Poynting Vector Research Articles

A ubiquitous, nearby reservoir of electromagnetic energy hidden in the fourth spatial dimension as a consequence of Kelvin’s rule (for constant electric currents) and of the Poynting vector

When applying what is called Kelvin’s principle to the elementary currents of two permanent magnets that attract each other, an apparent energy paradox appears. For Kelvin’s principle says that when constant electric currents are displaced with respect to one another, the mechanical work yielded as a result of the action of magnetic forces is equal in amount to the increase (not decrease) in the energy of the total magnetic field. The energy provided by the power supply in order to keep the currents constant is thus twice as large as the mechanical work yielded during the displacement of the current-carrying wires. But when dealing with permanent magnets and their polarization currents, there is still the yield of mechanical work and also the increase in energy of the total magnetic field, but no such thing as a visible power supply. In this article, things are analyzed by using the Poynting vector as an instrument. As a result, the topological assumption of a hidden reservoir of energy sitting in the direction of a fourth spatial dimension turns out to be indispensable in order to save the principle of local conservation of energy and of action by contact. A recognition of this kind was foreshadowed by Mie 100 years ago, who postulated that, in certain, but nevertheless common situations, energy flowed into ambient space out of the particles themselves both in the gravitational and the electromagnetic case.

The Cluster Virtual Observatory for ULF Waves

AbstractSince its launch in 2000, the Cluster fleet visited a vast domain of the circum‐terrestrial environment, from the upstream solar wind and the distant tail, down to the plasmasphere, scanning in detail all magnetospheric regions during over two solar cycles. This led to an unprecedentedly rich data collection of multi‐point measurements which will be used for years to come to decipher the mechanisms of Solar‐Terrestrial interactions. The large volume of data gathered by Cluster requires special strategies to make efficient use of it. To address this issue we constructed a browsable database containing parameters of the detected Ultra low frequency waves and of the spacecraft formation geometry. The primary data used to derive the parameters are the magnetic field, the electric field and the electron density. The data is resampled to a cadence of 1 s and processed using a sliding analysis window of 2,048 s with a step of 256 s over 24 hr intervals. This results in time‐frequency arrays for each parameter covering the 0.5 mHz to 0.5 Hz frequency range. The database is accessible at http://plasma.spacescience.ro/cluster.html. In total there are 47 wave parameters in the database, among them being the ellipticity, the degree of polarization, the (unsigned) wave vector direction, and the Poynting vector. Plots for the planarity, elongation, and degeneration of the Cluster tetrahedron are also available. At the moment, the database covers measurements made between 01 January 2001 and 31 December 2020 with more data being added in time. Here we present this database, discuss the methods used to derive the parameters and give practical examples.

Thermal Effect of the Back Radiation from Disk to Head after Laser Heating in HAMR

In a heat-assisted magnetic recording, the thermal effect of the head/disk interface has an important influence on the stability of the recording data. In this paper, we will discuss the thermal radiation from the disk, more specifically, the magnetic recording layer, which is at high temperature after laser heating, to the magnetic head, which is at room temperature. The radiative heat flux can be represented by the Poynting vector. In the near-field band, an effective way to obtain the electromagnetic fields is to solve the Maxwell’s equations combined with fluctuational electrodynamics. The near-field back radiation between specific head and disk material is calculated by the fluctuation-volume-current method. The radiative heat energy will induce the thermal deformation of the magnetic head, which will be discussed by the simulation, laying the foundation for adjusting and controlling the flying status.

Design and Analysis of the Low Bend Losses 2D Photonic Crystal Fiber-based Rhombic Ring Resonator for Magnetic Field Sensor

We designed and analyzed a magnetic field sensor with low bend losses 2D photonic crystal fiber based on a rhombic ring resonator. The proposed design consists of silicon rods with a diameter of 200 nm in the X and Z directions, which are 61 × 61 silicon rods. The Refractive Index (RI) of silicon is n = 3.48 at λ = 1.55 mm and the number of air holes along the direction is 33 × 33. It was found that the photonic crystal fibers used the photonic band gap phenomenon to guide light but rather an area of the fiber core with a lower refractive index of 0.9 nm. It is important to note that there are low bend losses in 2D photonic crystal fibers, enabling response to small changes in the magnetic fluid viscosity, refractive index, and other physical parameters. The flow of electromagnetic energy, indicated by the Poynting vector (s), indicates that the magnitude of the power carrier per unit area in the direction of S is approximately 1.23 W/m2.

Focusing a vortex beam with circular polarization: angular momentum

Based on the Richards-Wolf formalism, we obtain two different exact expressions for the angular momentum (AM) density in the focus of a vortex beam with the topological charge n and with right circular polarization. One expression for the AM density is derived as the cross product of the position vector and the Poynting vector and has a nonzero value at the focus for an arbitrary integer number n. The other expression for the AM density is deduced as a sum of the orbital angular momentum (OAM) and the spin angular momentum (SAM). We reveal that at the focus of the light field under analysis, the latter turns zero at n = –1. While both these expressions are not equal to each other at each point of space, 3D integrals thereof are equal. Thus, exact expressions are obtained for densities of AM, SAM and OAM at the focus of a vortex beam with right-hand circular polarization and the identity for the densities AM = SAM + OAM is shown to be violated. Besides, it is shown that the expressions for the strength vectors of the electric and magnetic fields near the sharp focus, obtained by adopting the Richards-Wolf formalism, are exact solutions of the Maxwell's equations. Thus, Richards–Wolf theory exactly describes the behavior of light near the sharp focus in free space.

Superposition of nondiffracting beams characterized by a caustic of the hyperbolic umbilical type

The aim of the present work is to introduce two monochromatic solutions to the scalar wave equation in free space, characterized by a caustic with a singularity of the hyperbolic umbilical type. The first solution, is a superposition of half-Mathieu beams, and the second one, is a superposition of parabolic beams. Since these solutions are determined by two particular complete integrals of the eikonal equation in free space, we compute their geometrical wavefronts, the caustic regions, and the corresponding Poynting vectors. Finally, we remark that, under certain conditions, these solutions describe three-dimensional accelerating beams in free space, propagating along semielliptical and parabolic paths, respectively.

Nanoimprint Meta‐Device for Chiral Imaging

AbstractThe polarization of light is a valuable information channel that has been studied extensively in optical devices. There has been limited progress in developing low‐refractive index contrast and large‐scale chiral meta‐devices that are easy to integrate and mass‐produce. In this image, a chiral imaging meta‐device with a large area and broadband chirality control is experimentally demonstrated. The centimeter‐scale Moiré meta‐device is achieved using nanoimprint technology. The Poynting vector and singularity features in the near field and chiral optical response in the far field are discussed. The proposed Moiré meta‐devices can achieve circular dichroism (CD) of more than 10%. Further chiral imaging harnessing CD mechanisms are demonstrated, which may lead to significant potential in various fields, including encryption and security, materials science, biochemistry, and medicine.

Mechanically tuned cholesteric elastomer waveguide slab

In this research, a planar waveguide whose core is a cholesteric liquid crystalline elastomer whose helical axis is perpendicular to its planar boundaries, is studied. The electrodynamics equations are established, together with the constitutive equations. The mechanical stress is tuned through elastic deformations in the parallel direction along the helix axis, in order to control the propagation parameters. The resulting equations system is solved numerically by assuming the guide to be surrounded either by air or vacuum. The propagation parameter and the ratio between the magnetic and electrical modes are obtained as a function of frequency, which provides the band structure of the aforementioned modes. The amplitudes of the profiles of the electromagnetic fields and the Poynting vector distributions are also sought as a function of position. Finally, the mixing of transverse electric and magnetic modes to generate new eigenmodes and their conditions for propagation within the waveguide, are also studied.

Radiation force of compressional plane waves on a sphere embedded in an elastic medium

The aim of this work is to derive exact partial-wave series expressions for the radiation force of plane compressional progressive waves propagating inside an elastic medium and incident upon an embedded elastic sphere. The analytical modeling is needed to provide fundamental physical understanding of the underlying phenomenon of mode conversion and its contribution to the acousto-elastic radiation force, and in experimental design. In the context of linear elasticity theory, a rigorous derivation for the acousto-elastic radiation force, based on the integration of the time-averaged radial component of the elastodynamic Poynting vector (or power flow density), is presented and discussed. Initially, the elastic scattering problem is determined and subsequently used to derive the mathematical expression for the acousto-elastic radiation force of progressive compressional waves. The method is also verified using the extended optical theorem for elastic compressional plane waves. Extension to the case of elastic plane standing wave is also provided. Particular importance is made on the contributions of elastic mode preservation (P → P) and mode conversion (P → S) to the acousto-elastic radiation force. Numerical computations for the dimensionless radiation force efficiency and its components demonstrate the importance of compressional-to-shear mode conversion in the scattering by the sphere encased in a linearly-elastic medium. The analytical formalism presented here can be used to validate numerical methods, and the results of the simulations can be utilized as a priori knowledge in optimizing and designing acousto-elastic radiation force experiments involving elastic compressional progressive waves on a sphere in acoustically-engineered materials applications, elasticity imaging methods, activation of implantable devices, characterization of biological tissue, and non-destructive evaluation to name some examples.

Post‐Sunset Field‐Line Resonances at Equatorial Latitudes Observed by Swarm

AbstractIn this study employing data from the Swarm satellites at an altitude of ≈500 km, we present evidence of field‐line resonances (FLRs) in the Pc2‐3 (0.02–0.2 Hz) frequency band in the undisturbed post‐sunset region of the equatorial ionosphere. We identify 26 events extending to magnetic latitudes as low as 2°, which was previously thought to be too low for FLRs to exist due to ionospheric damping. Identification of FLRs is supported by a narrow‐band fundamental and first harmonics, an oscillating field‐aligned Poynting vector, a relative phase shift between E and δB of ≈90°, and in one case observation of one wave in conjugate hemispheres by two satellites separated by 4 min. We show that, contrary to the non‐uniform trend of ground‐based observations, the fundamental frequencies of these occurrences decline monotonically with increasing field‐line length. Their frequencies differ from those of ground‐based magnetometer observations reported in the literature.

Properties of the Airy beam by means of the quantum potential approach

By using the quantum potential approach, we show that: the Airy beam determines a Hamiltonian system with one degree of freedom for a particle of mass m = 1 evolving under the influence of a quantum potential, such that its associated quantum force is constant, the integral curves of the Poynting vector are parabolic ones and turn out to be a subset of solutions of the corresponding Hamilton equations, the geometrical light rays associated with the Airy beam, are given by the tangent lines to the zeroes of the quantum potential, and the caustic coincides with the zeros of the quantum potential. Furthermore, we present a derivation of the Airy beam from the quantum potential equations by assuming that the quantum force is constant.

Angle-Selective Photodetection in Ge/Si Quantum Dot Photodiodes Enhanced by Microstructured Hole Arrays

We report on the near-infrared (NIR) photoresponse of a micropatterned Ge/Si quantum dot (QD) pin photodiode at different angles of radiation incidence. The photon-trapping hole array was etched through the n+-type top contact layer to reach the buried QDs. The normal-incidence responsivity was observed to be resonantly increased at wavelengths of 1.4, 1.7, and 1.9 μm by factors of 40, 33, and 30, respectively, compared with the reference detector without holes. As the incident angle θ increases, the resonance peaks are disappeared and at θ>40∘ a new resonance with a 25× enhancement arises at a wavelength of 1.8 μm. Simulation of the near-field intensity, Poynting vector distribution and wave polarization showed that at small θ, the strong electric field is primarily localized under the air holes (1.4 μm, TM mode) or between the holes (1.7 and 1.9 μm, TE modes) inside the region occupied by QDs, resulting in the strong NIR photocurrent. At large θ, the dominant resonance detected at 1.8 μm is the result of coupling between the TE and TM modes and formation of a mixed near-field state.

Enhanced Spin Hall Shift by Multipoles of Different Orders in Spherical Particles

The spin–orbit interaction of light is universal in the process of light scattering, and an important aspect is the spin Hall effect. The spin Hall effect of light also exists in a three-dimensional (3D) system. When circularly polarized light is incident on a spherical particle, the transverse displacement of the particle relative to the scattering plane can be observed due to the spiraling of the Poynting vector in the far field. In general, the spin Hall shift of light is negligible and difficult to detect in experiments. In this paper, we use a high-refractive-index (HRI) core-shell structure to excite high-order multipoles and explore the interaction between different order multipoles to enhance the spin Hall shift in the microwave band. We show that there exist some angles that increase the spin Hall shift when two particular multipoles are equal and dominated. Our work provides a new perspective for understanding the interaction between light and particles and enhances the spin Hall shift of the sphere in the microwave band.

Nonreciprocal radiative heat transfer between Weyl semimetal nanoparticles mediated by graphene nanoribbons

We demonstrate tunable thermal rectification enabled by near-field radiative heat transfer between two Weyl semimetal nanoparticles above graphene nanoribbons by rotating the particles and varying their loss factors. We show that, through the rotation, the thermal rectification, quantified by the ratio between the heat powers in the forward and backward directions, is significantly enhanced thanks to the nonreciprocal particles and the substrate that are more strongly coupled than the counterpart systems having reciprocal particles. We reveal that nonreciprocal particles induce spinning Poynting vectors, whose directions can be controlled by rotating the particles and can selectively couple to surface modes excited in the graphene nanoribbons. In addition, by optimizing the loss factor of the particles, the ratio is further improved. Interestingly, we find that when the rotation angles and the loss factor are appropriately chosen, thermal rectification disappears despite nonreciprocal materials in the system. Similarly, the rectification disappears when certain symmetry is satisfied in the system. Our results provide important understanding of nonreciprocal near-field radiative heat transfer in particle-substrate systems involving Weyl semimetals that offer multiple control knobs.

Ghost surface polaritons at oblique antiferromagnetic surface

We investigated hybrid-polarization surface magnon polaritons at the oblique surface of antiferromagnet (AF) in an external magnetic field pointed along the AF easy axis, where the easy axis does not lie in the AF surface. According to the direction of surface-polariton propagation, there are two specific geometries. In geometry-I, where the direction of propagation is vertical to the easy axis, we found two hybrid-polarization surface polaritons (HSPs), which are highly nonreciprocal. They are one ordinary hybrid-polarization surface polariton (called a HSP still) and one ghost surface polariton (GSP-I). GSP-I can exist not only inside but also outside the AF reststrahlen frequency bands and originates from the external magnetic field. In Geometry-II with the easy axis in the propagation plane, we predicted another ghost surface polariton (GSP-II). GSP-II is a TE surface wave and is reciprocal. Another difference between the two GSPs is that the Poynting vector of GSP-I is of oscillation-attenuation but that of GSP-II monotonously decays with the distance from the surface and GSP-II exists only in the reststrahlen band without external magnetic field. This study further enlarges the family of surface polariton and widens the window of polariton application.

Unique Huygens-Fresnel electromagnetic transportation of chiral Dirac wavelet in topological photonic crystal

Light propagates in various ways depending on environment, including uniform medium, surface/interface and photonic crystals, which appears ubiquitously in daily life and has been exploited for advanced optics technology. We unveiled that a topological photonic crystal exhibits unique electromagnetic (EM) transport properties originating from the Dirac frequency dispersion and multicomponent spinor eigenmodes. Measuring precisely local Poynting vectors in microstrips of honeycomb structure where optics topology emerges upon a band gap opening in the Dirac dispersion and a p-d band inversion induced by a Kekulé-type distortion respecting C6v symmetry, we showed that a chiral wavelet induces a global EM transportation circulating in the direction counter to the source, which is intimately related to the topological band gap specified by a negative Dirac mass. This brand-new Huygens-Fresnel phenomenon can be considered as the counterpart of negative refraction of EM plane waves associated with upwardly convex dispersions of photonic crystals, and our present finding is expected to open a new window for photonic innovations.

Analysis of Power Transfer Characteristics of IPT System With Near Field Magnetic Coupling

This article investigates the working principle of the inductive power transfer (IPT) system from the perspectives of electromagnetic field distribution. According to the limitations of frequency and transmission distance, it is proved in this paper that the IPT system works in the near field, where the energy density of the magnetic field is much stronger than that of the electric field. Therefore, only the magnetic field in the IPT system needs to be considered in approximate power analysis. The mutual inductance model of the IPT system is an approximate and simplified form of the electromagnetic field model. The complex form of the Poynting vector of the IPT system is integrated over an intermediate infinite plane of the two coils to reveal the power transfer characteristics including the active and reactive power. When the system is in full resonance, only active power is transferred without reactive power, which is consistent with the results obtained from the circuit model. This article is useful to provide an insight into the power flow and energy distribution of the IPT system.

Complete transport of intensity equation for phase retrieval of optical vortex beams

We derive the complete form of the transport of intensity equation (TIE) for an arbitrary wave field, in which additional terms describing the effect of optical vortices are included. The Poynting vector of optical vortices goes in a spiral around the vortex core through space. Consequently, the intensity variation is not observable in the manner of wave propagation, thereby precluding the possibility of phase retrieval via near-field intensity measurements. This difficulty is elegantly overcome by introducing a hard-edged aperture, as a common procedure to produce the required Neumann boundary signal, to break the azimuthal symmetry of the propagation, and visualize the rotation of the beam’s local Poynting vector around the aperture boundary. The basic principle, numerical solution, and practical implementation of how to use this new version of TIE for phase retrieval of arbitrary wave fields including optical vortices are developed. Based on the new approach, we present the first experimental demonstration of non-interferometric phase retrieval of Laguerre–Gaussian vortex beams of different orders using only two near-field intensity measurements. Our results consummate the basic theoretical framework of TIE and represent an important step towards phase retrieval of arbitrary wave fields carrying phase singularities.

Power flux in the Schumann resonance band linked to the eruption of Tonga volcano on Jan. 15, 2022. (Two point measurements of Umov-Poynting vector)

Observations and model computations are compared of the Umov – Poynting vector (UPV) in the Schumann resonance (SR) band during the eruption of Tonga volcano on Jan. 15, 2022. The volcanogenic SR signals were recorded at the dual site: at the Cumiana observatory (44.96° N and 7.42° E) in the vertical electric field component and at the Sos Enattosobservatory (40.47° N, 9.48° E) in the two orthogonal ELF components of horizontal magnetic field. Initially, we present computations in the update model of the Earth – ionosphere cavity with the global lightning stroke distribution found by the Worldwide Lightning Location Network (WWLLN), which demonstrates the workability of our approach. The hodographs of UPV were obtained in the frequency (formally rigorous) and the time domain during the major phase of eruption. The positions of both of them suitably agree with each other and indicate on the wave arrival from the compact area around volcano during the major phase of Tonga eruption. The UPV magnitude indicates that the contribution from the Tonga volcano has elevated the observed level of ELF power flux by the factor of six relative to the quiet condition.

Adherence to and Deviation from the Inverse-Square Law of Intensity for Sound and Light

The concept of intensity—defined as power output per unit area—is often introduced when discussing sound waves and then revisited (via the Poynting vector) in discussing electromagnetic waves. The discussion is generally limited to isotropic media, with reflections and the resulting interference between waves being considered only in a limited context (such as resonances): the intensity is thus presented as obeying an inverse-square law with respect to the distance between source and observer. However, most actual demonstrations of the intensity–distance relationship (e.g., a speaker placed in a room) take place in an enclosed area, which results in reflections from the room’s boundaries (walls, ceiling, and floor) as well as from other objects in the room (desks, people, etc.). A consequence of these reflections is that the wave is no longer truly propagating in a uniform manner, but instead can interfere with its own reflections. The result of this interference is that the intensity does not ultimately follow an inverse-square law.