Instabilities of waves in nonlinear disordered media

We develop a self-consistent theory of temporal fluctuations of a speckle pattern resulting from the multiple scattering of a coherent wave in a weakly nonlinear disordered medium. The speckle pattern is shown to become unstable if the nonlinearity exceeds a threshold value. The instability is due to a feedback provided by the multiple scattering and manifests itself in spontaneous fluctuations of the scattered intensity. The development of instability is independent of the sign of nonlinearity.     

Atherosclerotic plaque characterization by spatial and temporal speckle pattern analysis

Improved methods are needed to identify the vulnerable coronary plaques responsible for acute myocardial infraction or sudden cardiac death. We describe a method for characterizing the structure and biomechanical properties of atherosclerotic plaques based on speckle pattern fluctuations. Near-field speckle images were acquired from five human aortic specimens ex vivo. The speckle decorrelation time constant varied significantly for vulnerable aortic plaques (tau=40 ms) versus stable plaques (tau=400 ms) and normal aorta (tau=500 ms) . These initial results indicate that different atherosclerotic plaque types may be distinguished by analysis of temporal and spatial speckle pattern fluctuations.     

Experimental observation of speckle instability in Kerr random media

In a disordered nonlinear medium the transmitted speckle pattern was predicted to become unstable as a result of the positive feedback between intensity fluctuations and local variations of the refractive index. We show experimental evidence of speckle instability for light transversally scattered in a liquid crystal cell, where a two-dimensional controlled disorder is imprinted by suitable illumination of a photoconductive wall and nonlinearity is obtained through optical reorientation of the liquid crystal molecules. The speckle pattern spontaneously oscillates at discrete frequencies above a critical threshold, whose dependence on the scattering mean free path confirms the crucial role of disorder in the feedback process.     

Expansion of a Bose-Einstein condensate in the presence of disorder

Expansion of a Bose-Einstein condensate (BEC) is studied in the presence of a random potential. The expansion is controlled by a single parameter, (microtau(eff)/variant Planck's over 2pi), where micro is the chemical potential, prior to the release of the BEC from the trap, and tau(eff) is a transport relaxation time which characterizes the strength of the disorder. Repulsive interactions (nonlinearity) facilitate transport and can lead to diffusive spreading of the condensate which, in the absence of interactions, would have remained localized in the vicinity of its initial location.     

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.     

Nonlinear diffraction in photonic graphene

The nonlinear (NL) diffraction of wave packets in honeycomb lattices near Dirac points is studied. Strong nonlinearity can significantly deform the diffraction patterns from conical to triangular structure. This is described by a mean field discrete NL Dirac system and in the continuous limit by a higher-order NL Dirac system, which, in turn, is consistent with the trigonal warping of the dispersion relation. The anticontinuous limit is also examined and similar properties are obtained.     

等离子体中散斑光场的传输特性

为了深入了解激光驱动惯性约束核聚变系统中连续位相板所产生的散斑在抑制等离子体非线性效应时起到的作用,采用统计光学理论及矩阵光学方法,分析了散斑在等离子体中的传输特性,并通过数值模拟计算了散斑的自相关函数值.在此基础上,解释了散斑抑制等离子体非线性效应的机制,通过定量计算揭示了散斑光场的自相关长度在传输过程中的变化.结果表明,高密度等离子体中的散斑自相关长度更短,这有助于对等离子体中各类非线性效应的抑制.     

Understanding the exposure-time effect on speckle contrast measurements for laser displays

To evaluate the influence of exposure time on speckle noise for laser displays, speckle contrast measurement method was developed observable at a human eye response time using a high-sensitivity camera which has a signal multiplying function. The nonlinearity of camera light sensitivity was calibrated to measure accurate speckle contrasts, and the measuring lower limit noise of speckle contrast was improved by applying spatial-frequency low pass filter to the captured images. Three commercially available laser displays were measured over a wide range of exposure times from tens of milliseconds to several seconds without adjusting the brightness of laser displays. The speckle contrast of raster-scanned mobile projector without any speckle-reduction device was nearly constant over various exposure times. On the contrary to this, in full-frame projection type laser displays equipped with a temporally-averaging speckle-reduction device, some of their speckle contrasts close to the lower limits noise were slightly increased at the shorter exposure time due to the noise. As a result, the exposure-time effect of speckle contrast could not be observed in our measurements, although it is more reasonable to think that the speckle contrasts of laser displays, which are equipped with the temporally-averaging speckle-reduction device, are dependent on the exposure time. This discrepancy may be attributed to the underestimation of temporal averaging factor. We expected that this method is useful for evaluating various laser displays and clarify the relationship between the speckle noise and the exposure time for a further verification of speckle reduction.     

Dynamic oscillations of coupled domain walls

In domain wall (DW) excitation experiments, nonlinearity (NL) intrinsic to the DW dynamics is often hard to distinguish from perturbation due to the confining potential or DW distortion. Here we numerically investigate the dynamic oscillations of magnetostatically coupled DWs: a system well understood in the quasistatic limit. NL is observed, even for a harmonic potential, due to the intrinsic DW motion. This behavior is principally dependent on terms normally associated with the DW canonical momentum and is in contrast with a NL restoring potential. This NL is not observable in quasistatic measurements, relatively insensitive to the confining potential, and may be tuned by the nanowire parameters. The shown NLs are present in any DW restoring potential and must be accounted for when probing DW potential landscapes.     

Fluctuation theorem in quantum heat conduction

We consider steady-state heat conduction across a quantum harmonic chain connected to reservoirs modeled by infinite collection of oscillators. The heat, Q, flowing across the oscillator in a time interval tau is a stochastic variable and we study the probability distribution function P(Q). We compute the exact generating function of Q at large tau and the large deviation function. The generating function has a symmetry satisfying the steady-state fluctuation theorem without any quantum corrections. The distribution P(Q) is non-Gaussian with clear exponential tails. The effect of finite tau and nonlinearity is considered in the classical limit through Langevin simulations. We also obtain the prediction of quantum heat current fluctuations at low temperatures in clean wires.     

Measurements of femtosecond temporal speckle field of a random medium

The femtosecond temporal speckle field of a random medium is studied theoretically and experimentally. Femtosecond temporal speckle arises from the interference of multiple randomly scattered electric fields. The femtosecond temporal speckle field is measured with a cross-correlation frequency-resolved optical gating method. The spatial average of the speckle field yields a smooth transmitted profile. The speckle field is a circular complex Gaussian variable because the scattered light beams from different trajectories have no correlation with each other. The field and the intensity profiles of individual speckle spots fluctuate randomly in time. The ensemble average of the temporal intensity profiles converges, thereby yielding the photon travel time probability distribution function.     

微型激光光学引擎中光学噪音的抑制

分析了微型激光投影引擎的两种主要光学噪音|干涉网格和激光散斑产生的基理|提出采用振动的随机位相板同时实现干涉网格和激光散斑抑制的方法并进行了理论分析|自行设计了微型激光投影引擎,利用微型电控马达带动随机位相板振动,用CCD相机在不同的F#及曝光时间下对投影图像进行了采集,并对图像的散斑对比度行了测试.结果表明,通过静止的随机位相板可以很好地抑制干涉网格噪音|通过使随机位相板以大于视觉暂留效应形成的融合频率进行振动,可以同时抑制干涉网格和激光散斑,使得散斑对比度小于5%,达到投影观察的要求.     

Green's function estimation in speckle using the decomposition of the time reversal operator: application to aberration correction in medical imaging

The FDORT method (French acronym for decomposition of the time reversal operator using focused beams) is a time reversal based method that can detect point scatterers in a heterogeneous medium and extract their Green's function. It is particularly useful when focusing in a heterogeneous medium. This paper generalizes the theory of the FDORT method to random media (speckle), and shows that it is possible to extract Green's functions from the speckle signal using this method. Therefore it is possible to achieve a good focusing even if no point scatterers are present. Moreover, a link is made between FDORT and the Van Cittert-Zernike theorem. It is deduced from this interpretation that the normalized first eigenvalue of the focused time reversal operator is a well-known focusing criterion. The concept of an equivalent virtual object is introduced that allows the random problem to be replaced by an equivalent deterministic problem and leads to an intuitive understanding of FDORT in speckle. Applications to aberration correction are presented. The reduction of the variance of the Green's function estimate is discussed. Finally, it is shown that the method works well in the presence of strong interfering scatterers.     

Compressed ghost imaging based on differential speckle patterns

We propose a compressed ghost imaging scheme based on differential speckle patterns,named CGI-DSP.In the scheme,a series of bucket detector signals are acquired when a series of random speckle patterns are employed to illuminate an unknown object.Then the differential speckle patterns(differential bucket detector signals) are obtained by taking the difference between present random speckle patterns(present bucket detector signals) and previous random speckle patterns(previous bucket detector signals).Finally,the image of object can be obtained directly by performing the compressed sensing algorithm on the differential speckle patterns and differential bucket detector signals.The experimental and simulated results reveal that CGI-DSP can improve the imaging quality and reduce the number of measurements comparing with the traditional compressed ghost imaging schemes because our scheme can remove the environmental illuminations efficiently.     

串级散斑场动态特性的研究

本文用统计光学方法推导了由两个漫射体形成的串级散斑场的统计性质。得出了漫射体的运动速度v与相关时间ι_c成线性的关系,讨论了经过三次随机调制的串级散斑场的斑纹平均半径较之一次调制斑纹半径为小。理论与实验结果符合得很好。     

Use of dynamic speckle interferometry for contactless diagnostics of fatigue crack initiation and determining its growth rate

Steel 09G2S specimens are subjected to cyclic tests, and real-time monitoring of the initiation of a fatigue crack and its growth kinetics is performed by dynamic speckle interferometry. The time averaging of speckles are used to reveal a relation between the parameters that characterize random and deterministic changes in the relief height and speckle images of the surface near the notch during crack initiation.     

Induced spatiotemporal modulation instability in a noninstantaneous self-defocusing medium

We demonstrate theoretically and experimentally that induced spatiotemporal modulation instability can exist in a self-defocusing medium if the nonlinearity is noninstantaneous. We predict the growth rate as a function of the spatial and temporal frequencies of the modulation and the response time of the nonlinearity and confirm it by our experiments.     

Encryption and decryption using a sandwich phase diffuser made by using two speckle patterns and placed in the Fourier plane: Simulation results

In the present paper, we describe the encryption and decryption of two-dimensional images. The encryption is done by employing a sandwich phase diffuser made by using two elongated speckle patterns, and placed in the Fourier plane of a double random phase encoding system. After encryption, the two constituent phase diffusers of such a sandwich diffuser are separated. During decryption, if the conjugate of either of the two elongated phase speckle patterns is used, the image cannot be retrieved. Correct decryption is also not possible if a sandwich diffuser with any of the phase speckle patterns is shifted in position with respect to the other. For decryption, the encrypted image is Fourier transformed and multiplied by the conjugate of the sandwich diffuser, and then the product is further Fourier transformed. It is possible to generate the image only if both the elongated phase speckle patterns are matched point-to-point and then the proper conjugate is made. The use of elongated speckle patterns in constituting a sandwich phase diffuser makes the system less complicated as compared to the use of a sandwich diffuser made with normal speckle patterns, enabling an easy alignment of the random phase diffuser at the time of rejoining the constituent diffusers for making the right key. The ease of alignment is due to the reduction of the requirement of 360° scanning at the time of rejoining these diffusers with little reduction in the security of the system. Simulation results are presented in support of the proposed idea. For optical implementation, the decrypted image may be obtained by generating a phase conjugate wave by the phase conjugation technique, and passing through the same sandwich phase diffuser. To evaluate the reliability of the technique, mean square error (MSE) between the decrypted and original image has been calculated.     

A stochastic model for metabolizing systems with computer simulation

A stochastic model for a first-order metabolizing system which was studied in the deterministic sense by Branson and others is formulated and a detailed study of the random integral equation arising in the probabilistic model is presented. The equation is used to describe the evolution in time of the amount of metabolite present in the system. Specifically we present a study of the random integral equation of the Volterra type given by $$M\left( {t; \omega } \right) = M\left( {0; \omega } \right)e^{ - et} + \int_0^t {R\left( {\tau ; \omega } \right) e^{ - e\left( {t - \tau } \right)} d\tau , } t \geqslant 0$$ whereM(t; ω) is an unknown random function giving the amount of metabolite in the system at time t ≥ 0. This equation can be expressed in the general form $$x\left( {t; \omega } \right) = h\left( {t; \omega } \right) + \int_0^t {k\left( {t, \tau ; \omega } \right) f\left( {\tau , x\left( {\tau ; \omega } \right)} \right) d\tau } t \geqslant 0$$ which is of a type whose theoretical aspects have recently been studied by the present authors using as a basis the techniques of probabilistic functional analysis. Conditions are derived under which there exists a unique random solution to the above equation. The usefulness of the model is illustrated using computer simulation by considering a one-organ model, an organ-heart model, and a multicompartment model.     

Nonlinear soliton matching between optical fibers

In this Letter, we propose a generic nonlinear coupling coefficient, η(NL)2=η|γ/β?|(fiber2)/|γ/β?|(fiber1), which gives a quantitative measure for the efficiency of nonlinear matching of optical fibers by describing how a fundamental soliton couples from one fiber into another. Specifically, we use η(NL) to demonstrate a significant soliton self-frequency shift of a fundamental soliton, and we show that nonlinear matching can take precedence over linear mode matching. The nonlinear coupling coefficient depends on both the dispersion (β?) and nonlinearity (γ), as well as on the power coupling efficiency η. Being generic, η(NL) enables engineering of general waveguide systems, e.g., for optimized Raman redshift or supercontinuum generation.