Computer-generated holograms for producing fractal speckles

When a diffuser is illuminated by the coherent light with a negative power-law distribution, fractal speckles are produced in the far-field diffraction region. Fractal speckles have extremely long spatial correlation functions of the intensity distributions in comparison with ordinary speckles, which implies that they may extend measurement ranges in various metrological applications based on the spatial correlation of speckles. To have fractal speckles with satisfactory statistical properties, it is required to produce a power-law illumination profile with high quality. In this paper, we report on the computer-generated holograms for producing power-law intensities on the basis of the method of stationary phase, with the error-reduction algorithm combined with to suppress strong ringing of the intensity.     

Atomistic origin of urbach tails in amorphous silicon

Exponential band edges have been observed in a variety of materials, both crystalline and amorphous. In this Letter, we infer the structural origins of these tails in amorphous and defective crystalline Si by direct calculation with current ab initio methods. We find that exponential tails appear in relaxed models of diamond silicon with suitable extended defects that emerge from relaxing point defects. In amorphous silicon (a-Si), we find that structural filaments of short bonds and long bonds exist in the network, and that the tail states near the extreme edges of both band tails are also filamentary, with much localization on the structural filaments. We connect the existence of both filament systems to structural relaxation in the presence of defects and of topological disorder.     

Speckle size and decorrelation time; space-time correlation analysis of coherent light dynamically scattered from turbid media

We report on the dependence of the decorrelation time on the spatial intensity correlation of speckles generated in the far-field by back-scattered photons from turbid media. The effects contribute to an explanation of an earlier observation that the average Doppler width of the power spectrum of detector current fluctuations depends on the size of the illuminating laser beam. The space-time correlation of the speckles generated by a particle suspension illuminated by a collimated laser beam is analyzed from serial images taken by a high speed camera. It was found that larger spatial correlation distances, associated with large speckles, exhibit a slower temporal decorrelation.     

Dynamics of phason fluctuations in the i-AlPdMn quasicrystal

We report on the study of the dynamics of long wavelength phason fluctuations in the i-AlPdMn icosahedral phase using coherent x-ray scattering. When measured with a coherent x-ray beam, the diffuse intensity due to phasons presents strong fluctuations or speckles pattern. From room temperature to 500 degrees C the speckle pattern is time independent. At 650 degrees C the time correlation of the speckle pattern exhibits an exponential time decay, from which a characteristic time tau is extracted. We find that tau is proportional to the square of the phason wavelength, which demonstrates that phasons are collective diffusive modes in quasicrystals, in agreement with theoretical predictions.     

Scaling reduction of the contrast of fractal speckles detected with a finite aperture

It is known that speckle patterns with fractal properties, called fractal speckles, are produced by illuminating a diffuser with the coherent light having the intensity distribution obeying a negative power law. One of key properties of fractal speckles is the spatial correlation function obeying a negative power law, which implies that such speckles have scaling properties. In detecting fractal speckles, the effect of the spatial integration is inevitable in most cases since they have speckle grains of various scales including very fine ones. To evaluate this effect, in this paper, the contrast of spatially integrated intensity distributions is investigated theoretically and experimentally for fractal speckles. The results show that the contrast reduction with the size of the detector aperture obeys a negative power function related with the exponent of the intensity correlation coefficient of fractal speckles.     

The autocorrelation of speckles in deep Fresnel diffraction region and characterizations of random self-affine fractal surfaces

This paper studies the correlation properties of the speckles in the deep Fresnel diffraction region produced by the scattering of rough self-affine fractal surfaces. The autocorrelation function of the speckle intensities is formulated by the combination of the light scattering theory of Kirchhoff approximation and the principles of speckle statistics. We propose a method for extracting the three surface parameters, i.e. the roughness w, the lateral correlation length ξ and the roughness exponent α, from the autocorrelation functions of speckles. This method is verified by simulating the speckle intensities and calculating the speckle autocorrelation function. We also find the phenomenon that for rough surfaces with α= 1, the structure of the speckles resembles that of the surface heights, which results from the effect of the peak and the valley parts of the surface, acting as micro-lenses converging and diverging the light waves.     

Anomalous intensity of pinned speckles at high adaptive correction

Ground-based optical searches for faint stellar or planetary companions about other stars may be limited by speckle noise, which is the rapid intensity fluctuations that are due to motions of remnant atmospheric speckles. Adaptive optics (AO) can reduce residual wave-front phase errors to low values, substantially reducing the unwanted power in the speckle halo. At high correction, however, the noise in the halo will be dominated by anomalously bright "pinned" speckles that have a number of unusual properties. They can have negative intensities and will appear in spatially antisymmetric patterns; they are spatially pinned to Airy rings and have zero mean in a sufficiently long integration. Some of these properties may be used to reduce the unanticipated effect of pinned speckles on companion searches, depending on details of the AO system. But, in short exposures, pinned speckles dominate speckle noise over much of the inner halo for Strehl ratios S as low as 0.6 and over much of the outer halo too as Strehl and deformable-mirror actuator densities increase. I show that these anomalously bright pinned speckles are not included in the traditional expression for speckle power in an image, (1 - S), on which sensitivity estimates of future high-performance AO systems have been based.     

Long time tails in stationary random media. I. Theory

Diffusion of moving particles in stationary disordered media is studied using a phenomenological mode-coupling theory. The presence of disorder leads to a generalized diffusion equation, with memory kernels having power law long time tails. The velocity autocorrelation function is found to decay like t^–(d/2+1), while the time correlation function associated with the super-Burnett coefficient decays liket ^–d/2 for long times. The theory is applicable to a wide variety of dynamical and stochastic systems including the Lorentz gas and hopping models. We find new, general expressions for the coefficients of the long time tails which agree with previous results for exactly solvable hopping models and with the low-density results obtained for the Lorentz gas. Finally we mention that if the moving particles are charged, then the long time tails imply that there is an ^d/2 contribution to the low-frequency part of the frequency-dependent electrical conductivity.     

运动界面上反射超声散斑空间运动的研究

在Kirchhoff 衍射理论的基础上，应用随机信号相关原理，推导了作刚体运动的界面上反射超声散斑在空间运动时，保持其复振幅相关的必要条件.由此得到超声散斑的空间运动公式.界面、超声散斑和超声接收探头之间的相对运动，导致界面孔径的改变.分析表明，在保持界面孔径相关的条件下，界面所允许的最大平移量和转角值，与声源位置、接收用聚焦探头的数值孔径、超声入射角以及观察角有关.应用数字相关技术和三维扫描信号采集系统，根据散斑场子集相关系数的单峰性质，对超声散斑空间运动公式进行了实验验证.实验结果表明，理论分析所得的 关键词： 超声散斑 相关原理 空间运动     

用零相关相位板匀滑散斑的理论研究

对零相关相位板匀滑散斑的特性进行了理论分析和散值计算,结果表明尽管零相关相位板是针对入射场为平面波面而设计的,但在入射场的振幅和相位有一定起伏的情况下,其远场光斑的散斑对比度明显低于采用随机相位板的情形.因而用零盯关相位板匀滑散斑是一种更为有效的方法.     

Long-Time Tails, Weak Localization, and Classical and Quantum Critical Behavior

An overview is given of the long-time and long-distance behavior of correlation functions in both classical and quantum statistical mechanics. After a simple derivation of the classical long-time tails in equilibrium time correlation functions, we discuss analogous long-distance phenomena in nonequilibrium classical systems. The paper then draws analogies between these phenomena and similar effects in quantum statistical mechanics, with emphasis on the soft modes that underly long-time tails and related phenomena. We also elucidate the interplay between critical phenomena and long-time tails, using the classical liquid-gas critical point and the quantum ferromagnetic transition as examples.     

The Dynamics of Power laws: Fitness and Aging in Preferential Attachment Trees

Continuous-time branching processes describe the evolution of a population whose individuals generate a random number of children according to a birth process. Such branching processes can be used to understand preferential attachment models in which the birth rates are linear functions. We are motivated by citation networks, where power-law citation counts are observed as well as aging in the citation patterns. To model this, we introduce fitness and age-dependence in these birth processes. The multiplicative fitness moderates the rate at which children are born, while the aging is integrable, so that individuals receives a finite number of children in their lifetime. We show the existence of a limiting degree distribution for such processes. In the preferential attachment case, where fitness and aging are absent, this limiting degree distribution is known to have power-law tails. We show that the limiting degree distribution has exponential tails for bounded fitnesses in the presence of integrable aging, while the power-law tail is restored when integrable aging is combined with fitness with unbounded support with at most exponential tails. In the absence of integrable aging, such processes are explosive.     

Emergence of linear wave segments and predictable traits in saturated nonlinear media

We find the key behind the existence traits of asymptotic saturated nonlinear optical solitons in the emergence of linear wave segments. These traits, produced by the progressive relegation of nonlinear dynamics to wave tails, allow a direct and versatile analytical prediction of self-trapping existence conditions and simple soliton scaling laws, which we confirm experimentally in saturated-Kerr self-trapping observed in photorefractives. This approach provides the means to correctly evaluate beam tails in the saturated regime, which is instrumental in the prediction of soliton interaction forces.     

高分辨率主动声呐强混响抑制技术研究（英文）

Resolution enhancement of active sonar can suppress the reverberation.While it also makes the envelope data distribution diverge from Rayleigh distribution to K-distribution.The stronger scattering speckles,the heavier of the K-distribution tails.The envelope amplitudes of these strong scattering speckles are usually very big.As the interfering target,the strong reverberation decreases the performances of the background power level estimation and the target detection.The fuzzy statistical normalization processing(FSNP) is introduced to suppress the strong reverberation firstly in this paper.Then how the strong reverberation and the FSNP affect the distribution of K-distributed sonar data is studied.The influence on the constant false alarm rate(CFAR) detection performance caused by the strong reverberation and the FSNP is also simulated and analyzed.Performance comparisons between the CFAR detector based on FSNP and the conventional CFAR detectors are carried out.The simulation results show that the strong reverberation can make the shape parameter of the interfering K-distributed data become smaller than that of the original K-distributed data.While the FSNP can suppress the strong reverberation,increase the shape parameter value,and improve the performance of the shape parameter estimator and the CFAR detector.     

高分辨率有源声呐强混响抑制技术研究

有源声呐分辨率的提高可以抑制混响,但也使声呐包络数据的统计分布偏离瑞利分布,而更接近拖尾较重的K分布。强散射体所带来的强混响的幅值一般较大,它们使统计分布拖尾更严重,表征K分布的形状参数也越小。强混响作为目标干扰,严重影响了背景功率估计的准确性,从而降低了目标检测的性能。本文基于模糊统计理论,首先提出了用于抑制强混响的模糊统计归一化处理方法;然后对强混响和模糊统计归一化处理如何影响声呐数据分布和CFAR(Constant false-alarm rate)目标检测性能进行了仿真、研究和分析,最后对基于模糊统计归一化处理的CFAR检测性能和传统CFAR检测性能进行了仿真比较。仿真结果表明强混响目标干扰能使K分布数据的形状参数变小,而模糊统计归一化处理可抑制强混响目标干扰,增大包络数据分布的形状参数,提高形状参数估计性能和CFAR检测性能。      

Time behavior of the correlation functions in a simple dissipative quantum model

The force and velocity correlation functions for a particle interacting with a bath are calculated within a model allowing for finite memory effects. The relevance of a Brownian picture is delineated in view of the respective behavior of these functions and appears fully inadequate below some cross-over temperature; then, the interplay between quantum and thermal fluctuations yields some long time tails on the same time scale for both correlation functions. The real space transient diffusion coefficient is found to exceed its asymptotic Einstein value for most times in that regime. The limiting case of an infinitely short memory time is also investigated and is seen to produce weak divergences on a time scale which is small as compared to the other characteristic times.     

Relativistic entropy and related Boltzmann kinetics

It is well known that the particular form of the two-particle correlation function, in the collisional integral of the classical Boltzmman equation, fixes univocally the entropy of the system, which turns out to be the Boltzmann-Gibbs-Shannon entropy. In the ordinary relativistic Boltzmann equation, some standard generalizations, with respect to its classical version, imposed by the special relativity, are customarily performed. The only ingredient of the equation, which tacitly remains in its original classical form, is the two-particle correlation function, and this fact imposes that also the relativistic kinetics is governed by the Boltzmann-Gibbs-Shannon entropy. Indeed the ordinary relativistic Boltzmann equation admits as stationary stable distribution, the exponential Juttner distribution. Here, we show that the special relativity laws and the maximum entropy principle suggest a relativistic generalization also of the two-particle correlation function and then of the entropy. The so obtained, fully relativistic Boltzmann equation, obeys the H-theorem and predicts a stationary stable distribution, presenting power law tails in the high-energy region. The ensued relativistic kinetic theory preserves the main features of the classical kinetics, which recovers in the c \( \rightarrow\) ∞ limit.     

Single- and multi-peak solitons in two-component models of metamaterials and photonic crystals

We report results of the study of solitons in a system of two nonlinear-Schrödinger (NLS) equations coupled by the XPM interaction, which models the co-propagation of two waves in metamaterials (MMs). The same model applies to photonic crystals (PCs), as well as to ordinary optical fibers, close to the zero-dispersion point. A peculiarity of the system is a small positive or negative value of the relative group-velocity dispersion (GVD) coefficient in one equation, assuming that the dispersion is anomalous in the other. In contrast to earlier studied systems of nonlinearly coupled NLS equations with equal GVD coefficients, which generate only simple single-peak solitons, the present model gives rise to families of solitons with complex shapes, which feature extended oscillatory tails and/or a double-peak structure at the center. Regions of existence are identified for single- and double-peak bimodal solitons, demonstrating a broad bistability in the system. Behind the existence border, they degenerate into single-component solutions. Direct simulations demonstrate stability of the solitons in the entire existence regions. Effects of the group-velocity mismatch (GVM) and optical loss are considered too. It is demonstrated that the solitons can be stabilized against the GVM by means of the respective “management” scheme. Under the action of the loss, complex shapes of the solitons degenerate into simple ones, but periodic compensation of the loss supports the complexity.     

FLAKE STRUCTURE IN THE SPECKLE FIELD PRODUCED BY A FEW SCATTERERS

This paper reports a new phenomenon, namely, flake structure in the speckle field produced by a few scatterers. This structure appears in the off-axis region and its size is much larger than that of the normal speckles. The one-dimensional simulations show that as the roughness of the random surface sample increases or its lateral correlation length decreases, the flakes go farther away from the axis, their relative intensities increase, their sizes become bigger and the fluctuations in them decrease. A sub-scatterer model that we call isoclinic element is proposed to explain the formation and properties of flakes. Experimental evidence shows the existence of the flake structure.