak and strong fluctuation regimes respectively. However, with a modified quadratic coefficient, the renormalized GL model is able to explain certain experimental observations including the specific heat of complicated systems, such as the cup-rate superconductors and the β-pyrochlore oxides. It is clearly shown that the enhancement, suppression, or rounding of the specific heat jump of high-T_{c} cup-rate superconductors at the transition are indicative of the order parameter thermodynamic fluctuations according to the dimension and the nature of interactions.

A new study of turbulence effects in the marine environment on the intensity distributions of flat-topped Gaussian beams

In this study, we investigate the effects of maritime atmospheric turbulence on the propagation of flat-topped Gaussian beams within the regime of weak fluctuations. Based on the paraxial approximation and the Rytov theory, the statistical moments, the scintillation index, the probability of fade, and the duration of fade are studied analytically and numerically. The numerical results show that these parameters depend on the beam order, the beam waist, the refractive-index structure parameter, the inner scale of the turbulence and the wavelength.

Theoretical investigation on the Hollow Gaussian beams propagating in atmospheric turbulent

The effects of atmospheric turbulence on the propagation of Hollow Gaussian beams (HGBs) within the regime of weak fluctuations have been investigated using the paraxial approximation and the Rytov theory. The statistical moments, the scintillation index, the probability of fade, and the duration of fade are studied analytically and numerically. The numerical results show that these parameters depend on the beam order n, the spot size w0, the refractive index structure parameter n, and the wavelength λ.

Theoretical and experimental study of atmospheric turbulence measurement using two-aperture differential scintillation method

We report the basic theory and first horizontal results of a method called two-aperture differential scintillation method which is aimed at monitoring the vertical profile of atmospheric optical turbulence strength. The method is based on irradiance fluctuation of active light source, but can extract the optical turbulence information in the single-passage path. In this paper, the theoretical principle of two-aperture differential scintillation method is derived in detail. A concise expression is proposed for irradiance fluctuation structure function with differential aperture in the Rytov approximation under a weak fluctuation regime based on the cross-path theory. The mathematic relationship between irradiance fluctuation structure function and atmospheric optical turbulence strength is then developed. The effects of beacon aperture and beacon altitude on path weighting function of this method are analyzed for Kolmogorov turbulence. In order to test the validity of the new method, the experiments are conducted to compare the two-aperture differential scintillation method and single-aperture scintillation method in atmospheric boundary layer over 2 km horizontal single-passage path. In this arrangement, we employ a differential image motion monitor system to measure differential scintillation. Simultaneously, a large aperture scintillation instrument is placed 5 m away at the same altitude to measure the single-aperture scintillation. It is shown that the results of atmospheric refractive index structure constant deduced from the two methods are in good agreement. The measurements of atmospheric coherence length for spherical wave corresponding to the two methods indicate a linear correction factor (R2) of 0.96, in a slope of 0.98 with an offset of -0.09 cm. Feasibility and effectiveness of two-aperture differential scintillation method are thus verified experimentally. The novel method can separate single-passage scintillation information of active beacon double-passage propagation, thereby providing an accurate technique for measuring the atmospheric turbulence of active beacon.

Estimation of Cn² based on scintillation of fixed targets imaged through atmospheric turbulence.

We define a pixel-based scintillation index for dynamic incoherent imaging of fixed high-contrast targets through atmospheric turbulence. We propose a simple setup to study this parameter varying the Cn(2) constant in controlled laboratory conditions (weak fluctuation regime). We find the semi-empirical relationship between the pixel-based scintillation index and the index of refraction structure constant, which we then employ to estimate Cn(2) successfully in an independent case in which this value was not known beforehand.

Fiber coupling efficiency for a Gaussian-beam wave propagating through non-Kolmogorov turbulence.

Nowadays it has been accepted that the Kolmogorov model is not the only possible turbulent one in the atmosphere, which has been confirmed by the increasing experimental evidence and some results of theoretical investigation. This has prompted the scientist community to study optical propagation in non-Kolmogorov atmospheric turbulence. In this paper, using the method of effective beam parameters and a non-Kolmogorov power spectrum which has a more general power law instead of standard Kolmogorov power law value 11/3 and a more general amplitude factor instead of constant value 0.033, the fiber coupling efficiency for a Gaussian-beam wave has been derived for a horizontal path in both weak and strong fluctuation regimes. And then the influence of spectral power law variations on the fiber coupling efficiency has been analyzed. It is anticipated that this work is helpful to the investigations of atmospheric turbulence and optical wave propagation in the atmospheric turbulence.

Temporal power spectrum of irradiance fluctuations for a Gaussian-beam wave propagating through non-Kolmogorov turbulence.

In the past decades, both the increasing experimental evidence and some results of theoretical investigation on non-Kolmogorov turbulence have been reported. This has prompted the study of optical propagation in non-Kolmogorov atmospheric turbulence. In this paper, based on the thin phase screen model and a non-Kolmogorov power spectrum which owns a generalized power law instead of standard Kolmogorov power law value 11/3 and a generalized amplitude factor instead of constant value 0.033, the temporal power spectrum of irradiance fluctuations for a Gaussian-beam wave is derived in the weak fluctuation regime for a horizontal path. The analytic expressions are obtained and then used to analyze the influence of spectral power law variations on the temporal power spectrum of irradiance fluctuations.

Renormalization group calculations for wetting transitions of infinite order and continuously varying order: Local interface Hamiltonian approach

We study the effect of thermal fluctuations on the wetting phase transitions of infinite order and of continuously varying order, recently discovered within a mean-field density-functional model for three-phase equilibria in systems with short-range forces and a two-component order parameter. Using linear functional renormalization group calculations within a local interface Hamiltonian approach, we show that the infinite-order transitions are robust. The exponential singularity (implying 2-α(s)=∞) of the surface free energy excess at infinite-order wetting as well as the precise algebraic divergence (with β(s)=-1) of the wetting layer thickness are not modified as long as ω<2, with ω the dimensionless wetting parameter that measures the strength of thermal fluctuations. The interface width diverges algebraically and universally (with ν([perpendicular])=1/2). In contrast, the nonuniversal critical wetting transitions of finite but continuously varying order are modified when thermal fluctuations are taken into account, in line with predictions from earlier calculations on similar models displaying weak, intermediate, and strong fluctuation regimes.

Performance of retro reflector-modulated links under weak turbulence

A method for the evaluation of performance of free space optical communications systems utilising modulating retro reflectors under weak turbulence is presented. The model considers the effects of system physical parameters, such as the modulating retro reflector effective size and receiver aperture diameter, on the bit-error rate (BER) and the capacity. Different spatial spectrums are used with the model and the effect of aperture averaging is evaluated directly from the normalised spatial covariance in each case. The log-normal distribution is adopted for the evaluation of BER in the weak fluctuation regime. Finally, for the first time the capacity of a system using modulated retro reflectors is calculated using a recently proposed closed-form expression. The model can be used as a performance metric in network routing algorithms.

Inner- and outer-scale effects on the scintillation index of an optical wave propagating through moderate-to-strong non-Kolmogorov turbulence

By use of the generalized von Kármán spectrum model that features both inner scale and outer scale parameters for non-Kolmogorov turbulence and the extended Rytov method that incorporates a modified amplitude spatial-frequency filter function under strong-fluctuation conditions, theoretical expressions are developed for the scintillation index of a horizontally propagating plane wave and spherical wave that are valid under moderate-to-strong irradiance fluctuations. Numerical results show that the obtained expressions also compare well with previous results in weak-fluctuation regimes. Based on these general models, the impacts of finite inner and outer scales on the scintillation index of an optical wave are examined under various non-Kolmogorov fluctuation conditions.

Scintillation index and performance analysis of wireless optical links over non-Kolmogorov weak turbulence based on generalized atmospheric spectral model

Based on the generalized spectral model for non-Kolmogorov atmospheric turbulence, analytic expressions of the scintillation index (SI) are derived for plane, spherical optical waves and a partially coherent Gaussian beam propagating through non-Kolmogorov turbulence horizontally in the weak fluctuation regime. The new expressions relate the SI to the finite turbulence inner and outer scales, spatial coherence of the source and spectral power-law and then used to analyze the effects of atmospheric condition and link length on the performance of wireless optical communication links.

Log-amplitude variance for a Gaussian-beam wave propagating through non-Kolmogorov turbulence

In the past decades, both the increasing experimental evidences and some results of theoretical investigation on non-Kolmogorov turbulence have been reported. This has prompted the study of optical propagation in non-Kolmogorov atmospheric turbulence. In this paper, using a non-Kolmogorov power spectrum which owns a generalized power law instead of standard Kolmogorov power law value 11/3 and a generalized amplitude factor instead of constant value 0.033, the log-amplitude variances for a Gaussian-beam wave are derived in the weak-fluctuation regime for a horizontal path. The analytic expressions are obtained and then used to analyze the effect of spectral power-law variations on the log-amplitude fluctuations of Gaussian-beam wave.