Layer Of Random Medium Research Articles

An Effective Fractional Paraxial Wave Equation for Wave-Fronts in Randomly Layered Media with Long-Range Correlations

An Effective Fractional Paraxial Wave Equation for Wave-Fronts in Randomly Layered Media with Long-Range Correlations

Scattering and Emission of Electromagnetic Waves From Random Layered Media With Random Rough Interfaces: A Partially Coherent Cascading Approach

A partially coherent approach for computing the electromagnetic response of a layered medium having random rough interfaces and a random dielectric profile is presented as an alternative to the full-wave solution of the problem. The statistical nature of this problem, in particular, the random dielectric profile, introduces randomness in the phase of the electromagnetic field such that the field loses its phase coherency after traveling in the layered medium for a few correlation lengths of the permittivity. In this situation, there is a coherency length within which a coherent solution of Maxwell’s equation is required. For the distances beyond this coherency length, a combined coherent–incoherent cascading approach can be applied to reduce the computational complexity of the problem. The coherent response of each “block” within the medium (with a length approximately the coherency length) can be cascaded incoherently ignoring the phase response without losing accuracy. Cascading equations for block bistatic scattering are applied, and solutions of the equivalent block parameters are obtained by iteration up to the second order of multiple scattering. The proposed method is described in this article, and the numerical results are shown to compare the proposed cascading approach with the results obtained from the fully coherent solution.

Reflection statistics of weakly disordered optical medium when its mean refractive index is different from an outside medium

Statistical properties of light waves reflected from a one-dimensional (1D) disordered optical medium [n(x) = n0+ dn(x), <dn(x)>=0] have been well studied, however, most of the studies have focused on the situation when the mean refractive index of the optical medium matched with the outside medium, i.e., n0= nout=1. Further, considering dn(x) as a Gaussian color noise refractive index medium with exponential spatial correlation decay length lc and k as the incident wave vector, it has been shown that for smaller correlation length limit, i.e., klc <<1, both the mean reflection coefficient <r> and std of r, σ(r), have same value, and they follow the relation <r>= σ(r) ∝ <dn2> lc. However, when the refractive index of the sample medium is different from the outside medium, the reflection statistics may have interesting features, which has not been well studied or understood. We studied the reflection statistics of a 1D weakly disordered optical medium with the mean background refractive index n0 being different from the outside medium nout (≠n0), to see the effect of mismatching (i.e., value of n0- nout) on the reflection statistics. In the mismatched case, the results show that the mean reflection coefficient <r> follows a form similar to that of the matched refractive-index case, i.e., <r(dn, lc)>∝ <dn2> lc, with a linear increased shift, which is due to 1D uniform background reflection from a slab. However, σ(r) is shown to be σ(r) ∝ (<dn2>lc)1/2, which is different from the matched case. This change in std of r is attributed to the interference between the mismatched-crerated edge mediated multiple scattering that are coupled with the random scattering. Applications to light scattering from random layered media and biological cells are discussed.

Localization length fluctuation in randomly layered media

Localization properties of the two-component randomly layered media (RLM) are studied in detail both analytically and numerically. The localization length is found fluctuating around the analytical result obtained under the high-frequency limit. The fluctuation amplitude approaches zero with the increasing of disorder, which is characterized by the distribution width of random thickness. It is also found that the localization length over the mean thickness periodically varies with the distribution center of random thickness. For the multi-component RLM structure, the arrangement of material must be considered.

Nonlinear spatial focusing in random layered media by spectral pulse shaping

We demonstrate numerically a method of focusing two-photon fields inside one-dimensional random media. The approach is based on coherent control of backscattering achieved by adaptive spectral pulse shaping. The spectral phases of a femtosecond laser pulse are adjusted for the constructive interference of its backward-traveling components, resulting in an enhanced reflection from within the random system. A delayed forward-propagating second pulse overlaps with the controlled reflection, increasing the interpulse multiphoton field at a location determined by the delay between the two pulses. The technique is shown to be robust against the variations of the disorder and to work with realistic pulse-shaping parameters, hence enabling applications in controlling random lasing and multiphoton imaging in scattering materials.

Multi-level Monte Carlo finite volume methods for uncertainty quantification of acoustic wave propagation in random heterogeneous layered medium

We consider the very challenging problem of efficient uncertainty quantification for acoustic wave propagation in a highly heterogeneous, possibly layered, random medium, characterized by possibly anisotropic, piecewise log-exponentially distributed Gaussian random fields. A multi-level Monte Carlo finite volume method is proposed, along with a novel, bias-free upscaling technique that allows to represent the input random fields, generated using spectral FFT methods, efficiently. Combined together with a recently developed dynamic load balancing algorithm that scales to massively parallel computing architectures, the proposed method is able to robustly compute uncertainty for highly realistic random subsurface formations that can contain a very high number (millions) of sources of uncertainty. Numerical experiments, in both two and three space dimensions, illustrating the efficiency of the method are presented.

Multi-Level Monte Carlo Finite Volume methods for uncertainty quantification of acoustic wave propagation in random heterogeneous layered medium

We consider the very challenging problem of efficient uncertainty quantification for acoustic wave propagation in a highly heterogeneous, possibly layered, random medium, characterized by possibly anisotropic, piecewise log-exponentially distributed Gaussian random fields. A multi-level Monte Carlo finite volume method is proposed, along with a novel, bias-free upscaling technique that allows to represent the input random fields, generated using spectral FFT methods, efficiently. Combined together with a recently developed dynamic load balancing algorithm that scales to massively parallel computing architectures, the proposed method is able to robustly compute uncertainty for highly realistic random subsurface formations that can contain a very high number (millions) of sources of uncertainty. Numerical experiments, in both two and three space dimensions, illustrating the efficiency of the method are presented.

Lasing characteristics of random cylindrical microcavity lasers

Room-temperature lasing characteristics of random cylindrical microcavity lasers, which can be realized by coating a layer of random gain medium onto the surface of an optical fiber with various diameters, was studied experimentally. It is shown that closed-loop random modes excited inside the random gain medium are strongly confined along the radial direction so that the spacing of lasing modes is controlled by the diameter of cylindrical microcavity. In addition, lasing threshold of the random gain medium can be reduced by an order of magnitude under the influence of radial optical confinement.

Coherent Raman spectroscopy through one-dimensional random scattering medium

We investigate the possibility of implementing coherent anti-Stokes Raman spectroscopy (CARS) with a single laser beam passed through a one-dimensional scattering object. The effect of the random scattering is emulated by shaping the laser pulses with a spectral mask corresponding to the transmission spectrum of a random layered medium. Raman resonances are retrieved through correlation analysis of the CARS spectrum. We study the effect of the scattering parameters on the resolution of the method, and show that improvement of the spectroscopic sensitivity can be achieved by compensating the phase distortions introduced by the scatterer.

Random Walk Approach for Wave Propagation through Atmospheric Layers for DInSAR Applications

The accuracy and reliability of the measured differential path in satellite synthetic aperture radar (SAR) interferometry are strongly affected by the uncertainty in the estimation of the atmospheric contribution. Changes in the physical parameters of the medium, due to turbulence layers or gas concentrations, induce slight variations in the curvature of the propagation path that finally generate an overall disturbance term that is usually comparable, or even larger, than the displacement to be observed. A stochastic model for the three dimensional path field is derived by considering a plane wave propagating in a random layered medium. In the vertical direction a piecewise-linear walk, made by straight ray subpaths, is assumed, wherein the length of each path (thickness of the layer) and the number of paths are modelled as random variables. Along the horizontal plane mutual interactions among cells are defined through an interaction equation that closely resembles typical competitions in biological evolution models. The resulting parametric model is fitted with observations from the residual atmosphere, as measured after topographic removal in SAR images, and results are shown.

Stochastic Flow Simulation and Particle Transport in a 2D Layer of Random Porous Medium

A stochastic numerical method is developed for simulation of flows and particle transport in a 2D layer of porous medium. The hydraulic conductivity is assumed to be a random field of a given statistical structure, the flow is modeled in the layer with prescribed boundary conditions. Numerical experiments are carried out by solving the Darcy equation for each sample of the hydraulic conductivity by a direct solver for sparse matrices, and tracking Lagrangian trajectories in the simulated flow. We present and analyze different Eulerian and Lagrangian statistical characteristics of the flow such as transverse and longitudinal velocity correlation functions, longitudinal dispersion coefficient, and the mean displacement of Lagrangian trajectories. We discuss the effect of long-range correlations of the longitudinal velocities which we have found in our numerical simulations. The related anomalous diffusion is also analyzed.

Cross Correlation and Deconvolution of Noise Signals in Randomly Layered Media

It is known that cross correlation of waves generated by noise sources, propagating in an unknown medium and recorded by a sensor array, can provide information about the medium. In this paper the medium is a three-dimensional small-scale randomly layered medium with slow macroscopic variations. The main objective here is to set forth a framework for analysis of cross correlations of waves generated by noise sources and propagating in such a medium and, moreover, to use this framework to design estimators for macroscale medium features. The noise sources are located at the bottom of a random medium slab and generate a random wave field that is scattered by the rapid random fluctuations of the medium and then recorded at the surface. Taking into account the pressure release boundary conditions at the surface, this situation corresponds to the so-called daylight configuration. The analysis is carried out in the asymptotic framework where the typical wavelength is small compared to the scale of the macroscopic variations of the background medium and large compared to the decoherence length of the microscopic random fluctuations of the medium. It is shown that the cross correlation of the waves recorded at the surface contains statistically stable information about the macroscopic background medium.

Interplay between generic and mesoscopic speckle statistics in transmission through random media

We explore the interplay between generic and mesoscopic aspects of speckle patterns appearing in a single polarization component of the transmitted field of multiply scattering media. The crucial role of phase singularities in speckle patterns of diffusing and localized microwave radiation in quasi-one-dimensional samples is demonstrated in the dynamics of local transmission, in the statistics of structural features within the speckle pattern and in the motion of singularities as the frequency is scanned. We also describe a crossover between one- and three-dimensional propagation in random layered media with transverse disorder associated with an optical delocalization transition. The transition occurs at the thickness beyond which singularities are formed in the transmitted speckle pattern as the transverse spread of the wave becomes larger than the field correlation length. These studies demonstrate the relationship between field structures within individual Gaussian speckle patterns and non-ergodic statistics of local and integrated transmission for diffusive and localized waves in ensembles of random samples.

Photon Delocalization Transition in Dimensional Crossover in Layered Media

We report a crossover in optical propagation in random layered media from localization towards diffusion as the interaction of the wave with the sample is transformed from one to three dimensional due to nonuniformity in the layer thickness. The crossover occurs at the point that the lateral spread of the wave equals the transverse coherence length in the transmitted speckle pattern.

Exact solution to the problem of nonlinear pulse propagation through random layered media and its connection with number triangles

An energy pulse refers to a spatially compact energy bundle. In nonlinear pulse propagation, the nonlinearity of the relevant dynamical equations could lead to pulse propagation that is nondispersive or weakly dispersive in space and time. Nonlinear pulse propagation through layered media with widely varying pulse transmission properties is not wave-like and a problem of broad interest in many areas such as optics, geophysics, atmospheric physics and ocean sciences. We study nonlinear pulse propagation through a semi-infinite sequence of layers where the layers can have arbitrary energy transmission properties. By assuming that the layers are rigid, we are able to develop exact expressions for the backscattered energy received at the surface layer. The present study is likely to be relevant in the context of energy transport through soil and similar complex media. Our study reveals a surprising connection between the problem of pulse propagation and the number patterns in the well known Pascal’s and Catalan’s triangles and hence provides an analytic benchmark in a challenging problem of broad interest. We close with comments on the relationship between this study and the vast body of literature on the problem of wave localization in disordered systems.

On the Application of the Radiative Transfer Approach to Scattering from a Random Medium Layer with Rough Boundaries

For studying the problem of scattering from a random medium layer with rough boundaries the radiative transfer (RT) approach is widely used. In order to better understand this procedure we compared it with the statistical wave approach. Two such wave approaches are presented in this paper: the surface scattering operator (SSO) approach, and the unified approach. In both wave approaches two conditions are essential for arriving at RT system: the ladder approximation to the intensity operator, and the quasi-stationary approximation of fields. With these approximations one arrives at the integro-differential equations of the RT system. However, to arrive at the RT boundary conditions, one has to impose further approximations. In the SSO approach weak surface correlation must be imposed. In the unified approach, one has to ignore the terms involving volumetric spectral densities, and consider only single scattering from the rough boundary when deriving the boundary conditions.

An Inverse Problem of the Theory of Wave Propagation in a Random Layered Medium

An Inverse Problem of the Theory of Wave Propagation in a Random Layered Medium

Analysis for creep behavior and collapse of thick-section composite structures

A nonlinear viscoelastic and multi-scale modeling framework is used for the analysis of creep behavior and collapse of thick-section and layered composite structures. Previously developed nonlinear viscoelastic micromodels by the authors [Haj-Ali RM, Muliana AH. Micromechanical constitutive framework for the nonlinear viscoelastic behavior of pultruded composite materials. Int J Solids Struct 2003;40(5):1037–57; Haj-Ali RM, Muliana AH. A multi-scale constitutive formulation for the nonlinear viscoelastic analysis of laminated composite materials and structures. Int J Solids Struct 2004;41(13):3461–90], are used in order to generate the effective viscoelastic response of both unidirectional and random layered media. These micromodels are integrated with a displacement-based finite element (FE) model to perform structural analysis. In this study, we investigate the nonlinear creep behavior and critical time for structural collapse of composite structures. To that end, long-term behavior of composite materials is calibrated for the proposed material models. Both 3D and shell based structural models are employed in this study. Numerical applications of the proposed multi-scale viscoelastic analysis are presented for creep analyses of axially compressed I-shaped thick-section composite columns and a laminated cylinder under surface pressure. It is shown that the compressive loading ratio, along with the residual stiffness of the structure after buckling, can affect the creep behavior and the magnitude of the critical time for initiation of unstable response. The proposed models are general and can be used to examine the serviceability life of these structures.

Imaging in Randomly Layered Media by Cross-Correlating Noisy Signals

We consider an active source embedded in a randomly layered medium. We study the cross-correlation functions of the signals recorded at a series of points located at the surface. We show that this information can be processed to locate and identify the source inside the medium. The analysis is based on a separation of scales technique and limit theorems for random differential equations. The statistical stability of the imaging method is proved. The analogy with the time reversal of waves is enlightened, but the main difference is also put forward: we propose a passive way of imaging an unknown medium without the use of any active device. Finally, we extend these ideas for the location of a scatterer illuminated by a controlled source located at the surface or by a set of unknown sources generating random noise.

Scattering from a layer of discrete random medium over a random interface: application to microwave backscattering from forests

The distorted Born approximation is used to calculate the bistatic scattering coefficients from a layer of sparsely distributed discrete dielectric scatterers over a random interface. After specializing to the backscatter case, the scattering coefficient is determined as a sum of direct, direct reflected and interface scatter contributions. The direct reflected term contains contributions from the average interface and the interface fluctuations. These direct reflected terms include both incoherent and coherent or enhancement terms. The results are applied to backscattering from a mature hemlock forest over a roughened ground. The model results show that the direct reflected surface fluctuation terms give the dominant contribution to backscatter at P band and are equal in magnitude to the volume scatter at L band. Use of these new results brings the model predictions and experimental results into agreement.