Time reversal of speckle noise

Focusing a wave in an unknown inhomogeneous medium is an open problem in wave physics. This work presents an iterative method able to focus in pulse-echo mode in an inhomogeneous medium containing a random distribution of scatterers. By performing a coherent summation of the random echoes backscattered from a set of points surrounding the desired focus, a virtual bright pointlike reflector is generated. A time-reversal method enables an iterative convergence towards the optimal wave field focusing at the location of this virtual scatterer. Thanks to this iterative time-reversal process, it is possible to focus at any arbitrary point in the heterogeneous medium even in the absence of pointlike source. An experimental demonstration is given for the correction of strongly distorted images in the field of medical ultrasound imaging. This concept enables envisioning many other applications in wave physics.     

Radiation properties of a uniaxial chiral quadratic inhomogeneous slab under oblique incidence

In this paper, the focussing of the transmitted electromagnetic field through a quadric inhomogeneous slab of lossless uniaxial chiral medium is derived using transmission coefficient under oblique incidence. The inhomogeneity in the uniaxial chiral slab has been incorporated through permittivity parameter. Asymptotic ray theory provides valid field everywhere except at focal point where it gives infinite value. Singularity of the field at focal point is addressed using Maslov's method. The derived analytical field expressions at caustic or focal point of uniaxial quadratic inhomogeneous slab have been solved numerically using MATHEMATICA. The effects of chirality parameter, axial permittivity, transvers permittivity, angle of incidence on the refracted field are discussed and the effects of Brewster angle on the focussed field are also discussed. The results obtained using Maslov's method are compared with Huygens–Kirchhoff's integral which are in good agreement.     

On the stability of capillary waves on the surface of a space-charged dielectric liquid jet moving in a material medium

We have derived and analyzed the dispersion equation for capillary waves with an arbitrary symmetry (with arbitrary azimuthal numbers) on the surface of a space-charged cylindrical jet of an ideal incompressible dielectric liquid moving relative to an ideal incompressible dielectric medium. It has been proved that the existence of a tangential jump of the velocity field on the jet surface leads to a periodic Kelvin–Helmholtz- type instability at the interface between the media and plays a destabilizing role. The wavenumber ranges of unstable waves and the instability increments depend on the squared velocity of the relative motion and increase with the velocity. With increasing volume charge density, the critical value of the velocity for the emergence of instability decreases. The reduction of the permittivity of the liquid in the jet or an increase in the permittivity of the medium narrows the regions of instability and leads to an increase in the increments. The wavenumber of the most unstable wave increases in accordance with a power law upon an increase in the volume charge density and velocity of the jet. The variations in the permittivities of the jet and the medium produce opposite effects on the wavenumber of the most unstable wave.     

TM模式下二维非磁化等离子体光子晶体的禁带调制特性分析

采用时域有限差分法(FDTD)中的分段线性电流密度卷积(PLCDRC)算法研究了TM波入射时二维非磁化等离子体光子晶体的禁带特性.从频域角度分析得到微分高斯脉冲的透射系数,并讨论该光子晶体的介质圆柱的介电常数、晶格常数、介质圆柱半径,周期常数和等离子体参数对其禁带特性的影响.结果表明,增加周期常数和等离子体碰撞频率不会改变禁带宽度,增加介质圆柱的相对介电常数和等离子体频率可以展宽禁带的宽度. 当填充率一定时,减小介质圆柱的半径和晶格常数可以实现禁带的拓展. 关键词： 等离子体 光子晶体 禁带 PLCDRC算法     

Telecommunication in a disordered environment with iterative time reversal

Abstract

We present a method to transmit digital information through a highly scattering medium in a MIMO-MU (multiple input multiple output multiple users) context. It is based on iterations of a time-reversal process, and permits us to focus short pulses, both spatially and temporally, from a base antenna to different users. This iterative technique is shown to be more efficient (lower inter-symbol interference and lower error rate) than classical time-reversal communication, while being computationally light and stable. Experiments are presented: digital information is conveyed from 15 transmitters to 15 receivers by ultrasonic waves propagating through a highly scattering slab. From a theoretical point of view, the iterative technique achieves the inverse filter of propagation in the subspace of non-null singular values of the time-reversal operator. We also investigate the influence of external additive noise, and show that the number of iterations can be optimized to give the lowest error rate.

(Some figures in this article are in colour only in the electronic version)     

Effective permittivity of periodic composite materials: Numerical modeling by the finite element method

The effective properties of composite materials are closely related to the composition and arrangement of its constituents. Many studies and articles are actively studying the dielectric properties of heterogeneous structures with random and periodic arrangement. In the quasistatic limit, we use the finite element method as a numerical tool to evaluate the effective permittivity of two and three component composites. Two heterostructures are investigated; the first is formed by crossed dielectric cylinders in permanent contact and arranged in three layers. The cylinders are immersed in a dielectric host medium. The second structure is similar to the first except that the tubes are covered by an interphase layer. The numerical tool used to extract the exact value of the effective permittivity takes into account all internal multipolar interactions which contribute to the polarization of the material medium. The impacts of the relative permittivity and volume fraction of cylinders, the thickness of interphase and its dielectric constant are reported. The Maxwell–Garnett theory fails to predict the effective permittivity of the studied structures for high volume fraction and permittivity contrast. To overcome this problem, an amendment was made to the McLachlan equation McQ also termed the Two Exponent Single Percolation Equation TESPE. The first exponent t is held equal to 1 and the other exponent s is depending on the volume fraction. s is calculated so that the whole values of the effective permittivity obtained by the McQ rule are exactly the same values obtained by the simulations. Finally, we obtained a chart and a model to find the values of s, a fast way that is very useful for practitioners and design engineers of composite materials.     

克尔效应对高斯光束聚焦特性的影响

利用菲涅尔—基尔霍夫衍射积分公式，研究薄片近似情况下的Kerr效应带来的波前畸变对高斯光束聚焦特性的影响.在相位延迟为－2~2 rad的范围内进行的模拟计算表明：正Kerr效应能提高高斯光束的聚焦强度、增大相对焦移量、提高聚焦光束的焦平面桶中功率和降低几何焦平面的峰值光强；而负Kerr效应，则会降低聚焦强度、增大相对焦移量、降低聚焦光束的焦平面桶中功率和几何焦平面的峰值光强.可以通过增大光束菲涅尔数来抑制Kerr效应对聚焦特性的影响.     

经颅超声聚焦方法和声场特性研究

基于高分辨的CT数据建立了非均匀颅骨仿真模型,该模型引入了颅骨的声衰减系数,深入研究和分析了声波时间反转法和超声相控阵法在颅脑中的聚焦方法及效果。颅骨具有较强的声波衰减特性,使用时间反转聚焦时需要进行幅度补偿,对于0.7MHz的频率信号,幅度补偿后的时间反转聚焦声场主瓣宽度窄、旁瓣低,焦点处声场比无幅度补偿的时间反转法提高8.86dB,比超声相控阵聚焦法提高7.89dB,具有很好的空间聚焦精度和聚焦效率。研究了颅骨衰减系数、声场焦点位置、声波频率、换能器阵列位置和方位等参数对聚焦声场的影响,结果表明,幅度补偿时间反转法比相控阵法具有更低的旁瓣,且高频时的聚焦效果比相控阵好,相控阵聚焦对换能器阵列的位置和方位比较敏感,而时间反转经颅超声聚焦对声传播路径和入射角具有更高的鲁棒性。      

Transmission mode time-reversal super-resolution imaging

The theory of time-reversal super-resolution imaging of point targets embedded in a reciprocal background medium [A. J. Devaney, "Super-resolution imaging using time-reversal and MUSIC," J. Acoust. Soc. Am. (to be published)] is generalized to the case where the transmitter and receiver sensor arrays need not be coincident and for cases where the background medium can be nonreciprocal. The new theory developed herein is based on the singular value decomposition of the generalized multistatic data matrix of the sensor system rather than the standard eigenvector/eigenvalue decomposition of the time-reversal matrix as was employed in the above-mentioned work and other treatments of time-reversal imaging [Prada, Thomas, and Fink, "The iterative time reversal process: Analysis of the convergence," J. Acoust. Soc. Am. 97, 62 (1995); Prada et al., "Decomposition of the time reversal operator: Detection and selective focusing on two scatterers," J. Acoust. Soc. Am. 99, 2067 (1996)]. A generalized multiple signal classification (MUSIC) algorithm is derived that allows super-resolution imaging of both well-resolved and non-well-resolved point targets from arbitrary sensor array geometries. MUSIC exploits the orthogonal nature of the scatterer and noise subspaces defined by the singular vectors of the multistatic data matrix to form scatterer images. The time-reversal/MUSIC algorithm is tested and validated in two computer simulations of offset vertical seismic profiling where the sensor sources are aligned along the earth's surface and the receiver array is aligned along a subsurface borehole. All results demonstrate the high contrast, high resolution imaging capabilities of this new algorithm combination when compared with "classical" backpropagation or field focusing. Above and beyond the application of seismo-acoustic imaging, the time-reversal super-resolution theory has applications in ocean acoustics for target location, and ultrasonic nondestructive evaluation of parts.     

Sound focusing in rooms: the time-reversal approach

New perspectives in audible range acoustics, such as virtual sound space creation and active noise control, rely on the ability of the rendering system to recreate precisely a desired sound field. This ability to control sound in a given volume of a room is directly linked to the capacity to focus acoustical energy both in space and time. However, sound focusing in rooms remains a complicated problem, essentially because of the multiple reflections on obstacles and walls occurring during propagation. In this paper, the technique of time-reversal focusing, well known in ultrasound, is experimentally applied to audible range acoustics. Compared to classical focusing techniques such as delay law focusing, time reversal appears to considerably improve quality of both temporal and spatial focusing. This so-called super-resolution phenomenon is due to the ability of time reversal to take into account all of the different sound paths between the emitting antenna and the focal point, thus creating an adaptive spatial and temporal matched filter for the considered propagation medium. Experiments emphasize the strong robustness of time-reversal focusing towards small modifications in the medium, such as people in motion or temperature variations. Sound focusing through walls using the time-reversal approach is also experimentally demonstrated.     

Time reversal and the inverse filter

To focus ultrasonic waves in an unknown inhomogeneous medium using a phased array, one has to calculate the optimal set of signals to be applied on the transducers of the array. In the case of time-reversal mirrors, one assumes that a source is available at the focus, providing the Green's function of this point. In this paper, the robustness of this time-reversal method is investigated when loss of information breaks the time-reversal invariance. It arises in dissipative media or when the field radiated by the source is not entirely measured by the limited aperture of a time-reversal mirror. However, in both cases, linearity and reciprocity relations ensure time reversal to achieve a spatiotemporal matched filtering. Nevertheless, though it provides robustness to this method, no constraints are imposed on the field out of the focus and sidelobes may appear. Another approach consists of measuring the Green's functions associated to the focus but also to neighboring points. Thus, the whole information characterizing the medium is known and the inverse source problem can be solved. A matrix formalism of the propagation operator is introduced to compare the time-reversal and inverse filter techniques. Moreover, experiments investigated in various media are presented to illustrate this comparison.     

声学脉冲序列及全透声机理研究

本文研究一维周期性层状结构中材料弹性模量时变因素作用下的声透射临界现象, 探究了这种声学脉冲序列及全透声现象的内在机理. 考虑弹性模量时变因素的影响, 通过求解波动方程, 运用分离变量法解得特征指数, 进而得到临界现象. 当调制幅值低于或等于临界值时, 周期性结构能够将入射波转化为一系列周期的毫秒级的反射脉冲序列; 尤其在调制幅值等于临界值时, 当周期性结构的层数达到16层时, 反射脉冲序列有完整的0和1 的波形; 当大于临界值时, 反射系数在50 ms内迅速衰减至0, 此时的结构相当于完全透声, 入射波可以无损地完全透过, 产生调制透声现象. 这些特殊的现象可为声波的动态控制、声脉冲序列的产生和声波的定向传播提供重要的理论依据, 在超声换能器及调制透声方面具有实际的工程应用前景.     

Robust time reversal focusing in the ocean

Recent time-reversal experiments with high-frequency transmissions (3.5 kHz) show that stable focusing is severely limited by the time-dependent ocean environments. The vertical focal structure displays dynamic variations associated with focal splitting and remerging resulting in large changes in focal intensity. Numerical simulations verify that the intensity variation is linked to the focal shift induced by phase changes in acoustic waves resulting from sound speed fluctuations due to internal waves. A relationship between focal range shift, frequency shift, or channel depth changes is illustrated using waveguide-invariant theory. Based on the analysis of experimental data and numerical simulations, methods for robust time-reversal focusing are developed to extend the period of stable focusing.     

Determination of the relative permittivity of the AlGaN barrier layer in strained AlGaN/GaN heterostructures

Using the measured capacitance--voltage curves and the photocurrent spectrum obtained from the Ni Schottky contact on a strained Al_0.3Ga_0.7N/GaN heterostructure, the value of the relative permittivity of the AlGaN barrier layer was analysed and calculated by self-consistently solving Schr?dinger's and Poisson's equations. It is shown that the calculated values of the relative permittivity are different from those formerly reported, and reverse biasing the Ni Schottky contact has an influence on the value of the relative permittivity. As the reverse bias increases from 0 V to --3~V, the value of the relative permittivity decreases from 7.184 to 7.093.     

Reconstruction of the spectrum of the relative permittivity of the plane-parallel plate from the angular dependences of its transmission coefficients

A method for unambiguously determining the frequency dependence of the relative permittivity of a homogeneous medium has been proposed and implemented from the measured angular dependences of the complex transmission spectra of pulsed terahertz radiation through a plane-parallel plate. It has been shown experimentally that the proposed method makes it possible to reconstruct the dielectric parameters of the plane under investigation, even in the presence of time overlapping of waves rereflected from the medium boundaries.     

Experimental study of composite medium with simultaneously negative permeability and permittivity

Inclassicalelectrodynamics,theresponse(typicallyfrequencydependent)ofamaterialtoelectricandmagneticfieldsischaracterizedbytwofundamentalquantities,thepermittivityeandthepermeabilitym.Bothmandearepositiveinmostmaterials.In1968,Veselago[1]predictedthattheelectromagneticwavepropagationinamediumhavingsimultaneouslynegativepermittivityandpermeabilityshouldgiverisetoseveralpeculiarcharacteristics.Butnoneofhispredictionsweretestedduringthelastcentury,becausenonaturalmaterialswithsimultaneouslynegativ…     

Formation of a reflected wave under propagation of a pulse with high peak intensity through a Kerr medium

Propagation through a Kerr medium of short pulses depending only on the longitudinal coordinate is investigated. High values of the peak intensity are considered for which the nonlinear part of the relative permittivity is on the order of unity. When a short pulse propagates through such a medium, the leading edge of the pulse is extended, while the trailing edge runs into the slowly propagating central part of the pulse; shock waves are generated at the trailing edge, giving rise to high spatial frequencies and backward reflected radiation. The duration of the pulse increases due to the high-frequency jet that forms at the trailing edge, and the peak intensity decreases. The spectrum of the backward reflected radiation is investigated as a function of the peak intensity of the pulse and the characteristics of the time dispersion of the medium.     

A finite element scheme to study the nonlinear optical response of a finite grating without and with defect

We present a simple numerical scheme based on the finite element method (FEM) using transparent-influx boundary conditions to study the nonlinear optical response of a finite one-dimensional grating with Kerr medium. Restricting first to the linear case, we improve the standard FEM to get a fourth order accurate scheme maintaining a symmetric-tridiagonal structure of the finite element matrix. For the full nonlinear equation, we implement the improved FEM for the linear part and a standard FEM for the nonlinear part. The resulting nonlinear system of equations is solved using a weighted-averaged fixed-point iterative method combined with a continuation method. To illustrate the method, we study a periodic structure without and with defect and show that the method has no problem with large nonlinear effect. The method is also found to be able to show the optical bistability behavior of the ideal and the defect structure as a function of either the frequency or the intensity of the input light. The bistability of the ideal periodic structure can be obtained by tuning the frequency to a value close to the bottom or top linear band-edge while that of the defect structure can be produced using a frequency near the defect mode or near the bottom of the linear band-edge. The threshold value can be reduced by increasing the number of layer periods. We found that the threshold needed for the defect structure is much lower then that for a strictly periodic structure of the same length.     

The accuracy evaluation method of baseline estimation algorithms in energy dispersive X-ray fluorescence spectrum analysis

In energy dispersive X-ray fluorescence analysis (EDXRF), many baseline estimation algorithms have been proposed for the accurate characteristic peak area. However, the true value of the characteristic peak area of measured spectrum is unknown and cannot be used to evaluate the accuracy of the baseline estimation algorithms. In this article, an assessment method was proposed based on Monte Carlo simulation, which can obtain the characteristic peak area, and evaluate the accuracy of the baseline estimation algorithms directly. Meanwhile, the accuracy and practicality of four baseline estimation algorithms were evaluated by the assessment method, which include statistics-sensitive nonlinear iterative peak-clipping (SINP), fast Fourier transform (FFT), adaptive iteratively reweighted penalized least squares (AirPLS), and automated iterative moving averaging (AIMA). Comparing the relative error of the characteristic peak area, AirPLS gave the best performance for baseline estimation in EDXRF.     

Time-reversal simulations for detection in randomly layered media

A time-reversal mirror is, roughly speaking, a device which is capable of receiving an acoustic signal in time, keeping it in memory and sending it back into the medium in the reversed direction of time. In this paper, we employ an accurate numerical method for simulating waves propagating in complex one-dimensional media. We use numerical simulations to reproduce the time-reversal self-averaging effect which takes place in randomly layered media. This is done in the regime where the inhomogeneities are smaller than the pulse, which propagates over long distances compared to its width. We show numerical evidence for possible use of an expanding window time-reversal technique for detecting anomalies buried in the medium.