Incident Spherical Wave Research Articles

Enhanced backscatter in LIDAR systems with retro-reflectors operating through a turbulent ocean

The enhanced backscatter (EBS) effect is examined for light propagation through a weakly turbulent ocean in a monostatic channel with a retro-reflector. Using the second-order Rytov theory to account for the turbulent medium perturbations of the optical wave, we numerically predict the appearance of the EBS in the average intensity for the incident plane and spherical waves within the first several meters of the channel. The influence of the size of the retro-reflector on the EBS factor is also revealed for both types of waves. Our predictions are instrumental for the development of LIDARs in turbulent waters for communications, imaging, and sensing.

Reciprocity relations for a conductive scatterer with a chiral core in quasi-static form

We analyse a scattering problem of electromagnetic waves by a bounded chiral conductive obstacle, which is surrounded by a dielectric, via the quasi-stationary approximation for the Maxwell equations. We prove the reciprocity relations for incident plane and spherical electric waves upon the scatterer. Mixed reciprocity relations have also been proved for a plane wave and a spherical wave. In the case of spherical waves, the point sources are located either inside or outside the scatterer. These relations are used to study the inverse scattering problems. doi:10.1017/S144618111800007X

RECIPROCITY RELATIONS FOR A CONDUCTIVE SCATTERER WITH A CHIRAL CORE IN QUASI-STATIC FORM

We analyse a scattering problem of electromagnetic waves by a bounded chiral conductive obstacle, which is surrounded by a dielectric, via the quasi-stationary approximation for the Maxwell equations. We prove the reciprocity relations for incident plane and spherical electric waves upon the scatterer. Mixed reciprocity relations have also been proved for a plane wave and a spherical wave. In the case of spherical waves, the point sources are located either inside or outside the scatterer. These relations are used to study the inverse scattering problems.

FZP Design Considering Spherical Wave Incidence

FZP Design Considering Spherical Wave Incidence

Forced sound transmission through a finite-sized single leaf panel subject to a point source excitation.

In the case of a point source in front of a panel, the wavefront of the incident wave is spherical. This paper discusses spherical sound waves transmitting through a finite sized panel. The forced sound transmission performance that predominates in the frequency range below the coincidence frequency is the focus. Given the point source located along the centerline of the panel, forced sound transmission coefficient is derived through introducing the sound radiation impedance for spherical incident waves. It is found that in addition to the panel mass, forced sound transmission loss also depends on the distance from the source to the panel as determined by the radiation impedance. Unlike the case of plane incident waves, sound transmission performance of a finite sized panel does not necessarily converge to that of an infinite panel, especially when the source is away from the panel. For practical applications, the normal incidence sound transmission loss expression of plane incident waves can be used if the distance between the source and panel d and the panel surface area S satisfy d/S>0.5. When d/S ≈0.1, the diffuse field sound transmission loss expression may be a good approximation. An empirical expression for d/S=0 is also given.

Microwave beam steering of planar antennas by hybrid phase gradient metasurface structure under spherical wave illumination

To facilitate the microwave beam steering of planar antennas in both elevation and azimuth planes, a radially gradient quasi-transparent hybrid metasurface (RGHMS) structure is proposed. The circular aperture of RGHMS is comprised of two different phase profiles in the single structure. Half of the circular aperture introduces a gradient phase shift, whereas the other half provides a constant phase shift to the incident spherical wave. Since the obtained wavefront modulation for the beam tilting is realized using the combination of aforementioned phase profiles in a single metasurface (MS), it is considered as a hybrid structure. The proposed circular RGHMS with a radius of 1.2λ0 is placed at a height of 0.43λ0 from the feed antenna by considering the geometrical centers of RGHMS and antenna aperture coinciding with each other. The in-plane translation of the RGHMS modulates the wavefront of the incident wave, which results in 0° to 18° beam steering of planar antenna in the elevation plane. Moreover, in-plane rotation of RGHMS around the antenna axis facilitates the beam steering in the azimuth plane with a full 360° azimuthal coverage. The proposed structure is designed at the center frequency of 10 GHz and introduces uniform beam shapes with the gain of 12.3–14.3 dBi during the beam steering. The strategy of combining two different types of phase profile in a single MS eludes the requirement of the phase correcting lens, and thus can directly be illuminated through the spherical wavefront of antenna in the near field. Moreover, the microwave beam steering in both planes with fairly high gain and compact configuration is revealed.

On the impact of the type of wave incidence in multiple-cylinder diffraction analysis at millimeter-wave frequencies

A comparison of plane against spherical-wave incidence consideration in multiple-cylinder diffraction analysis is performed, at several millimeter-wave frequencies, in order to clarify the margin in which both incidence results converge or differ. The mentioned comparison is carried out through a pair of two-dimensional (2D) hybrid uniform theory of diffraction-physical optics (UTD-PO) solutions (the plane-wave formulation for cylinders is firstly proposed in this work), and is intended to show the validity of each wave-incidence assumption in environments where millimeter or sub-millimeter-wave bands are being employed. In this sense, results can be used to achieve a more accurate and realistic planning of such radio communication systems when multiple-diffraction over rounded obstacles has to be considered (e.g. communication systems operating in stadiums).

Sound transmission of a spherical sound wave through a finite plate

For an incident plane wave on an infinite plate, a doubling of mass or frequency adds 6dB to the sound transmission loss (TL), but for an incident spherical wave on an infinite plate, a doubling of mass or frequency adds only 3dB to the TL. In reality, the discrepancies of the sound transmission due to plane wave and spherical wave incidence might not be so huge, since the influences resulted from the plate size and the distance between the source and the plate cannot be ignored. In this article, the sound transmission of a spherical wave through a finite plate is theoretically analyzed through the modal expansion method. The transmission losses for typical plates are illustrated and as well are compared with that of the mass laws due to normal and spherical wave incidence, respectively. The effects of parameters such as the size of the plate, the distance between the source and the plate, and the horizontal shift of the plate are investigated. An indicator for the estimation of the TL through a finite plate due to a point source is given for the potential of practical applications.

Design and implementation of planar reflection spiral phase plate for beams with orbital angular momentum

In this study the authors report on a design of an offset-fed reflection planar spiral phase plate (SPP) to generate electromagnetic waves with orbital angular momentum (OAM). Detailed design guidelines and measurement procedures are given, respectively in this study. Through the use of a phase tuning technique, the proposed planar SPP converts incident spherical wave to beams with desired helical phase front. An experimental mode-2 OAM beam generation setup working at 94 GHz has been performed to verify the design method. Typical OAM phase and intensity patterns can be observed in the experiment. The OAM spectrum calculated from this experiment phase information proves the high purity performance of the OAM beams that this approach generated.

Volumetric impact of fault perturbation in the first Fresnel zone

Resolution within seismic imaging must be understood in all three dimensions to make quantitative approximations of subsurface geometries. Constructive interference of incident spherical waves within the first Fresnel zone will limit the resolution due to spatial aliasing. Motivated by the problem of estimating the influence of this effect on the volume uncertainty several interpretations of trapping faults, being equally probable within the first Fresnel zone, are perturbed and multiple realizations of a structural model constructed. After estimating the depth dependent mean frequency and velocity within a zone around the fault plane, the fault interpretations are stochastically perturbed. The frequency- and velocity-dependent perturbations of the dips are analytically derived based on geometric considerations. The anticipated maxima of the repositioned fault dips specify thresholds for deterministic definitions of high and low cases for the fault geometries in a framework. The structural models, resulting from repositioning the faults, show significant alterations of the hanging-wall and footwall horizon terminations due to the varying dips and repositioning of the interpretation. We have applied our to the structural and stratigraphic interpretation obtained for a prospect in the Gulf of Mexico. The spatial variations of the bounding faults result in a spread of volumetric outcomes when analyzing the gross rock volume of the compartment.

Scattering theorems of elastic waves for a thermoelastic body

In the present work, the scattering problem of an elastic wave by a penetrable thermoelastic body in an isotropic and homogeneous elastic medium is considered. The corresponding scattering problem is formulated in a suitable compact form, and taking into account the physical parameters of the thermoelastic body and integral representations for the total exterior elastic and the total interior thermoelastic field are presented. Using asymptotic analysis of the fundamental solution of the Navier equation, expressions of the far‐field patterns are obtained, and reciprocity theorems for plane and spherical wave incidence are established. Finally, a general scattering theorem for plane wave incidence is also presented. Copyright © 2016 John Wiley & Sons, Ltd.

Utra-thin anisotropic transmitting metasurface for polarization beam splitter application**Project supported by the National Natural Science Foundation of China (Grant No. 61372034).

We report a polarization beam splitter based on phase gradient metasurface for microwave frequency region. The metasurface is constructed by anisotropic cells with independent phase response for differently-polarized waves. Through putting different gradient phases for orthogonally-polarized waves on a focusing metasurface, the anisotropic sample has the ability to enhance gain and split orthogonally-polarized waves. The simulation results indicate that the incident spherical waves are converted into plane waves and split into an x-polarized wave with a refraction angle of −24° and a y-polarized wave with a refraction angle of 37.6° in the y direction. For verification, a metasurface sample with a size of 102.5 mm ×102.5 mm is fabricated and measured. The consistence between numerical and experimental results validates the improved gain of 10.5-dB against the feed source and the splitting effect. Moreover, the thickness of the proposed metasurface is 3 mm which is ultra-thin against the wavelength at 15 GHz. The proposed prescription opens a new route to the applications of anisotropic metasurface in microwave band.

On dynamical justification of quantum scattering cross section

We suggest a dynamical justification of quantum differential cross section in the context of long-time transition to stationary regime for the Schrödinger equation. The problem has been stated by Reed and Simon. Our approach is based on spherical incident waves produced by a harmonic source and the long-range asymptotics for the corresponding spherical limiting amplitudes. The main results are as follows: i) the convergence of spherical limiting amplitudes to the limit as the source goes away to infinity, and ii) the proof of the coincidence of the corresponding limit scattering cross section with the universally recognized formula. The main technical ingredients are the Agmon–Jensen–Kato's analytical theory of the Green function, Ikebe's uniqueness theorem for the Lippmann–Schwinger equation, and some refinement of classical long-range asymptotics for the Coulomb potentials.

Acoustic behavior of porous ceiling absorbers based on local and extended reaction.

The acoustic behavior of ceiling absorbers can be predicted under different surface reaction assumptions: Local and extended reaction. This study aims to experimentally validate acoustic transfer functions near a ceiling absorber in an anechoic chamber based on the two surface reaction models. First, a ceiling absorber with two mounting conditions is modeled by equivalent fluid models, such as Delany-Bazley's, Miki's, and Komatsu's model, in various ways: (1) Local vs extended reaction and (2) plane-wave vs spherical-wave incidence. For a single absorber under anechoic conditions, the acoustic transfer functions for four source-receiver pairs are simulated using a pressure-based image source model, and then compared with measurements. For a rigid backing condition, both the local and extended reaction models agree well with the measurement. For an absorber backed by an air cavity, the extended reaction model agrees better at larger incidence angles at lower frequencies than the local reaction model.

Response of distributed fiber optic sensor cables to spherical wave incidence

A generalized multi-layered infinite-length fiber optic cable is modeled using the exact theory of three-dimensional elasticity in cylindrical coordinates. A cable is typically composed of a fiber optic (glass) core surrounded by various layered materials such as plastics, metals, and elastomers. The cable is excited by an acoustic spherical wave radiated by a monopole source at an arbitrary location in the acoustic field. For a given source location and frequency, the radial and axial strains within the cable are integrated over a desired sensor zone length to determine the optical phase sensitivity using an equation that relates the strain distribution in an optical fiber to changes in the phase of an optical signal. Directivity results for the cable in a free-field water environment are presented at several frequencies for various monopole source locations. Some comparisons of the sensor directional response resulting from nearfield (spherical wave) incidence and farfield (plane wave) incidence are made. [Work supported by NAVSEA Division Newport ILIR Program.]

Fourier-Based Imaging for Multistatic Radar Systems

Fourier-based methods for monostatic and bistatic setups have been widely used for high-accuracy radar imaging. However, the multistatic configuration has several characteristics that make Fourier processing more challenging: 1) a nonuniform grid in k-space, which requires multidimensional interpolation methods, and 2) image distortion when the incident spherical wave is approximated by a plane wave. This contribution presents a Fourier-based imaging method for multistatic systems, solving the aforementioned limitations: the first, by using k-space partitioning and applying interpolation in each domain; the second, by approximating the spherical wave with multiple plane waves. Both solutions are fully parallelizable, thus allowing calculation time savings. Validation and benchmarking with a synthetic aperture radar backpropagation algorithm have been performed through 2-D and 3-D simulation-based examples. Imaging results from radar measurements have been assessed.

Elastic scattering by unbounded rough surfaces: solvability in weighted Sobolev spaces

This paper is concerned with the variational approach in weighted Sobolev spaces to time-harmonic elastic wave scattering by one-dimensional unbounded rough surfaces. The rough surface is supposed to be the graph of a bounded and uniformly Lipschitz continuous function, on which the total elastic displacement satisfies either the Dirichlet or impedance boundary condition. We establish uniqueness and existence results at arbitrary frequency for both elastic plane wave and point source (spherical) wave incidence in the two-dimensional case. In particular, our approach covers the elastic scattering from periodic structures (diffraction gratings), and we prove quasiperiodicity of the scattered field whenever the incident field is quasiperiodic. Moreover, the diffraction grating problem is also uniquely solvable in the presented weighted Sobolev spaces for a broad class of non-quasiperiodic incident waves.

Transmission of a spherical sound wave through a single-leaf wall: Mass law for spherical wave incidence

This paper examines the sound insulation of a single-leaf wall driven by a spherical wave. The transmitted sound field of an infinite elastic plate under a spherical wave incidence is theoretically analyzed and insulation mechanisms are considered. The displacement of the plate is formulated using the Hankel transform in wavenumber space and the transmitted sound pressure in the far-field is obtained by Rayleigh’s formula in an explicit closed form. Moreover, a reduction index is also derived in a closed form by introducing an approximation into the vibration characteristics of the plate. Deterioration of the insulation performance under the spherical wave incidence is caused by an apparent decrease of wall impedance that depends on the directivity of the transmitted sound wave. The mass law for a spherical wave incidence is different from that for a normal plane wave incidence: doubling the weight of the wall or the frequency gives an increase of 3dB (c.f. 6dB for a normal plane wave incidence), which is also smaller than the field incidence mass law.

Rayleigh scattering of sound by spherically symmetric bodies

An obstacle’s shape is often approximated by a sphere in analyses of sound scattering by air bubbles, objects on or near the seafloor, marine organisms, clouds of suspended particles, etc. Here, an asymptotic technique is developed to study low-frequency sound scattering from spherically symmetric inhomogeneous obstacles. The obstacle can be fluid, solid, or a fluid-filled solid shell. Physical properties of the obstacle are arbitrary piece-wise continuous functions of the distance to its center. The radius of the obstacle is assumed to be small compared to the wavelengths of sound in the surrounding fluid as well as of compressional and shear waves inside the obstacle. General properties of the sound scattering by spherically symmetric bodies are established. Resonant Rayleigh scattering is studied in detail. For plane and spherical incident waves, it is discussed which physical and geometrical parameters of the obstacle can be retrieved from the scattered acoustic field.

Formation of nonlinear holographic images in a system of periodically located nonlinear mediums

The formation of nonlinear holographic images in a system of periodically located nonlinear mediums is studied. Analytical expressions which describe the magnitudes and locations of intensity maximums depending on the corresponding image number are derived. Comparison with numerical calculation results is presented. Dependence of a refraction index on intensity leads to beam self-focusing (1), transverse instability (2) and to formation of nonlinear holographic images (NHI) of obstacles in the optical path of powerful laser systems (3). In Ref. (4) it has been shown that at value of B-integral of only 0.2rad a round opaque obscuration increases the intensity peak which exceeds the average level by almost 1.5 times, and for a phase obstacle the peak excess is 2.5. One can present a disk amplifier as a system of periodically located (SPL) nonlinear mediums (NM). Formation of NHI in SPLNM differs from the NHI formation in continuous media with the same value of B-integral. For the first time this problem has been considered in Ref. (3). However, these authors (3) focused only on the analysis of the intensity dependence upon the size of an obscuration at a single point of space. Accidentally for SPLNM configuration considered in Ref. (3), the intensity in the chosen point is not a peak one. The locations of the NHI and their intensity were not explored. In Refs (5, 6 )t he results of peak intensity calculations for the various elements of the NIF laser chain with account for NHI formation were published. In Refs (7-9) the process of the NHI formation in a SPLNM was viewed in more details and it was shown that for KNM there are K NHI. However the chosen model parameters (number of NM, increment of B-integral for one NM, thickness of NM, size of the beam) are far from the parameters of typical disk amplifiers. In this paper, we are considering the simplified system of infinitely thin NM without energy gain and losses. According to expression (39) in Ref. (3), when the powerful plane wave and spherical scattered wave incident on the single NM, the new wave is generated. For the infinitely thin NM the complex amplitude A1 of this wave in the plane of NHI is equal to A1 =− iBA ∗ (1)