Spherical Wave Research Articles

Acoustic recording of near-surface turbulence on Mars

To study Mars chemistry, SuperCam onboard the NASA Perseverance rover fires bursts of 30 laser shots at rocks. Its microphone records the shock wave generated between 2 and 15 kHz by each laser-induced plasma for distances between 2 m and 8 m, at varying local times, from strong thermal turbulence during daytime, to weaker one at dusk or dawn. In each case, the scintillation index (the normalized variance of the intensity), and travel time are calculated. Based on extensive literature on the propagation of a spherical wave through a turbulent medium, there are enough statistics to constrain the field that causes the dispersion of acoustic data. Initial results show that data are well modeled by a Gaussian field. A negative time shift, ∼0.5% at 6 m, is observed: the resulting velocity is higher than the mean speed of sound (fast path effect). The variance of arrival times leads to a 15 cm characteristic scale during daytime. Fluctuations of the scintillation index allow the strength of the turbulence field to constrained. Other turbulence models are tested, including the Kolmogorov energy-cascade which typically prevails on Earth for the inertial regime, but has been challenged several times on Mars.

Elastic wave radiation and reception of a borehole dipole source in a vertically transverse isotropic formation

Single-well acoustic imaging using a dipole tool has been applied in anisotropic formations. For this application, the effect of anisotropy on the radiation and reception of acoustic waves in the borehole needs to be analyzed and a proper analysis method needs to be developed. We use the far-field asymptotic solution of the wavefield to calculate the radiation pattern of the dipole source in a borehole penetrating vertically transverse isotropic (VTI) formation. We model the spherical wave propagation characteristics of the radiated and reflected waves in the VTI formation and the receiving of the waves in the borehole for the on- and off-axis positions. Based on the developed analytical modeling methods, we study systematically the effects of the formation anisotropy on the radiation pattern and borehole response characteristics. Our modeling result demonstrates that due to the coupling between the longitudinal and the transverse particle motions, quasi-P-(qP-) and quasi-SV-(qSV-) wave radiation patterns contain two components. The result also indicates that the anisotropy causes the arrival time of the SH-reflection wave to differ from that of the qSV wave, and the misposition of the imaged targets would occur if the velocity measured along the borehole is used for migration. The azimuth sensitivity of the off-axis data can be used to help eliminate the 180° ambiguity for the dipole acoustic imaging in the VTI formation. Understanding the effects of anisotropy on borehole acoustic imaging can help improve the accuracy of the imaging result in anisotropic formations.

Estimation of Absorbed Power Density Based on Spherical Wave Expansion to Plane Wave Expansion for Exposure Assessment at 30 GHz

The international guidelines and standard specified the area-averaged absorbed/epithelial power density (APD/EPD) as the basic restriction at frequencies above 6 GHz. Assessment methods for APD are current under the consideration of standardization organizations. In this study, we first showed the enhancement of the APD due to the antenna/body interaction using full-wave simulations. We then proposed a hybrid method combining the spherical near-field measurement and numerical simulation of the exposure dose in human body, using an equivalent source reconstructed on the total field/scattered field boundary using the spherical wave expansion to plane wave expansion. By comparing with the full-wave simulated APD at 30 GHz for various antenna arrays, the proposed method gives a rather accurate estimation of the upper bound of the area-averaged APD (with relative differences < 28%). It can be utilized as an efficient method for electromagnetic safety assessment as the need for specific measurement equipment is eliminated.

A modified convolution model for calculating the far field directivity of a parametric array loudspeaker.

The far field directivity is a straightforward indicator to describe the radiation pattern of the audio sound generated by a parametric array loudspeaker (pal), but its accurate and computationally efficient prediction is still challenging at present. This paper derives two-dimensional (2D), three-dimensional (3D), and 3D axisymmetric convolution models for calculating the far field directivity based on the quasilinear solution of Westervelt equation. The obtained expressions are expressed as linear and spherical convolutions of the ultrasound directivity and Westervelt directivity for 2D and 3D models, respectively. To improve prediction accuracy, the obtained expression is multiplied by an effective directivity resulted from the aperture factor of audio sound. The calculated directivities are compared against the exact solution obtained using the cylindrical and spherical wave expansions for 2D and 3D models, respectively. Numerical results with piston, apodized, and steerable profiles in both 2D and 3D models show that the proposed modified convolution model agrees well with the exact solution. It is also found that sidelobes appear in the audio sound directivity at large aperture sizes and high audio frequencies due to the aperture factor of audio sound, which can be predicted with the proposed method with a relatively low computational expenditure.

Spherical vector waves: their generation using a 4π optical array

Spherical vector waves (SVW) are the natural basis that correlates internal multipole transitions of atomic systems to specific configurations of the electromagnetic field. We theoretically identify the SVW fields that could be approximately generated from incident cylindrical beams using a 4π optical array. A comparison is made between the near electromagnetic field of ideal SVW to that of the spherical spots generated by cylindrical incident laser beams with the selected angular spectra and a finite lens aperture of the 4π system. The fidelity is taken as figure of merit. Some challenges on the implementation of the SVW are briefly discussed.

Diffraction for the Dirac–Coulomb Propagator

The Dirac equation in $$\mathbb {R}^{1,3}$$ with potential $${\textsf{Z}}/r$$ is a relativistic field equation modeling the hydrogen atom. We analyze the singularity structure of the propagator for this equation, showing that the singularities of the Schwartz kernel of the propagator are along an expanding spherical wave away from rays that miss the potential singularity at the origin, but also may include an additional spherical wave of diffracted singularities emanating from the origin. This diffracted wavefront is $$1-{\epsilon }$$ derivatives smoother than the main singularities, for all $${\epsilon }>0,$$ and is a conormal singularity.

GRIN-lens-based in-line digital holographic microscopy.

In-line digital holographic microscopy (DHM) provides three-dimensional images with large fields of view and depths of field and micrometer-scale resolution, using a compact, cost-effective, and stable setup. Here, we develop the theoretical background and experimentally demonstrate an in-line DHM based on a gradient-index (GRIN) rod lens. In addition, we develop a conventional pinhole-based in-line DHM with different configurations to compare the resolution and image quality of both GRIN-based and pinhole-based systems. We show that in a high-magnification regime, where the sample is positioned near a source that produces spherical waves, our optimized GRIN-based setup provides better resolution (∼1.38µm). Furthermore, we employed this microscope to holographically image dilute polystyrene micro-particles with diameters of 3.0 and 2.0µm. We investigated the effect of light source-detector and sample-detector distances on the resolution, by both theory and experiment. Our theoretical and experimental results are in good agreement.

Nyquist Sampling Conditions of Some Diffraction Algorithms with Adjustable Magnification.

Diffraction algorithms with adjustable magnification are dominant in holographic projection and imaging. However, the algorithms are limited by the Nyquist sampling conditions, and simulation results with inappropriate parameters sometimes appear with aliasing. At present, many diffraction algorithms have been proposed and improved, but there is a need for an overall analysis of their sampling conditions. In this paper, some classical diffraction algorithms with adjustable magnification are summarized, and their sampling conditions in the case of plane wave or spherical wave illumination are analyzed and compared, which helps to select the appropriate diffraction algorithm according to the specific parameter conditions of the simulation to avoid aliasing.

An evaluation of scintillation index in atmospheric turbulent for new super Lorentz vortex Gaussian beam

Super Lorentz vortex Gaussian beam (SLVGB) is propagated via the turbulent atmosphere parameters. The benefit key of the SLVGB wave model is that the unlimited bandwidth wave and a spherical wave are involved. Additionally, Huygens Fresnel integral was used for schoolwork to study the propagation of SLVGB in a slant direction via a moderate turbulent medium. On the other hand, applying the crude international telecommunication union (ITU-R) model possible. Moreover, the Kolmogorov turbulent power spectrum model is applied, and the source field is dispersed by the zenith angle to the receiver plane. Additionally, examine the contour of the source field and the SLVGB intensity. To investigate various parameters such as source size, mode, scintillation index, topological charge, and others that are associated with the beam of super Lorentz vortex Gaussian are entirely understood, the outcomes were examined, and obtained other references to build the beam of slant path propagation in turbulent; the form constants are especially in comparison and matching. Our graphical findings indicate that the parameters happened randomly in the scintillation index and intensity of the SLVGB, resulting in a novel beam technical configuration. To summarize, this article is advantageous for remote sensing and uses an optical communications system and laser applications.

A numerical and experimental study on positive diffusive ionization waves in different N2/O2 mixtures: the role of photoionization

A diffusive ionization wave can be generated by an ultrafast high voltage far exceeding the inception threshold, and is featured by its unique and repetitive conical morphology. A combinative experimental and numerical study of the diffusive ionization waves is conducted in this work to investigate the role of photoionization in different N2/O2 mixtures with oxygen concentrations of 20%, 2%, 0.2%, 1 ppm, and pure nitrogen. In all gas mixtures, the ionization wave first forms a spherical shape after its inception then a conical when it approaches the plane electrode. Compared with typical filamentary streamers and inception cloud generated by low overvoltage, photoionization in a diffusive ionization wave takes effects mainly before the formation of the spherical ionization wave, and affects slightly the propagation velocity, discharge morphology, and the width (diameter) of the ionization wave. When the pin-to-plane electrode gap distance is kept 16 mm, in the atmospheric pressure simulation with an 85 kV voltage pulse, the maximum ionization width decreases from 11.4 mm in the 20% mixture to 9.1 mm in pure nitrogen. In the 200 mbar pressure experiment with a 16 kV voltage pulse, the maximum ionization width decreases from 12.5 mm in the 20% mixture to 11.6 mm in pure nitrogen. E in the inception cloud diameter estimation function (D= 2 U E −1) is modified to estimate the width of the ionization wave during its spherical propagation stage. It is shown that the estimation results at 180–205 kV cm−1 are in good agreement with the simulation results at atmospheric pressure air.

Back-Projection Imaging for Synthetic Aperture Radar with Topography Occlusion

When synthetic aperture radar (SAR) is conducting remote sensing or terrain mapping, its radar beam is inevitably occluded by the variations in the under-test topography. Although back-projection algorithm (BPA) can theoretically directly solve the imaging problems of topography variations that most current SAR imaging algorithms cannot handle, these BPAs only solve the phase focusing of SAR echo signal, and do not consider the mismatch of SAR imaging results caused by topography occlusion. To solve the mis-imaging issue of the occluded area generated by BPA under the case of topography variation, a topography-based BPA (Topo-BPA) is proposed in this paper. Firstly, a new beam occlusion judgment algorithm based on spherical wave assumption is proposed, and its core is depression angle interpolation and depression angle updating. Then, the proposed Topo-BPA embeds the proposed beam occlusion judgment algorithm before the classical BPA, which not only did not reduce the focus depth of BPA, but improved the imaging accuracy of classical BPA. Finally, numerical experiments have demonstrated the superiority of the Topo-BPA’s performance in comparison with classical BPA.

Escape from a black hole with spherical warp drive

In this paper, a class of the warp drive (WD) type metrics is proposed in the form of spherical and plane waves or shells. In particular, these metrics can describe the passage of spherical WD through the horizon of a black hole (BH) from the inside out. In this metrics, nonsingular evolution of physical fields is possible, which is demonstrated by examples of scalar, vector and fermion fields. The passage of a warp-wave through the fields is accompanied by soliton-like configurations (kinks). The limiting case of Planck-scale WD can lead to the evaporation of singularities inside BHs with the escape of particles and information into outer space, and the EPR = WD conjecture can also be proposed.

Adapting a Blu-ray optical pickup unit as a point source for digital lensless holographic microscopy.

The adaptation of an off-the-shelf Blu-ray optical pickup unit (OPU) into a highly versatile point source for digital lensless holographic microscopy (DLHM) is presented. DLHM performance is mostly determined by the optical properties of the point source of spherical waves used for free-space magnification of the sample's diffraction pattern; in particular, its wavelength and numerical aperture define the achievable resolution, and its distance to the recording medium sets the magnification. Through a set of straightforward modifications, a commercial Blu-ray OPU can be transformed into a DLHM point source with three selectable wavelengths, a numerical aperture of up to 0.85, and integrated micro-displacements in both axial and transversal directions. The functionality of the OPU-based point source is then experimentally validated in the observation of micrometer-sized calibrated samples and biological specimens of common interest, showing the feasibility of obtaining sub-micrometer resolution and offering a versatile option for the development of new cost-effective and portable microscopy devices.

A reconfigurable polarization converter and related application as horn antenna cladding

In this paper, a transmissive reconfigurable polarization converter (RPC) based on an active metasurface is proposed, which can regulate the ideal plane wave and the spherical wave as a cladding of the horn antenna. The metasurface unit is composed of a single-layer F4B dielectric substrate and two double-cross metal strips with a p–i–n diode on the top and seven vertical metal strips on the bottom. One RPC prototype with 15 × 15 units has been fabricated and measured when it regulates an ideal plane wave. By controlling the states of diodes, the RPC can realize the linear-to-circular polarization conversion (LCPC) or the linear polarization maintaining (LPM) function from 2.5 to 3.64 GHz. Furthermore, the RPC is used as the cladding of a horn antenna for high integration in practical applications. The measured results show that this RPC-antenna system can still achieve LCPC or LPM function from 3.1 to 4.5 GHz. It is worth mentioning that the 3 dB axial ratio beam width of RPC can cover from −65° to 65° in LCPC. The proposal has advantages of a wideband, simple biasing network, and easy fabrication and integration, which can be widely applied in modern wireless communication systems.

Extended reacting boundary modeling of porous materials with thin coverings for time-domain room acoustic simulations

Modeling of acoustic boundary conditions has a significant impact on the accuracy of room acoustic simulations, which play an important role in the design phase of indoor built environments in order to improve the acoustical comfort. In this work, a numerical framework based on the discontinuous Galerkin (DG) method is presented for modeling extended reacting boundaries of porous absorbers covered by thin materials. The domain decomposition methodology is applied by treating the porous material as a subdomain. Equivalent fluid models are used to depict the acoustic properties of porous materials, whose effective density and compressibility as irrational functions are approximated by multipole rational functions in the frequency domain. By employing the auxiliary differential equation approach to calculate the time convolution, the augmented time-domain governing equations of porous materials can be expressed in the same unified hyperbolic form as the linear acoustic equations, which further enables a consistent upwind numerical flux formulation throughout the whole domain. The numerical coupling across the interface between propagation media is handled by solving the underlying Riemann problem. Compared to existing approaches with the DG method for extended reacting boundaries modeling for room acoustics, the derived upwind numerical flux formulation does not involve the computation of auxiliary variables. The presented framework yield a well-posed linear hyperbolic system with admissible boundary conditions as guided by the “uniform Kreiss condition” (Kreiss, 1970). Acoustic properties of the covering materials are illustrated by considering a limp permeable membrane model. A local time-stepping approach is utilized to improve computational efficiency. Numerical validations against analytical solutions in 1D are performed to verify the desired high-order convergence rate. A 3D case study on modeling spherical wave fronts demonstrates the broadband accuracy of the formulation.

Phase detection of electron vortex beams on structured charge distribution

Recent advances in the production of so-called twisted electron (electron vortex) beams with sub-nanometer spot size offer unique opportunities to explore the role of orbital angular momentum (OAM) on electromagnetic microstructures. We address here the interaction between the OAM and an external electric field based on the Aharonov–Casher effect. Taking an inhomogeneous electric field generated by a point charge as an example, we show that the deformation of twisted electron's wavefront is very sensitive to the location and orientation of point charges and can be clearly visualized by interference patterns with a spherical wave. This phase shifting detection provides a high resolution representation for the structure and distribution of charged nanoparticles.

The Singularity of the Big Bang Can Be Described in Greater Depth than the Limits of the Planck Time and Length

In this paper, we determine the frequency, energy and momentum of the primordial spherical wave at the birth of our universe, which are consistent with the fact that the total energy of our universe was created in the hot Big Bang. With this, we also indirectly demonstrate the consistency of previous works on the hypothesis of primary particles, by using their results. We obtain a hyper-high initial frequency of the spherical wave, which is not in contradiction with string theory.

A Plane Wave Equivalent Model for Forward Scatter Shadow Ratio in Spherical Wave and Its Application in Shadow Profile Retrieval

A Plane Wave Equivalent Model for Forward Scatter Shadow Ratio in Spherical Wave and Its Application in Shadow Profile Retrieval

The problem of propagation of a one-dimensional plastic wave in the environment with linear and polyline unloading

Problems of propagation of plane and spherical waves in a nonlinearly compressible medium with linear and broken line unloading under intense loads are considered. The solutions of the problems are constructed in the opposite way, assuming that the medium at the shock wave front is instantly loaded in a nonlinear manner, and behind the front in the perturbed region, the medium is irreversibly unloaded. For a specific structure of the medium, the results of calculations are presented in the form of graphs of pressure, velocity of the medium at the layer boundary, at the shock wave front and in the disturbed region as a function of time. The influence of the nonlinear properties of the medium on the distribution of the dynamic characteristics of shock-wave processes in it has been studied.

Lateral resolution enhanced interference microscopy using virtual annular apertures

The lateral resolution in microscopic imaging generally depends on both, the wavelength of light and the numerical aperture of the microscope objective lens. To quantify the lateral resolution Ernst Abbe considered an optical grating illuminated by plane waves. In contrast, the Rayleigh criterion holds for two point sources or point scatterers separated by a lateral distance, which are supposed to emit spherical waves. A portion of each spherical wave is collected by the objective lens and results in an Airy disc corresponding to a diffraction limited intensity point spread function (PSF). If incoherent illumination is employed the intensity PSFs related to different scatterers on an object are added resulting in the well-known Rayleigh resolution criterion. In interference microscopy instead of the intensity the electric field scattered or diffracted by an object will be affected by the transfer function of the optical imaging system. For a reflective object the lateral resolution of an interference microscope can be again characterized by the Abbe limit if the object under investigation is a grating. However, if two irregularities on a flat surface are being imaged the resolution no longer obeys the Rayleigh criterion. Instead, it corresponds to an optical system with an annular aperture and thus surpasses the prediction given by the Rayleigh criterion. This holds true for both, amplitude as well as phase objects, as it will be elucidated in this study by theoretical considerations, simulation results and an experimental proof of principle.