Discrete Scatterers Research Articles

Solvable models for neutral modes in fractional quantum Hall edges

We describe solvable models that capture how impurity scattering in certain fractional quantum Hall edges can give rise to a neutral mode---i.e., an edge mode that does not carry electric charge. These models consist of two counterpropagating chiral Luttinger liquids together with a collection of discrete impurity scatterers. Our main result is an exact solution of these models in the limit of infinitely strong impurity scattering. From this solution, we explicitly derive the existence of a neutral mode and we determine all of its microscopic properties including its velocity. We also study the stability of the neutral mode and show that it survives at finite but sufficiently strong scattering. Our results are applicable to a family of Abelian fractional quantum Hall states of which the $\ensuremath{\nu}=2/3$ state is the most prominent example.

Using frequency-sum beamforming in passive cavitation imaging

Passive Cavitation Imaging (PCI) is a method for locating cavitation emissions to study biological effects of ultrasound on tissues. In this method, an image is formed by beamforming passively recorded acoustic emissions with an array. The image resolution depends on the ultrasound frequency and array geometry. Acoustic emissions can be scattered due to tissue inhomogeneity, which may degrade the image resolution. Emissions at higher frequencies are more susceptible to such degradation. Frequency-sum beamforming is a nonlinear technique that alters this sensitivity to scattering by manufacturing higher frequency information from lower frequency components via a quadratic product of complex signal amplitudes. This presentation evaluates the performance of frequency-sum beamforming in a scattering environment using simulations and experiments, conducted in the kHz and MHz frequency regimes. First, 50 and 100 kHz signals were broadcasted from a single source to an array of 16 hydrophones in a water tank with and without discrete scatterers. Second, a tissue-mimicking phantom perfused with microbubbles was insonified at 2 MHz, and the emissions were received by a 128-element linear array. The performance of frequency-sum beamforming was compared to conventional delay-and-sum and minimum variance beamforming in mild and strong scattering environments. [Work partially supported by NAVSEA through the NEEC.]

Theoretical Characterization of X-Band Multiincidence Angle and Multipolarimetric SAR Data From Rice Paddies at Late Vegetative Stage

Various polarimetric decomposition techniques have been proposed and demonstrated for more than 20 years. However, they still have never been operational applications because of insufficient validations. The true composition ratio of scattering mechanisms within a radar backscatter has to be known. To achieve this, a novel comprehensive approach to accurately identify the contribution of each scattering mechanism by a multiincidence angle and multipolarimetric (MIMP) synthetic aperture radar (SAR) observation combined with a theoretical model simulation is introduced. Rice paddies in Niigata City in Japan having a simple vegetation structure without topography were observed by X-band polarimetric and interferometric SAR 2 (Pi-SAR2), by gradually varying the flight path in terms of incidence angle. In addition to the MIMP SAR observation, a dominant scattering mechanism is reliably isolated through the theoretical characterization of the data by a discrete scatterer model. In the case of the rice paddies at a late vegetative stage, a dominant scattering on HH gradually varies from the double-bounce scattering to the volume scattering of rice grains in terms of incidence angle, whereas VV is affected by various volume scatterings of grains, leaves, and stems at the small, medium, and large incidence angles, respectively. HV is simply affected by the volume scattering of grains at the small incidence angle, and then it gradually switches to the volume scattering of the stalks. This brand new approach by the MIMP SAR observation with the theoretical modeling for this specific stage could take forward the polarimetric decomposition studies.

Dispersion relations for stationary light in one-dimensional atomic ensembles

We investigate the dispersion relations for light coupled to one-dimensional ensembles of atoms with different level schemes. The unifying feature of all the considered setups is that the forward and backward propagating quantum fields are coupled by the applied classical drives such that the group velocity can vanish in an effect known as "stationary light". We derive the dispersion relations for all the considered schemes, highlighting the important differences between them. Furthermore, we show that additional control of stationary light can be obtained by treating atoms as discrete scatterers and placing them at well defined positions. For the latter purpose, a multi-mode transfer matrix theory for light is developed.

Formulation of sound propagation and scattering in forests as a radiative transfer theory

Several approaches have been used in the literature to characterize sound scattering in forests. In this presentation, an approach based on the radiative transfer equation (RTE) is considered. Although the RTE has been used for other types of scattering problems, it is new to forest acoustics. The RTE is an integro-differential equation for the specific intensity, which is the average power flux density within a unit solid angle in a certain direction of propagation. It describes the processes of sound scattering and absorption by discrete scatterers such as tree trunks, branches, and leaves. RTE is applied to sound propagation in a four-layer forest model (ground, trunks, canopy, and open air). The trunk layer is modelled with vertical cylinders, while the canopy layer is modeled by spheres. The scattering amplitudes and total scattering cross sections of these scatterers are identified. At the interface of the trunk layer and ground, the specific intensity is specularly reflected. Although the RTE is ba...

A method for estimating the 3-D structure function from 2-D histology sections

Understanding the fundamental scattering mechanism(s) in tissues is critical to the success of Quantitative Ultrasound (QUS) imaging. From a discrete scatterer point of view, the ultrasound scattered power depends not only on the properties of the individual scatterers (modeled by the form factor) but also on the spatial correlation among the scatterers (modeled by the structure function). Previously, the structure function was obtained from the ultrasound backscatter data for dense cell pellet biophantoms. This study introduces a method for obtaining the 3-D structure function from the digitized hematoxylin & eosin (H&E) stained histology images. The method starts with calculating the 2-D pair correlation function using the scatterer positions determined from a histology image. Assuming isotropic media with spherical scatterers, the 3-D pair correlation function is then estimated by numerically solving a stereological function that relates the 3-D pair correlation function with the 2-D pair correlation f...

Early Jurassic (Pliensbachian) brachiopod biogeography in the western Tethys: The Euro-Boreal and Mediterranean faunal provinces revised

The Pliensbachian brachiopod biogeography of the western Tethyan region and the Euro-Boreal vs. Mediterranean faunal provinciality is evaluated. The data base was developed from improved and mostly revised taxonomical data of 25 Pliensbachian brachiopod localities selected from Europe and North Africa. The revised list and presence-absence data of 405 Pliensbachian brachiopod species formed the taxonomic units of the numerical analysis based on similarity coefficients. Cluster analysis (hCA) carried out from the Jaccard and Raup-Crick coefficient data showed clear dichotomy between the Euro-Boreal and Mediterranean brachiopod biochores. Principal coordinates (PCO) technique and non-metric multi-dimensional scaling (NMDS), complemented with the minimal spanning trees, resulted in similar grouping of the Pliensbachian brachiopod faunas. In de-trended correspondence analysis (DCA), besides the clearly separated Euro-Boreal and Intra-Mediterranean units, the Peri-Mediterranean assemblage formed a discrete scatter between the two major biochores. The three Algerian faunas (Ouar, Trar, Ksou) appear in a somewhat marginal position within the Euro-Boreal province. The above Pliensbachian brachiopod biochores reveal very high degree of endemicity, probably related to the limited dispersal potential of brachiopods. From the complete data set distinctive Euro-Boreal and Mediterranean species, ten from both provinces, were selected. Ribbed spiriferinid morphotypes are frequent among the distinctive Euro-Boreal species, whereas, besides smooth spiriferinids, some rhynchonellid and terebratulid morphotypes with expanded anterior margins are common among the distinctive Mediterranean species. In the Early Jurassic Tethyan palaeogeography, the marked dichotomy between the Euro-Boreal and Mediterranean provinces is interpreted in terms of deep-sea/oceanic barriers, which isolated the intra-Tethyan microcontinent from the European and African shelf regions. Geographical position and local environmental factors caused the differentiation of the Peri-Mediterranean subprovince along the north-western margin of the microcontinent. This palaeobiogeographical unit formed an interface between the Intra-Mediterranean and the Euro-Boreal biochores.

The local density of optical states of a metasurface.

While metamaterials are often desirable for near-field functions, such as perfect lensing, or cloaking, they are often quantified by their response to plane waves from the far field. Here, we present a theoretical analysis of the local density of states near lattices of discrete magnetic scatterers, i.e., the response to near field excitation by a point source. Based on a pointdipole theory using Ewald summation and an array scanning method, we can swiftly and semi-analytically evaluate the local density of states (LDOS) for magnetoelectric point sources in front of an infinite two-dimensional (2D) lattice composed of arbitrary magnetoelectric dipole scatterers. The method takes into account radiation damping as well as all retarded electrodynamic interactions in a self-consistent manner. We show that a lattice of magnetic scatterers evidences characteristic Drexhage oscillations. However, the oscillations are phase shifted relative to the electrically scattering lattice consistent with the difference expected for reflection off homogeneous magnetic respectively electric mirrors. Furthermore, we identify in which source-surface separation regimes the metasurface may be treated as a homogeneous interface, and in which homogenization fails. A strong frequency and in-plane position dependence of the LDOS close to the lattice reveals coupling to guided modes supported by the lattice.

Artificial perfect electric conductor-perfect magnetic conductor anisotropic metasurface for generating orbital angular momentum of microwave with nearly perfect conversion efficiency

Orbital angular momentum (OAM) is a promising degree of freedom for fundamental studies in electromagnetics and quantum mechanics. The unlimited state space of OAM shows a great potential to enhance channel capacities of classical and quantum communications. By exploring the Pancharatnam-Berry phase concept and engineering anisotropic scatterers in a metasurface with spatially varying orientations, a plane wave with zero OAM can be converted to a vortex beam carrying nonzero OAM. In this paper, we proposed two types of novel perfect electric conductor-perfect magnetic conductor anisotropic metasurfaces. One is composed of azimuthally continuous loops and the other is constructed by azimuthally discontinuous dipole scatterers. Both types of metasurfaces are mounted on a mushroom-type high impedance surface. Compared to previous metasurface designs for generating OAM, the proposed ones achieve nearly perfect conversion efficiency. In view of the eliminated vertical component of electric field, the continuous metasurface shows very smooth phase pattern at the near-field region, which cannot be achieved by convectional metasurfaces composed of discrete scatterers. On the other hand, the metasurface with discrete dipole scatterers shows a great flexibility to generate OAM with arbitrary topological charges. Our work is fundamentally and practically important to high-performance OAM generation.

Frequency-sum beamforming in a random scattering environment

In a uniform environment, sound propagation direction(s) or the location of a sound source may be determined from array-recorded signals by beamforming. However, the beamforming results may be degraded when there is random scattering between the source and the receivers. Such sensitivity to mild scattering may be altered through use of an unconventional beamforming technique that manufactures higher frequency information from lower-frequency signal components via a quadratic product of complex signal amplitudes. This presentation will describe frequency-sum beamforming, and then illustrate it with simulation results and near-field acoustic experiments. The simulations suggest that frequency-sum beamforming may be beneficial when there is one loud source and the environment provides one primary propagation path. The experiments were conducted in either a 1.0-m-deep 1.07-m-diameter cylindrical water tank using 50 kHz and 100 kHz signals broadcast from a single source to an array of 16 hydrophones when discrete scatterers are present and absent from the tank or in a tissue-mimicking phantom with a dominant scatterer embedded and insonified at 2 MHz and the scatter received by a 128-element array. The results from frequency-sum beamforming are compared to the output of conventional delay-and-sum beamforming and minimum variance beamforming. [Work supported by NAVSEA through the NEEC.]

Modified atomic decay rate near absorptive scatterers at finite temperature

The change in the decay rate of an excited atom that is brought about by extinction and thermal-radiation effects in a nearby dielectric medium is determined from a quantummechanical model. The medium is a collection of randomly distributed thermally-excited spherical scatterers with absorptive properties. The modification of the decay rate is described by a set of correction functions for which analytical expressions are obtained as sums over contributions from the multipole moments of the scatterers. The results for the modified decay rate as a function of the distance between the excited atom and the dielectric medium show the influence of absorption, scattering and thermal-radiation processes. Some of these processes are found to be mutually counteractive. The changes in the decay rate are compared to those following from an effective-medium theory in which the discrete scatterers are replaced by a continuum.

Fundamentals of Optical Fiber Sensing Schemes Based on Coherent Optical Time Domain Reflectometry: Signal Model Under Static Fiber Conditions

The paper develops a statistical model for the signals received in phase-sensitive optical time domain reflectometry (OTDR) probed by highly coherent sources. The backscattering process is modelled by a set of discrete scatterers with properly chosen parameters. Explicit equations for calculating the amplitude and the phase of the backscattered signal are obtained. The developed model predicts spectral and autocorrelation characteristics of the amplitude signals that are validated by experimental results. Characteristics of the phase signals, practicable for studying the sensing applications of the OTDR system, are presented and studied as well, demonstrating good correspondence with experiment. A more detailed modelling of distributed vibration sensing systems and their response to disturbances along an optical fiber will be possible as an extension of the developed formalism.

A Dense Medium Microwave Backscattering Model for the Remote Sensing of Oil Palm

Very little work has been carried out to examine the potential of synthetic aperture radar (SAR) imaging data for growth monitoring, disease monitoring, and yield prediction of oil palm plantations. In this paper, we present a scattering model for oil palm based on the radiative transfer equations, solved iteratively up to the second order, to better understand the backscattering behavior of oil palm canopies for SAR image interpretation. The oil palm canopy is modeled as a multilayer background host medium embedded with discrete scatterers of different shapes, with elliptic disks representing the leaves and cylinders representing the fronds and trunks. We consider the effects of coherent scattering through the dense medium phase and amplitude correction theory, as well as the near-field interactions between closely spaced scatterers through the Fresnel phase and amplitude corrections. Ground-truth data are used as input parameters for the model. The model is used to calculate the backscattering coefficients of oil palm canopies at different stages of growth and for different polarizations, frequencies, and incident angles. Comparisons between model calculations and C-band scatterometer measurements of multipolarization backscattering coefficients of 4-year-old oil palm canopies in Bangi, Malaysia show good agreement. Our model also predicts that SAR images at L-band are more sensitive to changes in the structure of the canopies, particularly that of the fronds, so will be the best frequency for oil palm growth monitoring and disease detection.

Effective scatterer diameter estimates for broad scatterer size distributions.

Acoustic form factors have been used to model the frequency dependence of acoustic scattering in phantoms and tissues. This work demonstrates that a broad range of scatterer sizes, individually well represented by Faran theory or a Gaussian form factor, is not accurately described by a single effective scatterer from either of these models. Contributions from a distribution of discrete scatterer sizes for two different form factor functions (Gaussian form factors and scattering functions from Faran's theory) were calculated and linearly combined. Composite form factors created from Gaussian distributions of scatterer sizes centered at 50 µm with standard deviations of up to σ = 40 µm were fit to each scattering model between 2 and 12 MHz. Scatterer distributions were generated using one of two assumptions: the number density of the scatterer diameter distribution was Gaussian distributed, or the volume fraction of each scatterer diameter in the distribution was Gaussian distributed. Each simulated form factor was fit to a single-diameter form factor model for Gaussian and exponential form factors. The mean-squared error (MSE) between the composite simulated data and the best-fit single-diameter model was smaller with an exponential form factor model, compared with a Gaussian model, for distributions with standard deviations larger than 30% of the centroid value. In addition, exponential models were shown to have better ability to distinguish between Faran scattering model-based distributions with varying center diameters than the Gaussian form factor model. The evidence suggests that when little is known about the scattering medium, an exponential scattering model provides a better first approximation to the scattering correlation function for a broad distribution of spherically symmetric scatterers than when a Gaussian form factor model is assumed.

Ultrawideband Time-Reversal Imaging With Frequency Domain Sampling

A new ultrawideband (UWB) time-reversal imaging method based on the unconventional utilization of UWB frequency data is introduced. First, a set of monostatic antennas is used to acquire the scattering data for a given scenario. Then, a corresponding multistatic data matrix is formed by casting the fine and coarse frequency samples of the scattering information into matrix form. The resulting frequency-frequency monostatic matrix is later fed into the adapted DORT (French acronym for decomposition of the time-reversal operator) and MUSIC (Multiple-Signal Classification) algorithms. The performance of the proposed method is investigated numerically by applying it to discrete scatterers embedded in homogeneous and continuously random inhomogeneous media. The effect of frequency bandwidth on image resolution is studied. It is observed that wider frequency bandwidths yield to better focusing resolutions.

Investigation of the scattering characteristics from discrete random scatterers based on recursive aggregate T-matrix algorithm

In this paper, we derive in vector form the recursive aggregate T-matrix algorithm based on the principles of electromagnetic wave multipole expansion of vector spherical wave functions and the vector addition theorem. After that we establish a three-dimensional electromagnetic scattering model for multiple spherical scatterers by simulating the scattering of subsurface discrete random scatterers using the derived algorithm. Calculating the scattering from different sizes, randomly distributed spherical scatteres and analyzing the high-order scattering effects, we can conclude that the vector recursive aggregate T-matrix algorithm has a high computation accuracy, and contains the interaction effects among multiple scatterers, therefore we can calculate the total scattering effects accurately from multiple scatterers. The established model can be served as a powerful tool in applications for retrieving the impact caused by the scattering of subsurface discrete random scatterers in soil moisture from radar measurements.

Experimental Demonstration of Statistical Stability in Ultrawideband Time-Reversal Imaging

We experimentally verify the statistical stability of ultrawideband time-reversal-based imaging of targets in discrete random media using electromagnetic waves. The measurements are carried out using a time-domain radar system that provides useful bandwidth of up to 40 GHz. We study the effect of the excitation bandwidth, discrete scatterers permittivity and fractional volume, and radar aperture size on the image stability. We also address the problem of imaging nonstationary targets in random media, where we verify the statistical stability of a differential time-reversal technique suited for tracking.

Ultrasound-heated photoacoustic flowmetry

We report the development of photoacoustic flowmetry assisted by high-intensity focused ultrasound (HIFU). This novel method employs HIFU to generate a heating impulse in the flow medium, followed by photoacoustic monitoring of the thermal decay process. Photoacoustic flowmetry in a continuous medium remains a challenge in the optical diffusive regime. Here, both the HIFU heating and photoacoustic detection can focus at depths beyond the optical diffusion limit (~1 mm in soft tissue). This method can be applied to a continuous medium, i.e., a medium without discrete scatterers or absorbers resolvable by photoacoustic imaging. Flow speeds up to 41 mm·s-1 have been experimentally measured in a blood phantom covered by 1.5-mm-thick tissue.

Wideband Measurement-Based Modeling of Inter-Vehicle Channels in the 5-GHz Band

In this paper, we describe a new wideband single-input-single-output (SISO) channel model for vehicle-to-vehicle (V2V) channels, based on an extensive measurement campaign carried out at 5.2 GHz around Helsinki, Finland, in August 2007. Both the currently well-known non-stationary behavior and the measured characteristics of the V2V channel motivate the use of a geometry-based stochastic channel modeling (GSCM) approach rather than a classical tapped delay line (TDL) approach. For the time-variant contributions stemming from discrete scatterers, the propagation distance can be deterministically estimated (i.e., geometrically), whereas the fading can be modeled as the combination of a distance-decaying process and two stochastic small- and large-scale processes. The complete parameterization of the V2V wideband channel model, the recipe for its implementation, and the analysis of its validity are also provided in this paper.

Unraveling the chromophoric disorder of poly(3-hexylthiophene)

The spectral breadth of conjugated polymers gives these materials a clear advantage over other molecular compounds for organic photovoltaic applications and is a key factor in recent efficiencies topping 10%. However, why do excitonic transitions, which are inherently narrow, lead to absorption over such a broad range of wavelengths in the first place? Using single-molecule spectroscopy, we address this fundamental question in a model material, poly(3-hexylthiophene). Narrow zero-phonon lines from single chromophores are found to scatter over 200 nm, an unprecedented inhomogeneous broadening that maps the ensemble. The giant red shift between solution and bulk films arises from energy transfer to the lowest-energy chromophores in collapsed polymer chains that adopt a highly ordered morphology. We propose that the extreme energetic disorder of chromophores is structural in origin. This structural disorder on the single-chromophore level may actually enable the high degree of polymer chain ordering found in bulk films: both structural order and disorder are crucial to materials physics in devices.