Numerical, analytical, and experimental studies of scattering from very rough surfaces and backscattering enhancement

This paper Presents numerical simulations, theoretical analysis, and millimeter wave experiments for scattering from one-dimensional very rough surfaces. First, numerical simulations are used to investigate the effects of roughness spectrum, height variation, interface medium, polarization, and incident angle on the backscattering enhancement. The enhanced backscattering due to rough surface scattering is divided into two cases; the RMS height close to a wavelength and RMS slope close to unity, and RMS height much smaller than a wavelength with surface wave contributions. Results also show that the enhancement is sensitive to the roughness spectrum. Next, a theory based on the first- and second-order Kirchhoff approximation modified with angular and propagation shadowing is developed. The theoretical solutions provide a physical explanation of backscattering enhancement and agree well with the numerical results. In addition to the scattering of a monochromatic wave, the analytical results of the broadening and lateral spreading of a pulsed beam wave scattering from rough surfaces are also discussed. Finally, the existence of backscattering enhancement from one-dimensional very rough conducting surfaces with exact Gaussian statistics and Gaussian roughness spectrum is verified by a millimeter-wave experiment. Experimental results which show enhanced backscattering for both TE and TM polarizations for different angles of incidence are presented.     

Simplification of an analytical solution of the fourth-moment equation

The equation for the fourth moment of a wave propagating in a multiply scattering random medium has been solved by various methods. When the analytical solutions are compared with numerical solutions of the equation it is found that the fundamental solution together with a first-order correction term agree very closely with the numerical results over a wide range of distances and scattering strengths. Unfortunately, the correction term involves multiple integrals and so is difficult to evaluate. This paper shows how some of these integrations can be carried out and the results combined in such a way that an analytical form similar to the fundamental solution is obtained involving only a single integral. This simplified combined solution also agrees very closely with the numerical results.     

Numerical,analytical, and experimental studies of scattering from very rough surfaces and backscattering enhancement

Abstract

This paper Presents numerical simulations, theoretical analysis, and millimeter wave experiments for scattering from one-dimensional very rough surfaces. First, numerical simulations are used to investigate the effects of roughness spectrum, height variation, interface medium, polarization, and incident angle on the backscattering enhancement. The enhanced backscattering due to rough surface scattering is divided into two cases; the RMS height close to a wavelength and RMS slope close to unity, and RMS height much smaller than a wavelength with surface wave contributions. Results also show that the enhancement is sensitive to the roughness spectrum. Next, a theory based on the first- and second-order Kirchhoff approximation modified with angular and propagation shadowing is developed. The theoretical solutions provide a physical explanation of backscattering enhancement and agree well with the numerical results. In addition to the scattering of a monochromatic wave, the analytical results of the broadening and lateral spreading of a pulsed beam wave scattering from rough surfaces are also discussed. Finally, the existence of backscattering enhancement from one-dimensional very rough conducting surfaces with exact Gaussian statistics and Gaussian roughness spectrum is verified by a millimeter-wave experiment. Experimental results which show enhanced backscattering for both TE and TM polarizations for different angles of incidence are presented.     

Transmission scatter cross sections across two-dimensional random rough surfaces – full wave solutions and comparison with numerical results

Abstract

In this paper, the full wave expressions for the bistatic transmission scattering cross sections across two-dimensional random rough surfaces are obtained. The full wave analysis accounts for the surface height/slope correlations. Analytical and numerical comparisons of the full wave solutions with the small perturbation and physical optics solutions are made for isotropic random rough surfaces. The full wave results are also compared with the numerical results based on Monte Carlo simulations of one-dimensional random rough surfaces. Detailed consideration is given to illustrating the relationship between these full wave solutions and the original full wave solutions including the impact of accounting for the height/slope correlations in this analysis.     

Multiple scattering effects on the radar cross section (RCS) of objects in a random medium including backscattering enhancement and shower curtain effects

This paper presents a theory of the radar cross section (RCS) of objects in multiple scattering random media. The general formulation includes the fourthorder moments including the correlation between the forward and the backward waves. The fourth moments are reduced to the second-order moments by using the circular complex Gaussian assumption. The stochastic Green's functions are expressed in parabolic approximation, and the objects are assumed to be large in terms of wavelength; therefore, Kirchhoff approximations are applicable. This theory includes the backscattering enhancement and the shower curtain effects, which are not normally considered in conventional theory. Numerical examples of a conducting object in a random medium characterized by the Gaussian and Henyey-Greenstein phase functions are shown to highlight the difference between the multiple scattering RCS and the conventional RCS in terms of optical depth, medium location and angular dependence. It shows the enhanced backscattering due to multiple scattering and the increased RCS if a random medium is closer to the transmitter.     

Multiple scattering effects on the radar cross section (RCS) of objects in a random medium including backscattering enhancement and shower curtain effects

Abstract

This paper presents a theory of the radar cross section (RCS) of objects in multiple scattering random media. The general formulation includes the fourthorder moments including the correlation between the forward and the backward waves. The fourth moments are reduced to the second–order moments by using the circular complex Gaussian assumption. The stochastic Green's functions are expressed in parabolic approximation, and the objects are assumed to be large in terms of wavelength; therefore, Kirchhoff approximations are applicable. This theory includes the backscattering enhancement and the shower curtain effects, which are not normally considered in conventional theory. Numerical examples of a conducting object in a random medium characterized by the Gaussian and Henyey–Greenstein phase functions are shown to highlight the difference between the multiple scattering RCS and the conventional RCS in terms of optical depth, medium location and angular dependence. It shows the enhanced backscattering due to multiple scattering and the increased RCS if a random medium is closer to the transmitter.     

Influence of the Parameters of a Random Medium on the Characteristics of Transient Reflections

Based on the invariant imbedding method, we study numerically the statistical characteristics of the kernel of the backscattering operator in the case of normal incidence of a plane wave on a one-dimensional random medium with strong fluctuation intensities and various correlation radii of the irregularities. The local reflection coefficient of the medium is modelled by a centered Gaussian process with an exponential correlation function. The first eight one-point cumulants and the correlation functions of delta-pulse reflection are considered and the fluctuation phenomena are analyzed. The transition to the diffusion scattering regime is studded, and the numerical results are compared with the known analytical solutions.     

斜入射分层线性各向异性等离子体电磁散射时域有限差分方法分析

提出了斜入射分层线性各向异性等离子体电磁散射的时域有限差分(FDTD)方法,通过将二维麦克斯韦方程等价地转换为一维麦克斯韦方程,避免了用二维时域有限差分方法分析该散射问题,极大地提高了计算效率.分析推导了TEz和TMz波斜入射线性分层各向异性等离子体电磁散射的FDTD方法,然后通过该方法计算不同入射角的各向异性等离子板的电磁波反射系数,并与其解析解进行比较,结果表明该方法的准确性和有效性.最后,将该算法应用于计算涂覆分层各向异性等离子体金属板在不同入射角下的反射系数,分析了不同入射角对反射系数的影响.     

An approximate analytic solution of the steady state Brillouin scattering in single mode optical fiber without neglecting the attenuation coefficient

The analysis of steady state Brillouin scattering in a long single mode optical fiber is presented. Meanwhile, an approximate analytical functions of distributed Brillouin scattering and pump wave along the fiber with the fiber attenuation coefficient are obtained for the first time. A comparison is made among the analytical solutions with the attenuation coefficient, the analytical solutions without the attenuation coefficient and the exact numerical solutions. The results show that the analytical solutions with fiber attenuation coefficient are more close to the numerical solutions, which can be used to describe the power distribution of the pump wave and the Stokes wave along the long distance single mode optical fiber accurately.     

One-dimensional numerical simulations of random sound impulses

Abstract

We perform one-dimensional numerical simulations of small-amplitude acoustic pulses in space- and time-dependent random mass density and time-dependent velocity fields. Numerical results reveal that: (a) random fields affect the speeds, amplitudes and, consequently, shapes of sound pulses; (b) for weak random fields and short propagation times the numerical data converge with the analytical results of the mean field theory which says that a space-dependent (time-dependent) random field leads to wave attenuation (amplification) and all random fields speed up sound pulses; (c) for sufficiently strong random fields and long propagation times numerical simulations reveal pulse splitting into smaller components, parts of which propagate much slower than a wave pulse in a non-random medium. These slow waves build an initial stage of a wave localization phenomenon. However, this effect can be very weak in a real three-dimensional medium.     

平面光波导结构的FDTD分析

将各向异性理想匹配层(APML)吸收边界条件用于平面光波导结构的时域有限差分法(FDTD)分析中,导出了APML媒质中适用于角域和边缘的通用差分方程,并对平行介质带定向耦合器进行了数值模拟和验证,所得数值解与解析解非常一致.该方法可用于任意复杂结构的平面光波导的计算机辅助设计与分析.     

Semiclassical scattering on conical intersections

We apply a semiclassical approach to the scattering problem of a vibrational wave packet in the vicinity of a conical intersection of electronic energy surfaces and derive analytical expressions for the scattering matrix. The latter are valid when the scattering length that scales as square root(h) is small and a wave packet passes through the scattering region with a constant velocity. The analytical results are in excellent agreement with numerical simulations for a realistic set of parameters.     

Multiple Scattering Solution of Millimeter Wave Propagation in Strong Sandstorm

As the operating frequencies of communication systems more higher into the millimeter wave range, and the density of particles in medium is more denser, the effects of multiple scattering in sandstorm become more significant. This paper treats the problems of electromagnetic multiple scattering in strong sandstorm by the Monte Carlo method. Based on the analytical theory of multiple scattering, the millimeter wave propagation and scattering in discrete random media are investigated by means of the particle-tracking technique. The millimeter wave is regarded as a Markov chain of wave particle collisions in a medium in which it is scattered and absorbed. Considering the effect of multiple scattering, millimeter wave attenuation induced by strong sandstorm is simulated numerically. The values of theoretical calculation are in good agreement with the measured results of simulated experiment at 34 and 93 GHz.     

Scattering of electromagnetic wave from perfect electromagnetic conductor cylinders placed in un-magnetized isotropic plasma medium

The two dimensional analytical formulation of scattering of electromagnetic wave from a perfect electromagnetic conductor (PEMC) cylinder placed in un-magnetized isotropic plasma medium is presented. The extended classical scattering theory is used. The incident wave is taken as linearly polarized wave. The analytical theory is formulated for parallel polarization (TM) and also for perpendicular polarization (TE). The numerical computation results show that backscattering and forward scattering are sensitive to electron density and effective collision frequency of plasma medium. We placed different types of cylinders (PEC, PMC and PEMC) in un-magnetized plasma medium and concluded that stealth capability of plasma increases with the placement of PEMC cylinder in plasma medium.     

Dynamically compressed bright and dark solitons in highly anisotropic Bose-Einstein condensates

Bright and dark matter wave solitons are constructed analytically in a three-dimensional (3D) highly anisotropic Bose-Einstein condensate (BEC) with a time-dependent parabolic potential, and numerical simulations are performed to confirm the existence and dynamics of such analytical solutions. Different classes of bright and dark solitons are discovered among the solutions of the generalized anisotropic (3+1)D Gross-Pitaevskii equation. Our results demonstrate that the bright and dark solitary waves can be manipulated and controlled by changing the scattering length, which can be used to compress the second-order bright and dark solitons of BECs into desired peak density.     

Short pulse detection and imaging of objects behind obscuring random layers

This paper presents a theory of imaging objects behind layers of scattering media. The transmitter is a focused array or an aperture emitting a short pulse. The scattered pulse is received by a focused array or aperture. The received signal consists of two components: the pulse scattered from a random medium and from the target, and these two components can be distinguished by the use of ultra wide band (UWB) pulse. The second moment of the received signal includes the fourth-order moments of stochastic Green's functions, which are reduced to the second moments by the use of the circular complex Gaussian assumption, and of the generalized two-frequency mutual coherence function. This imaging theory is a generalization of optical coherence tomography (OCT), SAR and confocal imaging. It clarifies the relationships among resolution, coherence length, shower curtain effects and backscattering enhancement.     

Short pulse detection and imaging of objects behind obscuring random layers

This paper presents a theory of imaging objects behind layers of scattering media. The transmitter is a focused array or an aperture emitting a short pulse. The scattered pulse is received by a focused array or aperture. The received signal consists of two components: the pulse scattered from a random medium and from the target, and these two components can be distinguished by the use of ultra wide band (UWB) pulse. The second moment of the received signal includes the fourth-order moments of stochastic Green's functions, which are reduced to the second moments by the use of the circular complex Gaussian assumption, and of the generalized two-frequency mutual coherence function. This imaging theory is a generalization of optical coherence tomography (OCT), SAR and confocal imaging. It clarifies the relationships among resolution, coherence length, shower curtain effects and backscattering enhancement.     

随机介质中电磁波空间分布特性研究

采用随机介质统计模型和FDTD方法模拟了随机介质电场空间分布根据光子局域化理论,讨论了电场的空间分布和介电常数涨落的关系,结果表明,在一定的介质密度下,电磁场是局域化的,其空间分布和介质介电常数的涨落密切相关.     

Finite difference computation of head-related transfer function for human hearing

Modeling the head-related transfer function (HRTF) is a key to many applications in spatial audio. To understand and predict the effects of head geometry and the surrounding environment on the HRTF, a three-dimensional finite-difference time domain model (3D FDTD) has been developed to simulate acoustic wave interaction with a human head. A perfectly matched layer (PML) is used to absorb outgoing waves at the truncated boundary of an unbounded medium. An external source is utilized to reduce the computational domain size through the scattered-field/total-field formulation. This numerical model has been validated by analytical solutions for a spherical head model. The 3D FDTD code is then used as a computational tool to predict the HRTF for various scenarios. In particular, a simplified spherical head model is compared to a realistic head model up to about 7 kHz. The HRTF is also computed for a realistic head model in the presence of a wall. It is demonstrated that this 3D FDTD model can be a useful tool for spatial audio applications.     

Explanation of dijet asymmetry in Pb-Pb collisions at the Large Hadron Collider

We investigate the medium modification of a partonic jet shower traversing in a hot quark-gluon plasma. We derive and solve a differential equation that governs the evolution of the radiated gluon distribution as the jet propagates through the medium. Energy contained inside the jet cone is lost by dissipation through elastic collisions with the medium and by scattering of shower partons to larger angles. We find that the jet energy loss at early times is dominated by medium effects on the vacuum radiation, and by medium-induced radiation effects at late times. We compare our numerical results for the nuclear modification of the dijet asymmetry with that recently reported by the ATLAS Collaboration.