Wave Beam Research Articles

ЕФЕКТ АНОМАЛЬНО СИЛЬНОГО ПОГЛИНАННЯ ЕЛЕКТРОМАГНІТНОГО ВИПРОМІНЮВАННЯ ТОНКИМИ ПРОВІДНИКОВИМИ ВОЛОКНАМИ

Subject and Purpose. The effect of abnormally strong interaction of electromagnetic radiation with fine conductive fibers is сonsidered. Metal, semiconductor, or graphite fibers can heavily absorb electromagnetic radiation provided the fiber diameter is several hundred times smaller than the radiation wavelength. For the most effective transfer of radiation energy, a proper ratio of the radiation wavelength, fiber refractive index, and fiber diameter is sought. Methods and Methodology. The diffraction problem of a cylinder whose diameter is much smaller than the incident wavelength is treated. The formulas to compute the radiation absorption efficiency have a series appearance. The series coefficients depend on the diameter of the cylinder, its refractive index, and the wavelength. With the cylinder diameter much smaller than the wavelength, these coefficients can be series expanded in the small parameter, and it should suffice to take into account only the first term. The findings are experimentally verified by measurements of the microwave radiation energy transmitted to a fine graphite fiber. Results. Relationships have been determined of the fiber diameter, fiber conductivity, and wavelength when the effect of the electromagnetic radiation absorption was at its strongest. The experiment showed that even unfocused, an 8 mm wave beam transmitted more than 10% of the energy to a graphite fiber of a 12 μm diameter. The size of the fiber area struck by the beam was 300 times smaller than the beam cross-section. Conclusions. Conductive fibers of a cross-sectional diameter much smaller than the incident radiation wavelength strongly absorb this radiation. The absorption is at its strongest when the radiation wavelength in the fiber substance is approximately 10 times larger than the cross-sectional diameter of the fiber. The effect of the anomalously strong absorption of electromagnetic radiation can be used to transfer the electromagnetic radiation energy to fine-fiber targets no matter whether the radiation beam is focused or not. Also, this effect can be of use for making protective screens in the microwave region.

Radiation force characteristics of non-uniform chiral stratified particles in standing wave field

<sec> <b>Objective</b> With the development of optical technology, the investigation of light-field-particle interactions has gained significant momentum. Such studies find widespread applications in optical manipulation, precision laser ranging, laser gas spectroscopy, and related fields. In optical manipulation techniques, employing two or more laser beams proves more effective for capturing and manipulating particles than using a single beam alone. In addition, with the increasing demand for manipulating particles with complex structures, it is necessary to conduct in-depth research on the radiation force characteristics of double Gaussian beams on non-uniform chiral particles. This research aims to deepen our understanding of how optical fields influence particles, thereby offering fresh perspectives in manipulating and utilizing non-uniform chiral layered particles on both a microscale and a nanoscale.</sec><sec> <b>Method</b> Based on the generalized Lorentz-Mie theory (GLMT) and spherical vector wave functions (SVWFs), the total incident field of a double Gaussian beam can be expanded by using the coordinate addition theorem. The incident field coefficient and scattering coefficient of each region of the multilayer chiral sphere are obtained by enforcing boundary continuity and employing multilayer sphere scattering theory. The radiation force acting on non-uniform chiral layered particles within a double Gaussian beam is then derived through application of the electromagnetic momentum conservation theorem.</sec><sec> <b>Results and Discussions</b> The theory and programs in this paper is compared with those in existing literature. The influence of various parameters on the radiation force is analyzed in detail, such as the incident angle, polarization angle, beam waist width, beam center position, and internal and external chiral parameters. These results indicate that compared with a single Gaussian beam, counter-propagating Gaussian standing waves exhibit significant advantages in capturing or confining inhomogeneous chiral layered particles, offering enhanced particle manipulation capabilities. Additionally, by selecting an appropriate polarization state of the incident light, a delicate balance can be achieved among these parameters, effectively stabilizing the capture of inhomogeneous chiral particles.</sec><sec> <b>Conclusions</b> This study employs the generalized Lorenz-Mie theory and the principle of electromagnetic momentum conservation to derive analytical expressions for the transverse and axial radiation forces exerted by dual Gaussian beams on multi-layered chiral particles propagating in arbitrary directions. The research provides an in-depth analysis of how standing wave beams affect the radiation force behavior of non-uniform chiral particles. Numerical analysis reveals significant influences of beam waist, particle size, chiral parameters, polarization angle and mode, as well as particle refractive index on both transverse and axial radiation forces. This research is important in analyzing and understanding the optical properties of complex-shaped multilayer biological cells and realizing the applications in the micromanipulation of multilayer biological structures.</sec>

Behaviour of ultra-short radio waves refraction in the lower atmospheric layer of the coastal zone of the Bolshye Yeravninsky Lakes

The propagation of ultra-short waves is influenced by weather conditions. Meteorological inhomogeneities in the atmosphere cause refraction of the ultra-short wave beam. Measurements of meteorological parameters at h1 = 2 and h2 = 10 m have been carried out using an atmospheric-soil measuring complex installed in the coastal zone of Big Eravninsky Lakes at the Forest-Steppe permafrostecological station “Eravninsky” in Buryatia. There is a strong daily variability of the refractive gradient, and the refractive gradient values scatter ranges from –0.820 to +0.307 N-units In the lower ten-meter layer of the troposphere. It is discovered that in summer, meteorological conditions favorable for the superrefraction appearance are observed in this area.

“Cumulative effect” of second harmonic Lamb waves in a lossy plate

The second harmonic Lamb waves have high sensitivity to microstructural defects in materials and are therefore promising for incipient damage detection and monitoring of thin-walled structures. Existing studies have shown that the second harmonic Lamb waves can be cumulative with increasing propagation distance under the internal resonance conditions, which is conducive to nonlinear wave measurements in view of structural health monitoring. However, when propagating in a lossy structure with damping, the cumulative properties of the second harmonic Lamb waves are affected by energy dissipation and thus need to be re-examined. In this paper, a method for predicting the cumulative characteristics of second harmonic Lamb waves in damped plates is proposed. Instead of using material damping parameters which are difficult to obtain in practice, the proposed method relies on the attenuation patterns of Lamb waves at fundamental and double frequencies while taking into account the influence of the wave beam divergence. The proposed methodology is validated by finite element simulations and experiments. The results show that the cumulative second harmonic Lamb waves in the damped plate tend to increase and then decrease, and a “sweet” zone of relatively large amplitude can be predicted using the proposed method. The elucidation of the cumulative characteristics of the second harmonic Lamb waves provides guidance for effective system design for structural damage detection and monitoring applications.

Acoustic Bilayer Gradient Metasurfaces for Perfect and Asymmetric Beam Splitting

We experimentally and theoretically present a paradigm for the accurate bilayer design of gradient metasurfaces for wave beam manipulation, producing an extremely asymmetric splitting effect by simply tailoring the interlayer size. This concept arises from anomalous diffraction in phase gradient metasurfaces and the precise combination of the phase gradient in bilayer metasurfaces. Ensured by different diffraction routes in momentum space for incident beams from opposite directions, extremely asymmetric acoustic beam splitting can be generated in a robust way, as demonstrated in experiments through a designed bilayer system. Our work provides a novel approach and feasible platform for designing tunable devices to control wave propagation.

Exact analytical solutions for micrometer structured vortex beams with applications to optical tweezers

Bessel beams are widely known by their non-diffracting properties, i.e. beams that sustain their transverse profile along the propagation. It is also well known that by a suitable superposition of Bessel beams of the same frequency, but different longitudinal wave numbers, amplitudes and phases, it is possible to obtain a resulting beam whose longitudinal intensity pattern can be shaped along the propagation z-axis. Such approach, named Frozen Wave method, can be implemented through discrete or continuous superposition, the latter being more appropriate for obtaining spatially structured beams in micrometer domains. In previous studies, authors constructed analytical solutions for micrometer zero-order (i.e., null topological charge) Frozen Wave and, thereafter, of order one and two, by making use of a topological charge raising operator. In this paper, we present an analytical closed solution for the general case where the topological charge raising operator is applied an arbitrary number of times to a micrometer zero-order Frozen Wave beam, thus generating one of arbitrary topological charge. We also apply the new solutions to model optical tweezers (in Rayleigh regime) considering different light polarizations.

Numerical study on damaged ship rolling and capsizing in irregular beam waves during quasi-steady flooding

To study roll dynamics and capsizing occurrence of damaged ship in irregular beam waves, computational fluid dynamics is used to simulate damaged ship motions at rough sea to high sea states. The velocity-inlet boundary and momentum source are combined for wave generation. A modified formula is adopted to calculate turbulent viscosity to prevent unphysical decay of wave. The lateral drift restrained model is integrated with a combined dynamic mesh strategy to handle the ship's sway, heave and roll motions. Benchmarking study of irregular wave generation and roll response of damaged ship in regular waves is performed. Based on the simulations of motions of intact and damaged ships in irregular waves, the effects of cross flooding and damage orientation on the roll response of ship are discussed. For symmetrical flooding, the roll behaviour of ship is insensitive to the damage orientation. Due to the increase of roll damping, the roll response of damaged ship is smaller than that of intact ship. For asymmetric flooding, the ship is liable to roll toward the damaged side with a large angle. The probability of capsizing of ship caused by waveward damage is high at high sea state.

Sloshing Response of an Aquaculture Vessel: An Experimental Study

The sloshing response is crucial to the design and operation of aquaculture vessels and affects the safety of the culture equipment and the efficiency of the culture operation. A 1/50 scaled model was utilized to investigate the coupled sloshing response characteristics of a novel aquaculture vessel in a wave basin. Two wave directions (beam and head wave) and two filling levels (81.5% and 47.4%) are taken into account. The time-domain and frequency-domain characteristics of the sloshing response under the linear regular wave and extreme operational sea state were investigated using regular wave tests and irregular wave tests, respectively. The sloshing mechanism in the aquaculture tanks is complicated, due to the coupling effect between external waves, ship motion, and internal sloshing. In linear regular waves, the wave frequency mode dominates the sloshing response, which is larger under beam wave conditions than under head wave conditions and larger under half load conditions than full load conditions. The irregular wave test results confirmed the regular wave test conclusions, but the sloshing response has stronger nonlinearity, higher natural modes appeared, and the amplitude of the higher natural modes is also relatively larger.

On the effects of a nonlinear boundary with cubic stiffness on the reflection coefficients of time harmonic flexural waves in an Euler-Bernoulli beam

The reflection of time-harmonic flexural waves in a thin Euler-Bernoulli beam incident on a nonlinear boundary stiffness is studied. A set of waves at frequencies an integer multiple of a fundamental frequency is incident on the boundary, giving rise to an infinite set of reflected propagating and nearfield waves whose amplitudes are defined in terms of reflection coefficients. Equations for the wave amplitudes are truncated and solved numerically using the harmonic balance method. The boundary nonlinearity is assumed to be cubic with no quadratic term. Emphasis is placed on essential nonlinearity for which the linear stiffness is zero. This case is of interest due to stronger nonlinear effects being produced. The case with one incident propagating wave and two reflected propagating and nearfield waves is considered. It is seen that vibrational energy leaks from the 1st harmonic to the 3rd harmonic. A boundary configuration comprising linear springs is suggested, and the stiffness is calculated for this case and when the maximum leakage of energy occurs from the 1st harmonic to the 3rd harmonic, i.e., for the minimum reflection coefficient of the 1st harmonic. It is seen that the reflection coefficient of the incident wave at the fundamental frequency can be significantly less than 1.

Acoustic diffraction–resistant adaptive profile technology (ADAPT) for elasticity imaging

Acoustic beam shaping with high degrees of freedom is critical for applications such as ultrasound imaging, acoustic manipulation, and stimulation. However, the ability to fully control the acoustic pressure profile over its propagation path has not yet been achieved. Here, we demonstrate an acoustic diffraction–resistant adaptive profile technology (ADAPT) that can generate a propagation-invariant beam with an arbitrarily desired profile. By leveraging wave number modulation and beam multiplexing, we develop a general framework for creating a highly flexible acoustic beam with a linear array ultrasonic transducer. The designed acoustic beam can also maintain the beam profile in lossy material by compensating for attenuation. We show that shear wave elasticity imaging is an important modality that can benefit from ADAPT for evaluating tissue mechanical properties. Together, ADAPT overcomes the existing limitation of acoustic beam shaping and can be applied to various fields, such as medicine, biology, and material science.

Fourth-order moments analysis for partially coherent electromagnetic beams in random media

A theory for the characterization of the fourth-order moment of electromagnetic wave beams is presented in the case when the source is partially coherent. A Gaussian–Schell model is used for the partially coherent random source. The white-noise paraxial regime is considered, which holds when the wavelength is much smaller than the correlation radius of the source, the beam radius of the source, and the correlation length of the medium, which are themselves much smaller than the propagation distance. The complex wave amplitude field can then be described by the Itô-Schrödinger equation. This equation gives closed evolution equations for the wave field moments at all orders and here the fourth-order moment equations are considered. The general fourth-order moment equations are solved explicitly in the scintillation regime (when the correlation radius of the source is of the same order as the correlation radius of the medium, but the beam radius is much larger) and the result gives a characterization of the intensity covariance function. The form of the intensity covariance function derives from the solution of the transport equation for the Wigner distribution associated with the second-order wave moment. The fourth-order moment results for polarized waves are used in an application for imaging of partially coherent sources.

Enhancing interaction efficiency in traveling-wave devices with multiple beamlets and beam–beam interference

We demonstrate that beam–beam interference can significantly enhance the efficiency of multi-beam traveling-wave devices. Our theoretical analysis explains that a positive coupling of the space-charge field enhances the beam–wave interaction, resulting in increased efficiency in multi-beam devices with beam–beam interference. We validate this mechanism by performing particle-in-cell simulations on 670 GHz grid-loaded rectangular waveguide backward-wave oscillators. Both the multi-beam and single-beam devices exhibit the same dispersion of operating modes and operate under identical conditions. The simulation results indicate that the efficiency of the multi-beam device is up to 1.58 times higher than that of the single-beam device. Additionally, simulations are performed on the same structure at 340 and 1030 GHz, demonstrating efficiency improvements that support the proposed mechanism. These findings present a novel approach for increasing the efficiency of traveling-wave devices.

Numerical Investigation of Hydrodynamic Responses of a Moored Liquefied Natural Gas Ship under Multimodal Waves

Ocean waves typically consist of wind, sea, and swell trains. Conventionally, the treatment of multimodal waves has been to conceptualize them as a unified wave system and employ a single set of aggregate wave parameters for the representation of their collective characteristics. Nevertheless, a better understanding of multimodal waves is important when analyzing the interactions between waves and moored vessels, considering the pronounced sensitivity of a ship’s responses to wave periods and directions. Many spectral partitioning methodologies have been proposed to discern and segregate multimodal waves into two or more distinct wave systems, providing fundamental information for investigating moored ship responses to multimodal waves. Utilizing the wave spectra data acquired from a specific water region in South America, a comprehensive numerical study was undertaken by employing the specialized ocean engineering software ORCAFLEX 11.2e. The primary objective of this investigation is to analyze the dynamic response of a moored liquefied natural gas (LNG) vessel in ballast conditions subjected to waves defined by distinct wave identification methods (i.e., overall method and spectral partition method). Furthermore, the waves are categorized into two groups: beam waves and head waves. Results show that beam waves induce a substantial ship response, whereas head waves pose a comparatively lower risk to maritime vessels. Furthermore, the conventional overall wave approach tends to neglect the roll motion generated by multimodal waves when they propagate as head waves. Nevertheless, when the wave direction aligns with beam waves, the overall wave approach tends to produce the roll motion. These findings indicate the importance of considering multimodal waves in quay layout and mooring configuration design.

Internal shear layers in librating spherical shells: the case of attractors

Following our previous work on periodic ray paths (He et al., J. Fluid Mech., vol. 939, 2022, A3), we study asymptotically and numerically the structure of internal shear layers for very small Ekman numbers in a three-dimensional spherical shell and in a two-dimensional cylindrical annulus when the rays converge towards an attractor. We first show that the asymptotic solution obtained by propagating the self-similar solution generated at the critical latitude on the librating inner core describes the main features of the numerical solution. The internal shear layer structure and the scaling for its width and velocity amplitude in $E^{1/3}$ and $E^{1/12}$ , respectively, are recovered. The amplitude of the asymptotic solution is shown to decrease to $E^{1/6}$ when it reaches the attractor, as is also observed numerically. However, some discrepancies are observed close to the particular attractors along which the phase of the wave beam remains constant. Another asymptotic solution close to those attractors is then constructed using the model of Ogilvie (J. Fluid Mech., vol. 543, 2005, pp. 19–44). The solution obtained for the velocity has an $O(E^{1/6})$ amplitude, but a self-similar structure different from the critical-latitude solution. It also depends on the Ekman pumping at the contact points of the attractor with the boundaries. We demonstrate that it reproduces correctly the numerical solution. Surprisingly, the numerical solution close to an attractor with phase shift (that is, an attractor touching the axis in three or two dimensions with a symmetric forcing) is also found to be $O(E^{1/6})$ , but its amplitude is much weaker. However, its asymptotic structure remains a mystery.

Transformation of a fully nonlinear breather-like package of internal waves over a bottom step in a layered fluid

In this paper, we study the process of transformation of a localized wave packet over a bottom step in a three-layer fluid, in which the height of the step is equal to or exceeds the thickness of the lower layer; therefore, density stratification becomes two-layer in the shallow water zone. In numerical experiments, both the height of the step and the width of the step were varied. The problem is solved in the framework of a fully nonlinear model of hydrodynamics of an inviscid incompressible stratified fluid. The primary analysis consisted in estimating the values of dimensionless parameters used, as a rule, in runup problems: the Froude and Iribarren numbers, the ratio of the characteristic wavelength to the characteristic slope width, the ratio of the topographic slope to the characteristic wave beam angle. Since the “cutoff” line for the lower pycnocline is partially or completely located on a step, one could expect the effects of run-up, breaking or reflection of waves propagating along the lower pycnocline, but this doesn’t happen. It is shown that the reflection of the wave packet from the step is minimal in all cases considered, a strong steepening of the wave is observed, but no breaking occurs in this case — the wave then just quickly decays on the lower pycnocline. An analysis of the spectral amplitudes and energy fields allows us to conclude that there is a transfer of energy from the lower pycnocline to the upper one. The breather in a two-layer fluid cannot exist, but the wave packet formed in the upper pycnocline after its destruction has much higher energy than it has before the step.

Spatial–temporal engineering of light using Frozen Waves and Airy pulses

In this paper we combine two important theoretical methodologies, one related to the Frozen Wave beams (also referred to as Longitudinally Structured Light), which are non-diffracting beams whose longitudinal intensity pattern can be chosen a priori in a medium (absorbing or not), and the other related to the Airy-Type pulses, which are pulses resistant to dispersion effects in dispersive materials. As a result, a new method emerges capable of providing pulsed-beams resistant to three concomitant effects, i.e.: diffraction, dispersion, and attenuation; while concurrently the spatial variation of the wave along its axis of propagation can be engineered “at will”. The new approach can be seen as a generalization of the Localized Waves Theory in the paraxial regime and the new pulses can have potential applications in different fields such as optical communications, nonlinear optics, optical micromanipulations, optical microfabrication, and so on.

Seakeeping Behaviour of a Flettner Rotors-Propelled Catamaran in Beam Waves

This paper deals with the seakeeping of a catamaran propelled by Flettner rotors. The case study is an energy ship. The prediction of the roll motion of such a ship is of particular interest since she will mostly sail in beam seas. We used a numerical model based on the boundary element method to deal with the interactions of the ship with waves. It is supplemented by a model for the aerodynamic damping effect due to the rotors, the gyroscopic effects from the rotors and by the ITTC correction for roll damping. In the present study, it has been assumed that the Flettner rotors can be modelled as a distribution of elementary airfoils whose lift and drag depend on the local apparent wind speed. Interaction effects between the rotors and between the hull and rotors have been neglected. Regular waves have been investigated. For the considered case study, it is found that the Flettner rotors can have a small destabilizing effect or a small stabilizing effect on the ship motion depending on the ship speed and the rotors’ rotational speed.

Reflection of internal gravity waves in the form of quasi-axisymmetric beams

Preservation of the angle of reflection when an internal gravity wave hits a sloping boundary generates a focusing mechanism if the angle between the direction of propagation of the incident wave and the horizontal is close to the slope inclination (near-critical reflection). This paper provides an explicit description of the leading approximation of the unique Leray solution to the near-critical reflection of internal waves from a slope in the form of a beam wave. More precisely, our beam wave approach allows to construct a fully consistent and Lyapunov stable approximate solution, L2-close to the Leray solution, in the form of a beam wave, within a certain (nonlinear) time-scale. To the best of our knowledge, this is the first result where a mathematical study of internal waves in terms of spatially localized beam waves is performed.A beam wave is a linear superposition of rapidly oscillating plane waves, where the high frequency of oscillation is proportional to the inverse of a power of the small parameter measuring the weak amplitude of waves.Being localized in the physical space thanks to rapid oscillations (and high variations of the modulus of the wavenumber), beams are physically more relevant than plane waves/packets of waves, whose wavenumber is nearly fixed (microlocalized). At the mathematical level, this marks a strong difference between the previous plane waves/packets of waves analysis and our approach.The main novelty of this work is to exploit the spatial localization of beam waves to exhibit a spatially localized, physically relevant solution and to improve the previous mathematical results from a twofold perspective: 1) our beam wave approximate solution is the sum of a finite number of terms, each of them is a consistent solution to the system and there is no artificial/non-physical corrector; 2) thanks to the absence of artificial correctors (used in the previous results) and to the special structure of the nonlinear term, we can push the expansion of our solution to next orders, so improving the accuracy and enlarging the consistency time-scale.Finally, our results provide a set of initial conditions localized on rays, for which the Leray solution maintains approximately in L2 the same localization.

Ultrasonic testing for metal additive manufacturing: Experience with new course development

Metal additive manufacturing (AM) has brought about the need for nondestructive evaluation (NDE) methods to assess part quality. AM processes result in complex microstructures, porosity, material texture, and residual stresses all of which may vary spatially throughout the part. Thus, knowledge of ultrasonic NDE methods to characterize materials is relevant to the AM community. To address this challenge, a new graduate-level course entitled “Ultrasound for Metal Additive Manufacturing,” was created at the University of Nebraska-Lincoln. The course followed a cognitive-situative blended learning approach to give students practical ultrasonics training regardless of prior acoustics background. The theory introduced key topics including: the general wave equation, plane wave solutions, waves in isotropic solids, impact of material anisotropy, role of material interfaces, reflection and transmission, surface waves, scattering, dispersion, material dissipation, and scattering attenuation. A series of laboratory experiments allowed students to learn: experimental setups, signal processing, transducer properties and selection, beam mapping, wave speed and attenuation measurements, and diffuse-field measurements. Finally, each student developed a project incorporating ultrasound measurements into their individual AM research. Their findings were included in research articles, conference presentations, and PhD dissertations. This presentation will describe the course design, successes, and recommendations for future implementations.

Evaluation of the Fresnel approximation for the longitudinal particle displacement in shear wave beams

The longitudinal particle displacement in shear wave beams generated with disks that vibrate longitudinally at several hundred hertz is used to assess stiffness of soft tissue in vivo. Nonlinear elasticity of tissue, although less commonly used than linear stiffness, may be a more sensitive or specific biomarker of disease. A mathematical model for linear propagation of both transverse and longitudinal motion in a shear wave beam in an isotropic elastic half-space, and comparisons with measurements in tissue-mimicking phantoms, was published earlier this year [Archer et al., JASA 153, 1591 (2023)]. When including elastic nonlinearity in a propagation model, the complexity is reduced substantially by deriving an evolution equation based on the Fresnel approximation [Zabolotskaya, Sov. Phys. Acoust. 32, 296 (1986)]. For application to elastography, the parameter space in which the Fresnel approximation provides an accurate description of the longitudinal particle displacement must be established. In this presentation, the accuracy of the Fresnel approximation is assessed for linear shear wave beams, both unfocused and focused, by comparison with the existing mathematical model. Attention is devoted primarily to the longitudinal particle displacement in nearly incompressible media. [PGK is supported by the ARL:UT Chester M. McKinney Graduate Fellowship in Acoustics.]