Poynting Vector Research Articles

Compressive Sampling Framework for 2D-DOA and Polarization Estimation in mmWave Polarized Massive MIMO Systems

The polarized massive multiple-input multiple-output (MIMO) technique has been regarded as a promising solution to millimeter wave (mmWave) communication systems, because it experiences more degrees-of-freedom than the scalar configuration, and it represents a significant opportunity for secure communication. To deliver smart service to terminals, it is essential to provide base stations (BS) with the capability of terminal’s direction-of-arrival (DOA) awareness. In this paper, a compressive sampling (CS) framework is proposed for two-dimensional (2D) DOA and polarization estimation in mmWave polarized massive MIMO systems. The proposed approach first reduces the data volume via a reduced-dimension matrix. Then it computes the signal subspace via the eigendecomposition of the compressed array measurement. Thereafter, the rotational invariance characteristic is utilized to form a normalized polarization steering vector. Finally, 2D-DOA and polarization are estimated by incorporating the Poynting vector and the least squares (LS) techniques. The proposed architecture is computationally much more economical than existing algorithms. Besides, it allows a mmWave BS to provide comparable estimation performance with arbitrary sensor geometry, which is more flexible than most of the existing architectures. Furthermore, it is robust to the sensor position error. Numerical simulations verify the advantages of the proposed framework.

Plasmon mediated extra-ordinary optical transmission through an apertureless plasmonic metagrating

Extra-ordinary optical transmission (EOT) through subwavelength plasmonic nanoapertures is possible due to the funneling of light via surface plasmons (SPs) at the resonant wavelengths through the apertures. In this Letter, we experimentally demonstrate EOT through a plasmonic metagrating which does not have any open apertures. The plasmonic metagrating was fabricated by deposition of silver (Ag) on a one-dimensionally patterned flexible and transparent polydimethylsiloxane grating obtained via pattern imprinting and subsequent peeling off a commercially available blue ray disk. For normal incidence of transverse magnetic-polarized light on the top surface of plasmonic metagrating, transmission of light through it was obtained in the visible wavelength range of electromagnetic spectrum. Control experiments on variation of Ag film thickness were performed to attain optimal parameters for maximum transmission, followed by polarization and refractive index (RI) dependent performance of the plasmonic metagrating. Electric fields and Poynting vector profiles were simulated using a finite element method to explain the interaction of light with the plasmonic metagrating and the mechanism of plasmon mediated optical transmission. Such a large optical transmission is possible because the SP modes generated at metal–air interface penetrate through metagrating and couple with those supported by the metal–substrate interface. As a model application, RI sensing using the plasmonic metagrating was demonstrated. The present study shows that optical transmission is possible from apertureless structures and enriches literature with better understanding of EOT. Moreover, it opens avenues for development of flexible, cost-effective plasmonic metagratings for sensors, spectral filters, polarizers, etc.

Constituents of electromagnetic 2-D layered media Green's functions for all material types and radiation conditions

Layered media Green's functions (LMGFs) are obtained for line sources with complex longitudinal wavenumbers in planarly layered media by numerically evaluating Sommerfeld integrals. The results obtained in this article can be applied to the numerical analysis of structures in layered media composed of any combination of right-handed materials (RHMs) and left-handed materials (LHMs). In the derivation, due to the complex-valued longitudinal wavenumber values, two different boundary conditions are used to include plane waves with: (i) decaying and (ii) outgoing Poynting vectors in the LMGFs. As a result, two completely different LMGFs are obtained by using two different radiation conditions and corresponding Sommerfeld integration paths (SIP) that are rigorously tailored on the complex integrand plane. In this work, all the necessary numerical tools for calculating the 2-D LMGFs are provided to be implemented in a computer program from scratch.

Tight-focusing properties of propagable fractional-order vector vortex beams

We investigate the tight-focusing properties of propagable fractional-order vector vortex beams (VVBs). The superposition of the phase singularity from optical vortices (OVs) and polarization singularity from VVBs plays a significant role in creating propagable fractional-order VVBs. Applying this unique characteristic, we derive an integrated analytical model to calculate the tight-focused electromagnetic fields and Poynting vector distributions based on the Richards–Wolf vector diffraction integral. The results show that the tight-focusing intensity of fractional-order VVBs exhibits uniaxial symmetric distribution, in which an odd number of petals with non-uniform amplitude occurs as the beams pass through the polarizer. In contrast to classical integer-order OVs with homogeneously polarized states, propagable fractional-order VVBs show semi-circular patterns with different directions after the polarizer, owing to their intriguing polarization distributions. Besides, to deeply understand the focusing characteristics of the calculated fractional-order VVBs, the influence of different-order carrier VVBs and OVs is studied in detail. These results might provide a valuable reference for particle manipulation and optical trapping.

Negative refraction and exceptional point with Parity-Time symmetry in a piezoelectric mechanical metamaterial

In this work, negative refraction and exceptional point (EP) in piezoelectric mechanical metamaterials are considered, which corporates with the Parity–Time (PT) symmetry. The oblique incidence of anti–plane shear wave at the interface between a homogeneous medium and phononic crystal can excite multiple refraction modes. In periodic layers, propagation characteristics are illustrated by the dispersion relation and transfer matrix method. The normal mode decomposition is developed and time average Poynting vector is used to derive the refraction angle at the interface of piezoelectric metamaterials. The beam splitting is shown with different incident angles, as well as the pure negative refraction is achieved. Due to the mechanical and electric coupling, the complex conjugate of Bloch wave number appears in the dispersion relation and degenerates to the exceptional point. In addition, a defect layer is introduced to study the transmission coefficient of two phononic crystals with different arrangements. When the gain and loss are introduced into the metamaterials, the Parity–Time symmetry system is realized and a complete transmission with a unidirectional zero reflection at exceptional point can be achieved.

Imaging phonon eigenstates and elucidating the energy storage characteristics of a honeycomb-lattice phononic crystal cavity

We extend gigahertz time-domain imaging to a wideband investigation of the eigenstates of a phononic crystal cavity. Using omnidirectionally excited phonon wave vectors, we implement an ultrafast technique to experimentally probe the two-dimensional acoustic field inside and outside a hexagonal cavity in a honeycomb-lattice phononic crystal formed in a microscopic crystalline silicon slab, thereby revealing the confinement and mode volumes of phonon eigenstates—some of which are clearly hexapole in character—lying both inside and outside the phononic-crystal band gap. This allows us to obtain a quantitative measure of the spatial acoustic energy storage characteristics of a phononic crystal cavity. We also introduce a numerical approach involving toneburst excitation and the monitoring of the acoustic energy decay together with the integral of the Poynting vector to calculate the Q factor of the principal in-gap eigenmode, showing it to be limited by ultrasonic attenuation rather than by phonon leakage to the surrounding region.

Orbital Angular Momentum Encoded Beam Tracking and Wavefront Sensing

The working principle of conventional Shack-Hartmann-type wavefront sensors is based on a wavefront division by two-dimensional microlens arrays and a Poynting vector mapping by comparing the focal displacements to reference measurements. At complex phase distortions or steep phase gradients, however, wavefront reconstruction can suffer from ambiguities by crossing or overlapping neighboring sub-beams, or even by a complete loss of beam trajectories. Moreover, the recognition of sub-beams can additionally be affected by parasitic reflections at optical surfaces, or scattering in a medium. A possible solution of the problem is to work with arrays of well distinguishable sub-beams. Recently, high-resolution pixelated liquid crystal spatial light modulators became available which enable to flexibly generate spatially structured light and thus to realize advanced wavefront sensors with individually encoded beams. In our experimental study we investigated the specific advantages of orbital angular momentum beams for a robust beam tracking and wavefront reconstruction. As a key point for a wavefront reconstruction from vortex arrays, the reliable detection of spiral-like image features is addressed and related strategies are proposed.

Reciprocity Theorem Applied to Scattering Coefficients of 2-D Anisotropic Metasurface With Polarization Conversion

In this letter, the scattering coefficients of periodic metasurface are studied based on the reciprocity theorem. According to the vector wave function theory, the incident and scattered waves can be decomposed into a series of Floquet’s modes. Thereby, the solution of closed surface integral from reciprocity theorem can be conducted in terms of scattering coefficients. It is verified that the scattering coefficients are equal for the reciprocal incident and scattered Floquet’s modes, regardless of the metal structure and substrate layer. Note that the scattering coefficient is generally unequal to the ratio between electrical fields of incident and scattered Floquet’s waves due to the normalized Poynting vector along the normal direction of the metasurface. Finally, an example is designed to support the proposed theory with great consistence. The theory extends the existing reciprocity theorem to periodic metasurface, enriching the physical connotation of the surface electromagnetics.

Indicatrix of TE and TM- polarized wave velocities in crystal of classes 4mm, 3m, 6mm with magneto-electric effect

This work is devoted to the theoretical study of the laws of propagation of electromagnetic waves of TE and TM polarization in anisotropic media belonging to classes 4mm, 3m, 6mm, etc. having a magnetoelectric effect. The directions of the vectors of the phase and group velocities of the polarization waves TE and TM at the boundary of a uniaxial crystal with magnetoelectric properties are considered. In the analytical form, the values of the directions of the phase and group velocities of the TE and TM waves are indicated, depending on the direction of the wave vector of the incident wave. The consequences of the obtained results for uniaxial crystals in the absence of magnetoelectric properties are discussed. The solution of the tasks set in this paper is based on the use of the matrix method. On its basis, various problems of wave processes in an isotropic elastic medium, electromagnetic waves in crystals, the distribution of coupled elastic and electromagnetic waves in piezoelectric and piezomagnetic media with a magnetoelectric effect were previously considered. In the presence of a magnetoelectric effect for electromagnetic waves propagating through uniaxial crystals, the parameters of the wave vector, phase and group velocities are determined. The obtained results are analyzed for electromagnetic waves propagating through uniaxial crystals in the absence of a magnetoelectric effect. The indicatrices of the wave vectors propagating in the plane and the phase velocities of the TM polarization waves are limited ( 0 ) x z. Based on the Rayleigh equation, the values of the group velocity are obtained. The density of electromagnetic energy fluxes and their components are determined for TE and TM waves. The energy transfer rate and its direction are determined. It is shown that the group velocities and directions obtained from the Rayleigh equation and the Umov-Poynting vector do not coincide.

Chorus Wave Properties From Van Allen Probes: Quantifying the Impact of the Sheath Corrected Electric Field

AbstractA sheath impedance model has recently been developed to describe how the variable coupling impedance between the Van Allen Probes instrumentation and the ambient plasma affects both the amplitude and phase of electric field wave measurements. Here, the impact of this sheath correction on measured chorus wave properties, including electric field wave power and the Poynting vector, is directly quantified. It is found that the sheath‐corrected electric field wave power is typically between two and nine times larger than the uncorrected measurement, depending on wave frequency. The sheath correction typically increases the Poynting flux by a factor of ∼2, and causes the polar angle of the Poynting vector to switch hemisphere from parallel to anti‐parallel propagation in ∼2% of cases. The uncorrected data exhibit significant deviations from the theoretically predicted relationship between the wave vector and the Poynting vector whereas this relationship is well‐reproduced with the sheath‐corrected observations.

Dressed Airy Vortex Beam in a Hot Atomic Medium

AbstractIntroducing vortices into an Airy beam by the interference between the lobes of the Airy beam for the first time, the modulation of Airy vortices is experimentally and theoretically investigated by electromagnetically induced transparency (EIT) effect and changing the number of side lobes of the Airy beam. The formation and disappearance of vortices in Airy beams can be caused by changing the number of side lobes. The EIT effect can induce the movement of vortex phase singularity by regulating the intensities of lobes in Airy beams. However, changing the number of side lobes can change the energy distribution of the lobes through the energy flow due to the self‐healing of Airy beams, thus causing the displacement of vortex phase singularity. In addition, the simulation of the Poynting vector shows that the less the side lobes are blocked, the more energy can be retained in the main lobe and the unblocked side lobes, so that the overall shape of the Airy beam can be better maintained. Such studies provide a new method to acquire and adjust Airy vortex beams and can be applied in the realm of optical micromanipulation.

Energy flow in light scattering by a small conducting sphere

Radiation energy scattered by a small particle can be expected to travel from the particle to a detector in the far field along the field lines of the Poynting vector. We consider the scattering off a small conducting sphere, for which only the induced electric and magnetic dipole moments contribute to the emitted radiation. Field lines of the energy flow due to interference between fields radiated by the electric and magnetic dipoles appear to form closed loops in the vicinity of the particle. Energy flows out of the particle at one side and then returns to the particle at the other side, and as such, this energy flow does not contribute to the radiated power. At larger distances, energy flows away from the particle at one side of the particle, but on the other side, radiation flows from infinity toward the particle. The energy for the scattered radiation is provided by the incident field. The energy flow is due to interference between the incident field and the scattered radiation, known as extinction. The flow pattern of this energy exhibits numerous singularities and vortices, and closed-loop flows near the particle. In the far field, energy flows along counter-oriented field line bundles, with only the net power flowing inward.

Electromagnetic angular momentum in anisotropic media and Beth's torque

The interaction of radiation with material media is a very active area of research, in particular the interaction with new exotic materials. However, we find several controversies in this field, like the Abraham-Minkowski controversy, or the attribution of angular momentum to quasi-static fields.In the present work we show that besides the electromagnetic momentum density proportional to Poynting's vector, whose time derivative is force and therefore can produce a torque, there are other momentum densities implied by the macroscopic Maxwell equations transformed into momentum balance equations. These momentum densities are also related to forces and torques. We show in this way that torques like D × E and B × H appear in these balance equations transformed into balance equations of angular momentum. The density D × E was used by Beth [Phys. Rev. 50 115–125 (1936)] to measure the angular momentum of radiation fields in interaction with anisotropic dielectrics. Our analysis show that also static or quasi-static fields carry angular momentum and produce torques when interacting with anisotropic materials.

Energy flow of strongly focused cylindrical vector beams on higher-order Poincaré sphere

Energy flow is an important dynamic characteristic of light field that has recently gained tremendous interest due to its useful applications in light–matter​ interactions. Using the Richards–Wolf vectorial method, a model for calculating the transverse and longitudinal components of the electric and magnetic fields as well as the Poynting vector of tightly focused vector beams on a higher-order Poincaré sphere is presented. The evolution of the energy flow in the tightly focused field is explored from the perspective of the Poincaré sphere. In addition, its relation to the optical degrees of freedom of the input field is revealed based on the model. Calculations reveal that ellipticity and handedness affect the magnitude and direction of the transverse energy flow, respectively, and have almost no effect on the longitudinal energy flow, while the orientation has no effect on both transverse and longitudinal energy flows. These findings may be helpful in applications that enable transport of particles.

Features of the behavior of quantum fields in media with a negative refractive index as well as waves with negative energy

In this paper, waves in media with both negative electrical and magnetic permeability and waves of negative energy have been considered together. All conditions have been established under which the propagation of such waves in the corresponding media is possible, taking into account the requirement of the quanta energy positivity. For each of these conditions the direction of the Poynting vector has been established.

Investigation on the Electromagnetic Surface Waves for Single-Wire Power Transmission

Single-wire power transmission (SWPT) is a power transmission method that uses only one wire to realize long-distance transmission of power. For deep insight, the theory of electromagnetic surface waves in this article is applied to reveal the principle of a long-distance large-scale SWPT system. Maxwell's equations under two different media in this system are established, based on them and the boundary conditions on the interface of the media, the propagation law of electromagnetic field energy in the SWPT system is analyzed. A simulation model is built by high frequency simulator structure (HFSS). The distribution law of the Poynting vector in different situations is studied to verify the correctness of the theoretical analysis. Moreover, long-distance transmission experiments are carried in the campus. It is shown that the transmission power can reach 300 W or 135 W when the transmission distance is 100 m or 200 m, respectively.

Light and Radio Radiations from a Moving Charged Particle

Two types of electromagnetic radiation are identified: light radiation and radio radiation. Light radiation is due to aberration of electric field in the motion of a charged particle in an external electric field, where energy radiated, proportional to the square of amplitude of velocity, is the difference between change in potential energy and change in kinetic energy. This is so with electrons revolving in the electric field of the nucleus of an atom. Radio radiation, due to finite speed of light, whereby an oscillating charged particle generates a magnetic field in phase with an electric field, at a point in space, resulting in generation of energy, proportional to the square of amplitude of acceleration, as from a radio antenna. The electric field in the Poynting vector is the sum of external accelerating field and internal induction field due to acceleration of a charged particle, in accordance with Faraday’s law. The induction field also acts on the same charge creating it, to produce the inertial force, equal and opposite to the accelerating force, thereby explaining the cause of inertia. Radio radiation explains the presence of Cosmic Microwave Background Radiation as a local phenomenon from within the atoms of a body

Exact and geometrical optics energy trajectories in Bessel beams via the quantum potential

The aim of the present work is to show that any monochromatic solution to the scalar wave equation in free space defines a conservative Hamiltonian system, describing a particle of mass m = 1 / 2 and energy E = 1 , under the influence of the so-called quantum potential. We remark that the integral curves of its Poynting vector, exact optics energy trajectories, define a particular subset of solutions to the corresponding Hamilton equations. Furthermore, we introduce the zero quantum potential straight lines concept, as the family of tangent lines to the integral curves of the Poynting vector at the zeros of the quantum potential. These general results are applied to a family of plane waves and to Bessel beams. In the case of Bessel beams, we present a detailed study of the trajectories determined by the corresponding Hamiltonian system, and we show that the zero quantum potential straight lines coincide with the geometrical light rays, geometrical optics energy trajectories. Furthermore, we show that the areal velocity, determined by the exact optics energy trajectories, for non-zero order Bessel beams is not a constant of motion. However, its projection along the z ^ direction is a constant of motion because L z is a constant.

Generalized Poincaré Beams in Tight Focus

We study the tight focus of generalized (hybrid) Poincaré beams. A conventional Poincaré beam is a coaxial superposition of two optical vortices, one with left circular polarization and a topological charge (TC) of m, while the other has a right circular polarization and a TC of −m. The generalized Poincaré beams are also composed of two optical vortices, but their TCs are different, for instance, p and q. Here, we theoretically investigate the generalized Poincaré beams with the TCs p = m + 1 and q = −m in tight focus. In this case, both transverse components of the strength vector of the initial electric field have a topological charge of 1/2, and the beam itself is a cylindrical vector beam of fractional order m + 1/2. Analytical expressions are derived for the components of the strength vectors of the electric and magnetic field at the focus as well as for the intensity distribution, the longitudinal component of the spin angular momentum (SAM), and for the components of the Poynting vector (energy flow density). We show that the intensity at the focus has 2m − 1 local maxima residing evenly in a certain circle radius with the center on the optical axis. We also demonstrate that the radial spin and orbital Hall effects occur at the focus, i.e., the longitudinal SAM component has different signs in the circles of different radii, and the azimuthal component of the transverse Poynting vector also has different signs.

Loss-gain compensated anti-Hermitian magnetodielectric medium to realize Tellegen nihility effects.

Generalized duality transformations significantly modify the constitutive relations of electromagnetic media, preserving principal electromagnetic properties. Here, we contemplate transformation of Tellegen nihility as a specific type of extreme-property nonreciprocal bi-isotropic media and show that some intriguing electromagnetic properties of that medium can be realized in a particular class of isotropic magnetodielectric media without magnetoelectric coupling. We show that the permittivity and permeability of the corresponding transformed medium have equal absolute values and opposite signs. Depending on the value of the Tellegen parameter of the original medium, the transformed magnetodielectric medium can be Hermitian, non-Hermitian, or anti-Hermitian, which simultaneously exhibits loss and gain. Focusing on the latter class of anti-Hermitian media, we theoretically and numerically demonstrate that this extraordinary medium allows propagation of electromagnetic plane waves having zero time-averaged Poynting vector, similarly to the original Tellegen nihility media. Hopefully, this work can open novel opportunities for manipulating electromagnetic fields.