Showing papers on "Plane wave published in 2018"

Scattering on plane waves and the double copy

Abstract: Perturbatively around flat space, the scattering amplitudes of gravity are related to those of Yang–Mills by colour-kinematic duality, under which gravitational amplitudes are obtained as the ‘double copy’ of the corresponding gauge theory amplitudes. We consider the question of how to extend this relationship to curved scattering backgrounds, focusing on certain ‘sandwich’ plane waves. We calculate the 3-point amplitudes on these backgrounds and find that a notion of double copy remains in the presence of background curvature: graviton amplitudes on a gravitational plane wave are the double copy of gluon amplitudes on a gauge field plane wave. This is non-trivial in that it requires a non-local replacement rule for the background fields and the momenta and polarization vectors of the fields scattering on the backgrounds. It must also account for new ‘tail’ terms arising from scattering off the background. These encode a memory effect in the scattering amplitudes, which naturally double copies as well.

Photonic hook: a new curved light beam

Abstract: It is well known that electromagnetic radiation propagates along a straight line, but this common sense was broken by the artificial curved light—the Airy beam. In this Letter, we demonstrate a new type of curved light beam besides the Airy beam, the so-called “photonic hook.” This photonic hook is a curved high-intensity focus by a dielectric trapezoid particle illuminated by a plane wave. The difference between the phase velocity and the interference of the waves inside the particle causes the phenomenon of focus bending.

Instabilities of Internal Gravity Wave Beams

Abstract: Internal gravity waves play a primary role in geophysical fluids: They contribute significantly to mixing in the ocean, and they redistribute energy and momentum in the middle atmosphere. Until recently, most studies were focused on plane wave solutions. However, these solutions are not a satisfactory description of most geophysical manifestations of internal gravity waves, and it is now recognized that internal wave beams with a confined profile are ubiquitous in the geophysical context. We discuss the reason for the ubiquity of wave beams in stratified fluids, which is related to the fact that they are solutions of the nonlinear governing equations. We focus more specifically on situations with a constant buoyancy frequency. Moreover, in light of recent experimental and analytical studies of internal gravity beams, it is timely to discuss the two main mechanisms of instability for those beams: (a) the triadic resonant instability generating two secondary wave beams and (b) the streaming instability corr...

Diffraction by a Wide Slit

Abstract: The problem of diffraction of scalar waves by an infinite conducting plane with a slit is investigated. Approximate expressions for the near and far fields, taking into account the interaction between the edges, are derived in terms of the well‐known solutions for the field produced when an isolated conducting half‐plane is excited by (a) a plane wave, and (b) a line source. Results of numerical calculation are given for the case of a plane wave normally incident on the slit. Twelve values of slit width ranging from 0.96 to 2.5 wavelengths are considered. A comparison of transmission coefficients is given. It is found that the new approximate solution agrees well with the exact solution, and provides a significant correction to the noninteraction solution. The accuracy increases with the slit width, so that the result is useful in the range where interaction cannot well be neglected but where the exact solution converges so slowly that computation is impracticable.

A Novel Metasurface for Dual-Mode and Dual-Band Flat High-Gain Antenna Application

Abstract: A dual-mode and dual-band flat high-gain antenna based on anisotropic focusing metasurface (MS) is proposed in this communication. The elements of the MS can steer the reflected phases of ${y}$ -polarized waves around 10 GHz and the transmitted phases of ${x}$ -polarized waves around 14 GHz independently. The function of the anisotropic MS is to focus the incident plane waves around 10 and 14 GHz on spots with different focal lengths and spaces. To reduce the block effect of the reflection mode, an extra phase gradient is introduced to the initial phase distribution of the ${y}$ -polarization to deflect the reflection mode main-beam to an angle of 30°. Finally, the new high-gain antenna obtains a deflecting reflection beam with peak gain of 17.2 dB and a normal transmission beam with peak gain of 19.5 dB. Besides single-band working, the antenna can also operate at 10 and 14 GHz simultaneously with gains of 14.7 and 16.7 dB, respectively. Measured results make a good agreement with the simulated results.

Trident pair production in plane waves: Coherence, exchange, and spacetime inhomogeneity

Abstract: We study the trident process in inhomogeneous plane wave background fields. We obtain compact analytical expressions for all terms in the probability, including the exchange part, for an arbitrarily shaped plane wave. We evaluate the probability numerically using complex deformation of lightfront time integrals and derive various analytical approximations. Our results provide insights into the importance of the one-step and exchange parts of the probability relative to the two-step process, and into the convergence to the locally constant field approximation.

Achromatic electromagnetic metasurface for generating a vortex wave with orbital angular momentum (OAM)

Abstract: The vortex wave that carries orbital angular momentum has attracted much attention due to the fact that it can provide an extra degree of freedom for optical communication, imaging and other applications. In spite of this, the method of OAM generation at high frequency still suffers from limitations, such as chromatic aberration and low efficiency. In this paper, an azimuthally symmetric electromagnetic metasurface with wide bandwidth is designed, fabricated and experimentally demonstrated to efficiently convert a left-handed (right-handed) circularly polarized incident plane wave (with a spin angular momentum (SAM) of ћ) to a right-handed (left-handed) circularly polarized vortex wave with OAM. The design methodology based on the field equivalence principle is discussed in detail. The simulation and measurement results confirm that the proposed method provides an effective way for generating OAM-carrying vortex wave with comparative performance across a broad bandwidth.

A Digital Multibeam Array With Wide Scanning Angle and Enhanced Beam Gain for Millimeter-Wave Massive MIMO Applications

Abstract: A novel full-digital multibeam array with wide scanning angle and enhanced beam gain is proposed for millimeter-wave massive multiple-input multiple-output applications. The array consists of 16 dual exponentially tapered slot antenna (DETSA) elements. Each element is integrated with a radio frequency receiver, an intermediate frequency chain, and an analog-to-digital converter (ADC). The H-plane radiation pattern of the proposed DETSA is very wide to enable the beam scanning in the azimuth plane. The beam gain is further enhanced by employing a 1-D multilayered planar lens that transforms the spherical wave into a plane wave in the E-plane for increasing the beam gain and keeping the phase compensation unaltered in the H-plane. Meanwhile, the planar lens is optimized to guarantee the wide scanning angle. In addition, all the signals received by the 16 independent channels are converted to a digital signal via ADC simultaneously and then used for synthesizing the multibeam patterns in the digital domain. Furthermore, the calibration and the verification of the synthesizing weights are discussed in detail. The measured results show that a scanning coverage of ±40° in the H-plane (or in horizontal plane) and an estimated maximum gain of 24.8 dBi with a gain tolerance of 3 dB can be achieved by the proposed 16-element array with a 1-D lens.

Nonlinear trident pair production in an arbitrary plane wave: A focus on the properties of the transition amplitude

Abstract: The process of nonlinear electron-positron pair production by an electron colliding with an arbitrary plane-wave electromagnetic field (nonlinear trident pair production) is studied analytically and numerically. Special emphasis is put on the properties of the transition amplitude. In fact, its original expression as resulting from applying the Wick’s theorem turns out to be divergent. By utilizing a functional relation derived from gauge invariance, however, the amplitude is regularized and investigated in different regimes. In particular, the amplitude is divided into a two-step and a one-step contribution, depending on the scaling dependence on the laser pulse duration. The corresponding contributions to the positron angular distribution spectra and the resulting interference terms are studied numerically, emphasizing the possibility of measuring experimentally the one-step contribution.

Bending waves in the Milky Way’s disc from halo substructure

Abstract: We use $N$-body simulations to investigate the excitation of bending waves in a Milky Way-like disc-bulge-halo system. The dark matter halo consists of a smooth component and a population of subhaloes while the disc is composed of thin and thick components. Also considered is a control simulation where all of the halo mass is smoothly distributed. We find that bending waves are more vigorously excited in the thin disc than the thick one and that they are strongest in the outer regions of the disc, especially at late times. By way of a Fourier decomposition, we find that the complicated pattern of bending across the disc can be described as a superposition of waves, which concentrate along two branches in the radius-rotational frequency plane. These branches correspond to vertical resonance curves as predicted by a WKB analysis. Bending waves in the simulation with substructure have a higher amplitude than those in the smooth-halo simulation, though the frequency-radius characteristics of the waves in the two simulations are very similar. A cross correlation analysis of vertical displacement and bulk vertical velocity suggests that the waves oscillate largely as simple plane waves. We suggest that the wave-like features in astrometric surveys such as the Second Data Release from \textit{Gaia} may be due to long-lived waves of a dynamically active disc rather than, or in addition to, perturbations from a recent satellite-disc encounter.

Giant magnetoelectric field separation via anapole-type states in high-index dielectric structures

Abstract: The value of the spatial separation between electric and magnetic fields in an electromagnetic wave is fundamentally constrained by the nonlocal nature of Maxwell's equations While electric and magnetic energy densities in a plane wave propagating in vacuum are equal at each point of space, carefully designed photonic structures can lead to a spatial separation of the electric and magnetic fields Here, a set of high-index dielectric tubes was proposed and demonstrated to deliver a record high spatial separation overcoming the free space scenario by more than three orders of magnitude The separation effect in the structure is enabled by the near-field interference between an incident radiation and anapole-type states designed by tuning geometrical parameters of coupled dielectric tubes Near-field scanning of field components within the void structure confirmed the predicted values of magnetoelectric separation Furthermore, the near-field interference concept in application to magnetoelectric separation can be employed in a range of spectroscopic tests, where objects (eg, atoms with magnetic optical transitions) can be placed in voids Devices providing tunable separation between the fields are important in nano-optics for magnetic particle or atom detection and trapping, in medicine for magnetic resonance imaging, etc

Lossless Scalar Metasurfaces for Anomalous Reflection Based on Efficient Surface Field Optimization

Abstract: For polarization-preserving anomalous plane-wave reflections by impenetrable surfaces, an efficient numerical field optimization technique is presented for designing lossless metasurfaces. Auxiliary surface waves copolarized with the incident and reflected plane waves are introduced and optimized such that the scalar surface impedance characterizing the reflecting surface approach a purely reactive profile. The resulting inhomogeneous scalar reactance can be discretized for realization as a periodic metasurface. Full-wave simulation of a physical design that is directly translated from the optimized reactance profile shows near-perfect anomalous reflection.

A Millimetre-Wave Cuboid Solid Immersion Lens with Intensity-Enhanced Amplitude Mask Apodization

Abstract: Photonic jet is a narrow, highly intensive, weak-diverging beam propagating into a background medium and can be produced by a cuboid solid immersion lens (SIL) in both transmission and reflection modes. Amplitude mask apodization is an optical method to further improve the spatial resolution of a SIL imaging system via reduction of waist size of photonic jet, but always leading to intensity loss due to central masking of the incoming plane wave. In this letter, we report a particularly sized millimetre-wave cuboid SIL with the intensity-enhanced amplitude mask apodization for the first time. It is able to simultaneously deliver extra intensity enhancement and waist narrowing to the produced photonic jet. Both numerical simulation and experimental verification of the intensity-enhanced apodization effect are demonstrated using a copper-masked Teflon cuboid SIL with 22-mm side length under radiation of a plane wave with 8-mm wavelength. Peak intensity enhancement and the lateral resolution of the optical system increase by about 36.0% and 36.4% in this approach, respectively.

Real-Time Blood Velocity Vector Measurement Over a 2-D Region

Abstract: Quantitative blood velocity measurements, as currently implemented in commercial ultrasound scanners, are based on pulsed-wave (PW) spectral Doppler and are limited to detect the axial component of the velocity in a single sample volume. On the other hand, vector Doppler methods produce angle-independent estimates by, e.g., combining the frequency shifts measured from different directions. Moreover, thanks to the transmission of plane waves, the investigation of a 2-D region is possible with high temporal resolution, but, unfortunately, the clinical use of these methods is hampered by the massive calculation power required for their real-time execution. In this paper, we present a novel approach based on the transmission of plane waves and the simultaneous reception of echoes from 16 distinct subapertures of a linear array probe, which produces eight lines distributed over a 2-D region. The method was implemented on the ULAO-OP 256 research scanner and tested both in phantom and in vivo . A continuous real-time refresh rate of 36 Hz was achieved in duplex combination with a standard B-mode at pulse repetition frequency of 8 kHz. Accuracies of −11% on velocity and of 2°on angle measurements have been obtained in phantom experiments. Accompanying movies show how the method improves the quantitative measurements of blood velocities and details the flow configurations in the carotid artery of a volunteer.

Ultra-narrow photonic nanojets through a glass cuboid embedded in a dielectric cylinder.

Abstract: A glass cuboid, embedded inside a dielectric cylinder is studied when illuminated with a monochromatic plane wave. A photonic nanojet (PNJ) with a full-width at half-maximum (FWHM) waist of around 0.25λ0 is obtained outside the external surface of the cuboid. The influence of the parameters of a square section cuboid is studied. Three particular phenomena can be obtained and are discussed: an ultra-narrow PNJ on the external surface of the cuboid, a long photonic jet and the excitation of whispering gallery modes (WGMs). A parametric study, over the width and the height of a rectangular section cuboid, shows that these parameters can be used to control the photonic jet properties. We also study several other geometries of the insert, which shows that the key parameter is the refractive index of the inserted material. Finally, we show that by changing the incident angle we can obtain a curved photonic jet.

Bianisotropic Huygens’ Metasurface Pairs for Nonlocal Power-Conserving Wave Transformations

Abstract: Bianisotropic Huygens’ metasurfaces are subwavelength thin surfaces that have been used to achieve wide-angle reflectionless refraction of plane waves, among other applications. These metasurfaces can realize any wave transformation, with a lossless and passive structure, provided that local power is conserved over the metasurface at every point. However, there are numerous practical wave transformations that satisfy total power conservation, but break this local power conservation requirement, such as antenna beamforming. In this letter, a method for realizing these wave transformations using a pair of cascaded bianisotropic Huygens’ metasurfaces is proposed. A summation of plane waves is assumed between the two metasurfaces, and their coefficients are obtained based on the stipulated input and output waves. Finally, a case study of converting a cylindrical wave to a truncated plane wave is presented with full-wave simulations.

Uniqueness results on phaseless inverse scattering with a reference ball.

Abstract: This paper is devoted to the uniqueness in inverse acoustic scattering problems for the Helmholtz equation with phaseless far-field data. Some novel techniques are developed to overcome the difficulty of translation invariance induced by a single incident plane wave. In this paper, based on adding a reference ball as an extra artificial impenetrable obstacle (resp. penetrable homogeneous medium) to the inverse obstacle (resp. medium) scattering system and then using superpositions of a fixed plane wave and some point sources as the incident waves, we rigorously prove that the location and shape of the obstacle as well as its boundary condition or the refractive index can be uniquely determined by the modulus of far-field patterns. The reference ball technique in conjunction with the superposition of incident waves brings in several salient benefits. First, the framework of our theoretical analysis can be applied to both the inverse obstacle and medium scattering problems. Second, for inverse obstacle scattering, the underlying boundary condition could be of a general type and be uniquely determined. Finally, only a single frequency is needed.

Assessing the performance of the Tao-Mo semilocal density functional in the projector-augmented-wave method

Abstract: We assess the performance of the recently proposed Tao-Mo (TM) semilocal exchange-correlation functional [J. Tao and Y. Mo, Phys. Rev. Lett. 117, 073001 (2016)] using the projector-augmented-wave method with the plane wave basis set. The meta-generalized gradient approximation level semilocal functional constructed by Tao-Mo is an all-purpose exchange-correlation functional for the quantum chemistry and solid-state physics. The exchange of the TM functional is based on the density matrix expansion technique together with the slowly varying fourth order gradient expansion. The correlation functional corresponding to the exchange is based on the one-electron self-interaction-free Tao-Perdew-Staroverov-Scuseria functional. Our test includes solid-state lattice constants, bulk moduli, bandgaps, cohesive energies, magnetic moments and vacancy-formation energies of transition metals. It is observed that in the plane wave basis, the TM functional performs accurately in predicting all the solid state properties at the semilocal level.

Time-Domain Analysis of an Acoustic–Elastic Interaction Problem

Abstract: Consider the scattering of a time-domain acoustic plane wave by a bounded elastic obstacle which is immersed in a homogeneous air or fluid. This paper concerns the mathematical analysis of such a time-domain acoustic–elastic interaction problem. An exact transparent boundary condition (TBC) is developed to reduce the scattering problem from an open domain into an initial-boundary value problem in a bounded domain. The well-posedness and stability are established for the reduced problem. A priori estimates with explicit time dependence are achieved for the pressure of the acoustic wave field and the displacement of the elastic wave field. Our proof is based on the method of energy, the Lax–Milgram lemma, and the inversion theorem of the Laplace transform. In addition, a time-domain absorbing perfectly matched layer (PML) method is introduced to replace the nonlocal TBC by a Dirichlet boundary condition. A first order symmetric hyperbolic system is derived for the truncated PML problem. The well-posedness and stability are proved. The time-domain PML results are expected to be useful in the computational air/fluid–solid interaction problems.

Uniqueness results on phaseless inverse acoustic scattering with a reference ball

Abstract: This paper is devoted to the uniqueness in inverse scattering problems for the Helmholtz equation with phaseless far-field data. Some novel techniques are developed to overcome the difficulty of translation invariance induced by a single incident plane wave. In this paper, based on adding a reference ball as an extra artificial impenetrable obstacle (resp. penetrable homogeneous medium) to the inverse obstacle (resp. medium) scattering system and then using superpositions of a plane wave and a fixed point source as the incident waves, we rigorously prove that the location and shape of the obstacle as well as its boundary condition or the refractive index can be uniquely determined by the modulus of far-field patterns. The reference ball technique in conjunction with the superposition of incident waves brings in several salient benefits. First, the framework of our theoretical analysis can be applied to both the inverse obstacle and medium scattering problems. Second, for inverse obstacle scattering, the underlying boundary condition could be of a general type and be uniquely determined. Third, only a single frequency is needed. Finally, it provides a very simple proof of the uniqueness.

Near-perfect conversion of a propagating plane wave into a surface wave using metasurfaces

Abstract: Conversion between free-space and guided-wave propagation modes is an essential function in numerous microwave, optical, and acoustical devices. The performance of currently available wave couplers is far from perfect due to the presence of parasitic scattering and reflections, which have been considered unavoidable up till now. The authors propose a technique for converting a homogeneous plane wave into a surface wave with linear power growth using metasurfaces. With a dramatic enhancement of conversion efficiency, the proposed metasurface wave couplers will find numerous applications ranging from perfect leaky-wave antennas in the microwave range to ideal photovoltaic cells in the visible range.

A Luneburg lens for spin waves

Abstract: We report on the theory of a Luneburg lens for forward-volume magnetostatic spin waves and verify its operation via micromagnetic modelling. The lens converts a plane wave to a point source, and vice versa, by a designed graded refractive index, realized by modulating either the thickness or the saturation magnetization in a circular region. We find that the lens enhances the wave amplitude by about 5 times at the lens focus, and 47% of the incident energy arrives in the focal region. A lens with small deviations from the optimal profile can still result in good focusing if the index is graded smoothly.

A Nonlinear Beamformer Based on p-th Root Compression—Application to Plane Wave Ultrasound Imaging

Abstract: Ultrafast medical ultrasound imaging is necessary for 3D and 4D ultrasound imaging, and it can also achieve high temporal resolution (thousands of frames per second) for monitoring of transient biological phenomena. However, reaching such frame rates involves reduction of image quality compared with that obtained with conventional ultrasound imaging, since the latter requires each image line to be reconstructed separately with a thin ultrasonic focused beam. There are many techniques to simultaneously acquire several image lines, although at the expense of resolution and contrast, due to interference from echoes from the whole medium. In this paper, a nonlinear beamformer is applied to plane wave imaging to improve resolution and contrast of ultrasound images. The method consists of the introduction of nonlinear operations in the conventional delay-and-sum (DAS) beamforming algorithm. To recover the value of each pixel, the raw radiofrequency signals are first dynamically focused and summed on the plane wave dimension. Then, their amplitudes are compressed using the signed p t h root. After summing on the element dimension, the signed p-power is applied to restore the original dimensionality in volts. Finally, a band-pass filter is used to remove artificial harmonics introduced by these nonlinear operations. The proposed method is referred to as p-DAS, and it has been tested here on numerical and experimental data from the open access platform of the Plane wave Imaging Challenge in Medical UltraSound (PICMUS). This study demonstrates that p-DAS achieves better resolution and artifact rejection than the conventional DAS (for p = 2 with eleven plane wave imaging on experimental phantoms, the lateral resolution is improved by 21 % , and contrast ratio (CR) by 59 % ). However, like many coherence-based beamformers, it tends to distort the conventional speckle structure (contrast-to-noise-ratio (CNR) decreased by 45 % ). It is demonstrated that p-DAS, for p = 2 , is very similar to the nonlinear filtered-delay-multiply-and-sum (FDMAS) beamforming, but also that its impact on image quality can be tuned changing the value of p.

Sauter-Schwinger pair creation dynamically assisted by a plane wave

Abstract: We study electron-positron pair creation by a strong and constant electric field superimposed with a weaker transversal plane wave which is incident perpendicularly (or under some angle). Comparing the fully nonperturbative approach based on the world-line instanton method with a perturbative expansion into powers of the strength of the weaker plane wave, we find good agreement—provided that the latter is carried out to sufficiently high orders. As usual for the dynamically assisted Sauter-Schwinger effect, the additional plane wave induces an exponential enhancement of the pair-creation probability if the combined Keldysh parameter exceeds a certain threshold.

Pulse generation scheme for flying electromagnetic doughnuts

Abstract: Transverse electromagnetic plane waves are fundamental solutions of Maxwells equations. It is less known that a radically different type of solutions has been described theoretically, but has never been realized experimentally, that exist only in the form of short burst of electromagnetic energy propagating in free-space at the speed of light. They are distinguished from transverse waves by a doughnut-like configuration of electric and magnetic fields with a strong field component along the propagation direction. Here, we demonstrate numerically that such Flying Doughnuts can be generated from conventional pulses using a singular metamaterial converter designed to manipulate both the spatial and spectral structure of the input pulse. The ability to generate Flying Doughnuts is of fundamental interest, as they shall interact with matter in unique ways, including non-trivial field transformations upon reflection from interfaces and the excitation of toroidal response and anapole modes in matter, thus offering new opportunities for telecommunications, sensing, and spectroscopy.

A plane wave method combined with local spectral elements for nonhomogeneous Helmholtz equation and time-harmonic Maxwell equations

Abstract: In this paper we are concerned with plane wave discretizations of nonhomogeneous Helmholtz equation and time-harmonic Maxwell equations. To this end, we design a plane wave method combined with local spectral elements for the discretization of such nonhomogeneous equations. This method contains two steps: we first solve a series of nonhomogeneous local problems on auxiliary smooth subdomains by the spectral element method, and then apply the plane wave method to the discretization of the resulting (locally homogeneous) residue problem on the global solution domain. We derive error estimates of the approximate solutions generated by this method. The numerical results show that the resulting approximate solutions possess high accuracy.