Incident Spherical Wave Research Articles

Acoustic scattering by smooth and rough elastic cylinders insonified by directional sonars: Bistatic experiments.

Bistatic laboratory measurements are presented for acoustic scattering from both smooth and rough elastic cylinders insonified by directional spherical waves. A scattering model, accounting for incident directional spherical waves while assuming negligible end effects, was derived in a previous article [Mursaline, Stanton, Lavery, and Fischell, J. Acoust. Soc. Am. 154, 307-322 (2023)] but only evaluated for monostatic scattering by smooth cylinders. The evaluation is extended here to bistatic geometries for both smooth and rough cylinders. The effect of axi-symmetric Gaussian roughness (axi-symmetric random variations in cylinder radius) on the cylinder on overall scattering levels and resonances is investigated. Particular emphasis is given to the influence of roughness on the excitation of axially propagating guided wave resonances associated with oblique incident angles. Bistatic laboratory observations presented herein further substantiate the effects on scattering due to the properties of the incident field from practical sonars, such as spherical spreading, as observed in the above-mentioned article. For smooth cylinders, axially propagating guided wave resonances are seen to become more prominent during bistatic in-plane scattering compared to bistatic orthogonal-plane scattering and previously published monostatic data. For rough cylinders, both overall scattering levels and resonances are found to be diminished compared to the smooth case.

Fast and direct calibration for high numerical aperture quadriwave lateral shearing interferometry using geometry model with higher-order Taylor expansion

The current research on quadriwave lateral shearing interferometry (LSI) is primarily focused on the measurements of plane wave or quasiplane wave. When directly measuring spherical waves with high numerical apertures (NA>0.35), it will generate additional systematic errors, which affect measurement accuracy. To make the quadriwave LSI applicable to the measurements of a high-NA spherical wave, this paper proposes a fast and direct calibration method by establishing the geometry model of the quadriwave LSI with high-NA spherical wave incidence. The expression for the optical path difference represented systematic errors introduced by high-NA spherical waves in the shearing wavefronts are derived, which utilize a ninth-order Taylor expansion and Zernike polynomials fitting to achieve the high accuracy required by the high-NA spherical wave incidence. Then, the systematic errors are directly calibrated in the shearing wavefronts of four directions. This paper presents the theoretical analysis and verifies the feasibility and reliability of the proposed method through simulations and experiments, achieving a good measurement accuracy.

Analyzing radiowave multiple diffraction from a low transmitter in vegetated urban areas using a spherical-wave UTD–PO approach

This article introduces a uniform theory of diffraction–physical optics (UTD–PO) formulation for analyzing radiowave multiple diffraction emanating from trees and buildings in green urban areas, considering illumination from a low transmitter and assuming spherical-wave incidence. Based on Babinet’s principle, this solution models buildings as rectangular sections and accounts for the influence of tree crowns (assuming these rise above the average rooftop height) by incorporating appropriate attenuation factors/phasors into the diffraction phenomena of buildings. The validation of the formulation is achieved through measurements made at the 39 GHz 6G mmWave frequency on a scale model of a green urban environment comprising bonsai trees and bricks. The main advantage of the proposed solution is that the calculations only include single diffractions due to recursion, circumventing the need to use higher-order diffraction terms in the diffraction coefficients, thus reducing the computation time and power. Our results may be beneficial for the design of mobile communication systems, including 6G networks, situated in green urban areas and with transmission source positioned lower than the surrounding infrastructure.

In situ calibration of shear ratio for quadriwave lateral shearing interferometry using double-slit interference.

A new method, to the best of our knowledge, based on double-slit (DS) interference is proposed to accurately estimate the shear ratio of the system, with plane wave or spherical wave incidence. Existing shear ratio calibration methods, designed primarily for lateral shearing interferometry (LSI) with plane wave incidence, are not applicable to LSIs directly testing divergent or convergent spherical waves. Equations for calculating the shear ratio using the fringe spacing of the DS interferogram and the NA of the incident spherical wave are derived in this paper. The simulation result shows that the relative error of the shear ratio value is about 0.3%, when the shear ratio is 0.1. In the experiment, the quadriwave LSI is designed with a plug-in feature. The shear ratio at integer multiples of 1/6 Talbot distance from the modified Hartmann mask was calibrated using a DS, and the results were in good agreement with theoretical values, confirming the accuracy of the method. Subsequently, with the assistance of an inductance micrometer, the shear ratio was calibrated at intervals of 0.5mm, and the results closely matched the theoretical variation of the shear ratio caused by displacement, confirming the high precision of the method.

Resistance frequency selection surface framed reflector antenna for 5G OTA measurement

AbstractIndirect far field (IFF) over‐the‐air (OTA) test could be one of the most applicable test methods for 5G mmWave devices. The compact antenna test range (CATR) method has been introduced to the OTA test by 3GPP. Conventional metallic parabolic reflectors without edge treatment can lead to serious edge diffraction which results in high noise and low accuracy. The serrated reflector improves edge diffraction but performs poorly at low frequencies. Reflector antenna with a resistance frequency selection surface (RFSS) frame is proposed for 5G OTA CATR measurement at millimeter frequency, which collimates spherical incident waves into quasi‐plane waves in a relatively short distance, thus forming a quiet zone (QZ) in which large devices under test can be measured in small chamber. In this paper, the reflector with RFSS is investigated through the numerical and experimental methods, it is found that serrated RFSS frame with low edge diffraction could achieve the excellent QZ, which could be helpful in miniaturing CATR chambers for 5G OTA measurement.

Exploring the Validity of Plane and Spherical Millimeter-Wave Incidences for Multiple-Diffraction Calculations in Wireless Communication Systems

The focus of this work is to determine at which threshold can the results for both plane and spherical wave incidence assumptions either converge or deviate when performing multiple diffraction attenuation calculations. The analysis has been carried out—for various millimeter-wave frequencies, inter-obstacle spacings, and angles of incidence—by employing a pair of two-dimensional (2D) hybrid formulations based on both the uniform theory of diffraction and physical optics (UTD-PO). This way, we seek to demonstrate under which circumstances each wave incidence assumption can be valid in environments that entail millimeter-wave bands. Based on this, we may ensure the minimum necessary distance from the transmitter to the first diffracting obstacle for the convergence of the spherical wave incidence solution onto that of the plane wave with a relative error below 0.1%. Our results demonstrate that for less than four diffracting elements, the minimum necessary distance engages in quasi-linear behavior under variations in both the angle of incidence and obstacle spacing. Notably, the considered frequencies (60–100 GHz) have almost no bearing on the results. Our findings will facilitate the simplified, more accurate and realistic planning of millimeter-wave radio communication systems, with multiple diffractions across various obstacles.

Vibrations of a thin, prestressed, fluid-loaded spherical shell forced by a point sound source

This paper investigates vibrations of and sound scattering by a thin elastic spherical shell when static pressures are different in the fluids inside and outside the shell. The work is motivated by stratospheric balloons being employed to carry acoustic sensors and by the proposed use of large, encapsulated gas bubbles for passive suppression of underwater sound [O. A. Godin and A. B. Baynes, J. Acoust. Soc. Am., 143, EL67–EL73 (2018)]. Linearized equations of motion of thin, prestressed shells are derived from first principles. Differences in the fluid-loading terms from previously proposed ad hoc models are identified and their significance is analyzed. Analytic solutions are derived for vibrations of a spherical shell excited by an incident spherical sound wave and for acoustic fields in the internal and external fluids. The results are verified against exact solutions in several particular cases. The mathematical model of the shell vibrations is applied to characterize the influence of the shell’s material properties on passive suppression of underwater noise and to quantify the effect of wave scattering by the balloon on performance of balloon-borne infrasound sensors in the atmosphere. [Work supported by ONR.]

UTD-PO Solutions for the Analysis of Multiple Diffraction by Trees and Buildings When Assuming Spherical-Wave Incidence

This paper presents two uniform theories of diffraction–physical optics (UTD-PO) formulations to undertake analysis of radiowave multiple diffraction resulting from the presence of both buildings and trees in vegetated urban areas, with the assumption of spherical-wave incidence. The solutions presented consider buildings modeled as knife-edges and rectangular sections (the latter being more complex and realistic) and the effect of the tree canopy (the assumption is that this exceeds the height of the average rooftop) is taken into account by adding proper attenuation factors/phasors to building diffraction phenomena. The validation of these formulations has been undertaken by comparing with other methods and measurements performed at 39 GHz on a scaled-model of the environment under analysis, consisting of an array of bricks and bonsai trees. The chief advantage of the solutions put forward is that because of recursion, the calculations only include single diffractions. This avoids any requirement for higher-order diffraction terms in the diffraction coefficients, which means less computer time/power is demanded. The results of this work may be useful when planning future mobile communication systems, including 6G networks and beyond.

Design and application of ultra-thin focus transmitarray

An ultra-thin transmitarray (TA) working at 10 GHz with bandwidth of 1.15 GHz is proposed. The TA is designed by arranging two types of phase-shifting cells, with a thickness of only 2.8 mm (0.09 λ 0). The proposed focus TA has an obvious convergence effect for plane wave. It enhances the electric field intensity by 11.85 dB at the focus and can also transform the incident spherical wave into the plane wave. When a substrate cylinder antenna is loaded with the proposed TA, it reaches a peak gain of 17.8 dBi (increased by 8.8 dB) and its half-power beamwidth is reduced from 84° to 11°. The TA is fabricated and measured. The measured results are highly consistent with the simulated results, which validates the good performance of the TA.

A Novel Metasurface Lens Design for Synthesizing Plane Waves in Millimeter-Wave Bands

With the development of communication technology has come several measurement applications requiring plane-wave conditions for wireless-device characterizations in anechoic chambers. In this paper, a metasurface lens with a 2 × 2 feeding-antenna array is proposed and characterized to synthesize a plane wave in a near field for a fifth-generation (5G) millimeter-wave radio-frequency (RF) devices test. The metasurface lens, based on Jerusalem-cross elements printed on a printed circuit board (PCB) substrate, is used for controlling the phase-shift distribution of incident spherical waves. The lens has a size of 0.4 × 0.4 m and is designed to operate at a range from 24.25 GHz to 27.5 GHz, and its feeding-antenna array is located at a focal plane of the lens, which is parallel to the metasurface lens. The lens is studied and verified through simulations and experiments, and a uniform amplitude and phase-field distribution at a reduced distance of 1.2 m generated by the metasurface lens throughout a QZ are achieved. The worst-case amplitude and phase variation of the designed metasurface lens are ±0.75 dB and ±7.5°, respectively. The results show a plane-wave condition can be achieved in 5G millimeter bands through the proposed compact and effective metasurface lens. Moreover, the proposed metasurface lens is shown to be capable of reducing the plane-wave synthesizing distance compared to the compact antenna test range (CATR) with a significantly reduced system cost, making it an attractive alternative to antenna testing in 5G millimeter-wave frequency bands.

Acoustic Equivalent Lasing and Coherent Perfect Absorption Based on a Conjugate Metamaterial Sphere

Acoustic conjugate metamaterials (ACMs), in which the imaginary parts of the effective complex mass density and bulk compressibility are cancelled out in the refractive index, possess the elements of loss and gain simultaneously. Previous works have focused on panel ACMs for plane wave incidence. In this paper, we explore the extraordinary scattering properties, including the acoustic equivalent lasing (AEL) and coherent perfect absorption (CPA) modes, of a three-dimensional ACM sphere, where incident spherical waves with specific topological orders could be extremely scattered and totally absorbed, respectively. Theoretical analysis and numerical simulations show that the AEL or CPA mode with a single order can be realized with a small monolayer ACM sphere with appropriate parameters. A huge (relative to incident wavelength) ACM sphere with pure imaginary parameters could support the even- (or odd-) order AEL and odd- (or even-) order CPA modes simultaneously. In addition, the AEL and/or CPA with multiple orders could be realized based on a small multilayered ACM sphere. The proposed ACM sphere may provide an alternative method to design acoustic functional devices, such as amplifiers and absorbers.

Sidelobe Suppression of Metalens Antenna by Amplitude and Phase Controllable Metasurfaces

Amplitude and phase controllable metasurfaces are proposed to suppress the sidelobe levels (SLLs) of a metasurface lens (metalens). The amplitude-control metasurface is responsible for controlling the transmission amplitude with its unit cells’ phase shift variation less than ±10°. The phase-control metasurface is responsible for transferring the spherical incident waves to plane waves with its unit cell covering 360° transmission phase shift, while the transmittance remains higher than −1 dB. Both the metasurfaces are with symmetrical structures for dual-polarization. By integrating the amplitude and phase controllable metasurfaces, a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$9.7\lambda _{0} \times 9.7\lambda _{0}$ </tex-math></inline-formula> metalens operating at 28 GHz 5G bands is designed and successfully suppresses the SLL. Within the 3 dB gain bandwidth from 26.0 to 29.0 GHz, this metalens antenna achieves the SLL lower than −20.9 dB in H-plane and lower than −17.3 dB in E-plane. The maximum gain is 23.4 dBi at boresight, and the achieved SLL is −16.3 dB as its scanning angle reaches the maximum of ±29°. Compared with the phase-only metalens, the proposed metalens antenna realizes the maximum and minimum SLL suppression of 9.8 and 3.4 dB within the 3 dB gain bandwidth at a price of a gain drop of 0.8 dB at the designed frequency.

A high‐gain circular polarization beam scanning transmit array antenna

A high-gain circular polarization (CP) beam scanning antenna based on planar transmit array (TA) is proposed. The planar TA is implemented using rectangular patches and square rings, and it has different frequency responses to two orthogonal polarized incident waves owing to different phase distributions in x- and y-direction. The TA can convert a linearly polarized spherical incident wave into a circularly polarized transmitted plane wave. In addition, beam scanning is achieved by in-plane translation of the feed antenna. The procedure is demonstrated for high-gain beam steering implementation operating in CP at the Ku-band. Full-wave simulation results demonstrate that the designed antenna enables elevation beam scanning from −33.6° to +33.6°, with a peak gain of 26.4 dBi. Scanning loss is better than 5 dB and the axis ratio remains below 3 dB for the entire scanning range in the frequency band of 13.9–14.9 GHz. Moreover, a prototype is fabricated and the measured results have good agreement with the simulated results, which confirms the feasibility of using this technology to achieve a high-gain, CP, low-cost and low cross-polarization beam scanning antenna.

A note on the sound transmission of a spherical sound wave through a double plate structure.

The sound transmission of a spherical wave through a double plate structure is theoretically and numerically analyzed. Unlike the plane wave incidence, it is demonstrated that the sound transmission loss due to the spherical sound wave incidence follows a law of 9 dB/oct for a double-layered infinite plate. For a double-layered finite plate, the sound transmission loss is lying in between 9 dB/oct and 18 dB/oct in most frequency ranges, and depends heavily on the size and position of the plate relative to the source.

Characterizing the borehole response for single-well shear-wave reflection imaging

Single-well shear-wave imaging using a dipole source-receiver system is an important application for detecting geologic structures away from the borehole. This development allows for determining the azimuth information of the structures. Existing analyses, however, focus on the data received at the borehole axis and use the elastic reciprocity theorem to model the borehole radiation and recording. We have extended the existing analyses to model the radiation, reflection, and recording response of the borehole for azimuthally spaced receivers off the borehole axis. By treating the mirror image of the borehole source with respect to the reflector plane as a virtual source, the borehole reception problem was shown to be equivalent to the response of the borehole to the spherical wave incidence from the virtual source, which can be solved using the cylindrical-wave expansion method. An asymptotic solution using the steepest-descent method is obtained if the virtual source is far from the borehole. The analytical solution allows us to analyze the borehole response for azimuthally spaced off-axis receivers. The analysis results agree well with those from 3D finite-difference simulations. With this analysis, one can further model multicomponent shear-wave reflection data from the cross-dipole acoustic tool and study the azimuthal variation characteristics of the data. Our results reveal that, whereas the data characteristics are dominated by those of a dipole, nondipole responses due to the off-axis reception can be observed, the magnitude of the responses depending on the off-axis distance and frequency and on the formation elasticity. The nondipole response characteristics have the potential to resolve the 180°-ambiguity problem in the azimuth determination for dipole shear-wave imaging. Our findings, therefore, provide new information for shear-wave reflection imaging analysis and development.

Bayesian framework for three dimensional, near field source localization using spherical harmonics

Localization of sound sources relative to a receiver is of great interest in many acoustical applications. Within the near field of a spherical array, spherical wave incidence can be assumed and both direction of arrival and radial distance information can be extrapolated. This work presents a two-tiered Bayesian framework, using spherical harmonics, through which the directions of arrival and radial distance of a single, or multiple sources in the near field relative to a spherical microphone array receiver can be estimated. The first tier estimates the number of sources present in the sound field, while the second tier estimates the direction of arrival and radial distance parameters. Two models for spherical wave incidence on a spherical array, both based on spherical harmonic beamforming techniques, are formulated and analyzed. This work presents analysis of the Bayesian framework and both models to demonstrate the feasibility of model-based Bayesian inference for three dimensional source localization of one or more sources in complex noise environments.

Reflections in a moving mirror

Euclid's law of reflection, r = i, rests on three assumptions: Fermat's principle of least time, constancy of speed of light, and that the mirror is stationary. For a moving mirror, the corresponding law is known as the relativistic reflection law; however, it was first inferred prior to relativity. While modern derivations rely on Lorentz transformations or Maxwell's equations, the original derivation was an elegant application of geometric optics. In this paper, we develop a new geometric approach which shows that the relativistic reflection from a plane mirror is equivalent to the ordinary reflection from a certain hyperbolic mirror, and that the incident and reflected rays are the focal rays of the hyperbola. We demonstrate that incident concentric spherical waves reflect as non-concentric spherical waves, and thereby derive the Doppler effect formula. We conclude with a class project for students to derive a generalization of Snell's law of refraction for a particular type of a moving interface.

Nanosecond shock wave-induced surface acoustic waves and dynamic fracture at fluid-solid boundaries.

We investigate the generation and propagation characteristics of leaky Rayleigh waves (LRWs) caused by a spherical shock wave incident on a water-glass boundary both experimentally and numerically. The maximum tensile stress produced on the solid boundary is attributed to the dynamic interaction between the LRWs and an evanescent wave generated concomitantly along the boundary. The resultant tensile stress field drives the initiation of crack formation from pre-existing surface flaws and their subsequent extension along a circular trajectory, confirmative with the direction of the principal stress on the boundary. We further demonstrate that this unique ringlike fracture pattern, prevalent in damage produced by high-speed impact, can be best described by the Tuler-Butcher criterion for dynamic failure in brittle materials. The orientation of the ring fracture extension into the solid also follows closely with the trajectory of the local maximum tensile stress distribution.

Image conditions and addition theorems for prolate and oblate spheroidal-coordinate separation-of-variables acoustic multiple scattering models with perfectly-reflecting flat surfaces

Abstract Three-dimensional time-harmonic acoustic multiple scattering problems are considered for a finite number of prolate and oblate spheroidal objects adjacent to flat surfaces. Wave propagation by spheroids is modelled by the method of separation of variables equipped with the addition theorems in the spheroidal coordinates. The effect of flat surfaces is accounted for by using the method of images; hence, the flat surfaces are of (semi-)infinite extent and perfectly reflecting: either rigid or pressure release. Wedge-shaped acoustic domains are constructed including half-space and right-angled corners with the wedge angle of $\pi /n$ rad with positive integer $n$. First, Euler angles are implemented to rotate image spheroids to realize the mirror reflection. Then, the ‘image conditions’ are developed to reduce the number of unknowns by expressing the unknown expansion coefficients of image-scattered fields in terms of real counterparts. Use of image conditions to 2D wedges, therefore, leads to the $4n^2$-fold reduction in the size of a matrix for direct solvers and $2n$-times faster computation than the approach without using them; for 3D wedges, the savings are $16n^2$-fold and $4n$-times, respectively. Multiple scattering models (MSMs) are also formulated for fluid, rigid and pressure-release spheroids under either plane- or spherical-wave incidence; novel addition theorems are also derived for spheroidal wavefunctions by using two rotations of spherical wavefunctions and a $z$-axis translation in-between, which is shown numerically more efficient than other addition theorems based on an arbitrary-direction translation and a single rotation. Finally, MSMs using image conditions are numerically validated by the boundary element method for a configuration populated with both prolate and oblate spheroids.

Wide-Angle Beam Steering Based on an Active Conformal Metasurface Lens

This work experimentally demonstrates a wide-angle beam steering based on an active conformal metasurface lens. Integrated with microwave varactors, the transmission phase of this cylindrical metasurface lens can be tuned in a range up to 195° by direct-current (DC) bias voltages. By compensating the phase difference between different incidences, the proposed cylindrical lens can collimate the incident spherical wave front into a plane wave front with predefined deflection angle. By increasing the number of feeding sources, the beam steering range of conformal lens can be expanded to ±60°. Having advantages of low cost and simple structure, the proposed conformal lens can be extended to millimeter-wave band and enable a wide range of applications.