Poynting Vector Research Articles

Meta-optics empowered by all-silicon quarter-wave plates for generating focused vortex beams

The Poynting vector associated with the focused vortex beam (FVB) that carries orbital angular momentum (OAM) is oriented in a twisted manner relative to the principal axis of propagation. This characteristic has significant applications in advanced fields, including high-dimensional information processing, high-resolution imaging, and particle manipulation. Currently, complex optical systems that operate on alignment principles for generating FVBs have been miniaturized by metasurfaces, resulting in the achievement of polarization-dependent vectorized behavior. Nevertheless, generating and manipulating FVBs that carry OAM in the terahertz (THz) range remains a significant challenge. This difficulty arises particularly when utilizing quarter-wave plates (QWPs) that serve both polarization conversion and polarization filtering functions. Here, we experimentally demonstrate a planar all-dielectric array capable of generating FVBs with high power density within a single-handed circularly polarized channel. Engineered QWP meta-atoms are utilized as candidates for the efficient generation of the desired FVB through the application of dynamic phase gradients. A series of samples were fabricated to assess the effectiveness of this design strategy in converting an incident linearly polarized THz beam into arbitrary single-handed circularly polarized FVBs. Leveraging the high degree of freedom inherent in polarization multiplexing coding, the proposed QWP metasurface can generate FVBs exhibiting topological charge evolution along the longitudinal direction. This capability further underscores its robust polarization modulation proficiency. This work presents a generalized framework for the polarization-dependent generation of ultracompact structural optical fields, which may have potential applications in highly integrated THz communication systems.

Origins of Electromagnetic Radiation from Spintronic Terahertz Emitters: A Time-Dependent Density Functional Theory plus Jefimenko Equations Approach.

Microscopic origins of charge currents and electromagnetic (EM) radiation generated by them in spintronic THz emitters-such as, femtosecond laser pulse-driven single magnetic layer or its heterostructures with a nonmagnetic layer hosting strong spin-orbit coupling (SOC)-remain poorly understood despite nearly three decades since the discovery of ultrafast demagnetization. We introduce a first-principles method to compute these quantities, where the dynamics of charge and current densities is obtained from real-time time-dependent density functional theory, which are then fed into the Jefimenko equations for properly retarded electric and magnetic field solutions of the Maxwell equations. By Fourier transforming different time-dependent terms in the Jefimenko equations, we unravel that in the 0.1-30THz range the electric field of far-field EM radiation by the Ni layer, chosen as an example, is dominated by charge current pumped by demagnetization, while often invoked magnetic dipole radiation from the time-dependent magnetization of a single magnetic layer is a negligible effect. Such an effect of charge current pumping by a time-dependent quantum system, whose magnetization is shrinking while its vector does not rotate, does not require any spin-to-charge conversion via SOC effects. In the Ni/Pt bilayer, EM radiation remains dominated by the charge current within the Ni layer, whose magnitude is larger than in the case of a single Ni layer due to faster demagnetization, while often invoked spin-to-charge conversion within the Pt layer provides an additional but smaller contribution. By using the Poynting vector and its flux, we also quantify the efficiency of conversion of light into emitted EM radiation, and its angular distribution.

Optical skyrmion and its "zipper-like" topological behavior in an energy flux field.

The optical skyrmion and its topological behavior are analyzed in an energy flux field constructed by an X-type vortex in a high numerical aperture system. The conditions for the formation of a skyrmion structure in this field are discussed, showing that the vortex pattern of the transverse energy flow and the inverse energy flow are crucial for the skyrmions and also are controlled by the phase gradient of the X-type vortex. Notably, the "zipper-like" topological reaction, which is the first, to our knowledge, found in ferromagnetic materials, is observed, and the physical mechanism is also explained by the relation of orbital angular momentum density and Poynting vectors. The results will reach the topological theory and may have applications in optical traps and data storage.

The qP- and qSV-wave separation in 2D vertically transversely isotropic media and their applications in elastic reverse time migration

Compressional and shear wave separation is an important step in anisotropic elastic reverse time migration (ERTM). With separated wavefields, we can generate images between different wave types and reveal more subsurface physical properties, as well as remove unwanted crosstalk and improve image quality. Traditional Helmholtz decomposition based on divergence and curl operations for isotropic media cannot be directly extended to vertically transversely isotropic (VTI) media. Wave-mode separation methods, similar to the nonstationary spatial filter and Poynting vector, cannot preserve the phase and amplitude information of the original coupled wavefield, thus limiting their application in ERTM. Currently, the anisotropic wavefield decomposition methods include the wavenumber-domain approach, the low-rank approximation, and other separation approaches based on different approximations, e.g., weak or elliptical anisotropy. These methods are either computationally intensive or involve large separation errors, especially in models with strong heterogeneities and anisotropy. The VTI wavefield separation operator is essentially defined in a mixed space-wavenumber domain. We introduce scalar operators to transfer operations from this mixed space-wavenumber domain to the space domain. The local wave propagation direction in the scalar operators is estimated using the Poynting vector, which is highly computationally efficient in the space domain. When we apply the wave separation method to ERTM, we not only obtain the vectorized qP and qSV waves but also retrieve the scalar qP wavefield. The scalar and vector wavefields preserve the amplitude and phase information in the original coupled wavefield. For anisotropic ERTM, we suggest using the scalar imaging condition to generate the PP image and the magnitude- and sign-based vector imaging condition to produce the PS image, both having higher image accuracy than the dot-product imaging condition. Numerical examples are used to validate our anisotropic wavefield separation method and the related ERTM workflow.

Angle-dependent image-domain least-squares migration through analytical point spread functions

Image-domain least-squares migration (IDLSM) is an established approach to recover high-fidelity seismic images of subsurface reflectors; this is achieved by removing the blurring effects of the Hessian operator in the standard migration approach with the help of so-called point spread functions (PSFs). However, most of the existing IDLSM approaches recover an angle-independent image of the subsurface reflectors, which is not suitable for subsequent amplitude-variation-with-angle (AVA) analysis. To overcome this limitation, we have developed an angle-dependent IDLSM approach, denoted as AD-IDLSM, which can recover a high-fidelity and high-resolution angle-dependent reflectivity image of subsurface reflectors. The problem is formulated here as an angle-dependent image-domain inversion with PSFs computed by means of full-wave Green’s function. More specifically, we derive an analytical expression to compute angle-dependent PSFs by means of a wave-equation-based Kirchhoff migration (WEBKM) engine, where a localization assumption is made in both spatial directions to decrease the computational cost and memory overhead. The amplitude and traveltime of the Green’s functions involved in the WEBKM approach are estimated by the excitation amplitude and excitation time of the full-wave wavefield. The scattering angle is then approximately estimated from the Poynting vector of the excitation-time field. To stabilize the solution of AD-IDLSM, we use a regularization scheme that applies a second derivative along the direction of the reflection angle of angle-domain common-image gathers (ADCIGs) to ensure continuity in the amplitude variations versus angle and suppress migration artifacts. We demonstrate the effectiveness of the AD-IDLSM approach through two synthetic and one field marine data set; the presented results confirm that AD-IDLSM can create ADCIGs with higher spatial resolution, better amplitude fidelity, and fewer migration artifacts compared with those obtained by its migration counterpart. Moreover, AD-IDLSM amplitude variations with angle are shown to closely resemble the theoretical AVA curve of the reflectors.

Topological Structures of Energy Flow: Poynting Vector Skyrmions.

Topological properties of energy flow of light are fundamentally interesting and may introduce novel physical phenomena associated with directional light scattering and optical trapping. In this Letter, skyrmionlike structures formed by Poynting vectors are unveiled in the focal region of two pairs of counterpropagating cylindrical vector vortex beams in free space. The appearance of local phase singularities, and the distinct traveling and standing wave modes of different field components passing through the focal spot lead to a Néel-Bloch-Néel transition of Poynting vector skyrmion textures along the light propagating direction. By shaping the wave front of the incident beams with patterned amplitudes, the topological invariant of the Poynting vector skyrmions can be further tuned in a prospective area. This work expands the family of optical skyrmions and holds great potential in energy flow associated applications.

2D acoustic equation prestack reverse-time migration based on an optimized combined compact difference scheme

Abstract Reverse-time migration (RTM) is widely regarded as one of the most accurate migration methods available today. A crucial step in RTM involves extending seismic wavefields forward and backward. Compared to the conventional central finite-difference (CFD) scheme, the combined compact difference (CCD) scheme offers several advantages, including a shorter difference operator and the suppression of numerical dispersion under coarse grids. These attributes conserve memory and enhance effectiveness while maintaining the same level of differential precision. In this article, we begin with the five-point eighth-order CCD scheme and utilize the least squares method and Lagrange multiplier method to optimize the difference coefficients. This optimization is guided by the concept of dispersion-relation-preserving (DRP). The result is the acquisition of an optimized combined compact difference (OCCD) scheme, further enhancing the ability to suppress numerical dispersion. We thoroughly compare and analyze dispersion relationships and stability conditions. In addition, we examine several crucial steps in the RTM of the second-order acoustic wave equation. These steps include absorption boundary conditions, boundary storage strategy, and Poynting vector imaging conditions. Finally, we apply both the CCD and OCCD schemes in the RTM of the layered model, graben model, and SEG/EAGE salt model. We compare these results with those obtained from CFD's RTM. Numerical findings demonstrate that, in contrast to the CFD scheme, the CCD scheme effectively suppresses numerical dispersion and enhances imaging accuracy. Moreover, the optimized OCCD scheme further improves the ability to suppress numerical dispersion and can obtain better imaging results, which is an effective RTM method suitable for coarse grid conditions.

Investigation of an absorption plasmonic electro-optical modulator based on the free carrier dispersion effect in the aluminum doped zinc oxide layer

A plasmonic electro-optical modulator, which is based on the free carrier dispersion effect, has been introduced here. The structure of the proposed modulator is a substrate of fused silica/gold/aluminum doped zinc oxide/hafnium dioxide/gold/air. The free carrier dispersion effect occurs in the aluminum doped zinc oxide (AZO) layer. As the electrical permittivity of the AZO layer is near zero (the epsilon near zero effect) at a wavelength of 1.55 μm, the amplitude of an electrical field is high in this layer, therefore, the modulator is highly sensitive to the varying refractive index of this layer. By applying a voltage to two gold layers, the electrical charge density changes in the AZO layer. Therefore, the real and imaginary parts of the refractive index have been changed, which led to a change in the absorption of the modulator. In order to obtain the charge density distribution in the AZO layer, the Poisson equation is solved by using the finite difference method. To investigate modulator absorption, the Nelder-Mead method is implemented in order to solve the dispersion equation numerically. Finally, the magnetic field, the electric field, and the time average of the Poynting vector have been given by using the least squares approximation method.

Paraxial propagation characteristics of a controllable anomalous hollow vortex beam in free space

Propagation of a recently proposed controllable anomalous hollow vortex (CAHV) beam is investigated. Based on the integral formula of generalized Huygens–Fresnel diffraction, analytical expression for the CAHV beam through a paraxial ABCD optical system is derived. The factors that affect the intensity pattern are determined by the beam’s controllable parameters a, c x, c y, and the topological charge m. Results show that the Gaussian distribution features are controlled by parameter a, and the horizontal and vertical stretching deformations of the beam are adjusted by parameters c x and c y, respectively. For a controllable anomalous hollow (CAH) beam, when propagating in free space, it could initially maintain anomalous hollow property and the size of the spot increases with the increase of the propagation distance. Due to the CAHV beam carries the optical vortex, a dark hollow channel appears in the center of the beam during propagation, and the channel structure changes with the increase of topological charge. Additionally, the Poynting vector of CAHV beam proves the direction of energy flow corresponding to the intensity distribution. Results obtained in this paper could have potential applications in particle trapping and optical control.

A decomposition of light’s spin angular momentum density

Light carries intrinsic spin angular momentum (SAM) when the electric or magnetic field vector rotates over time. A familiar vector equation calculates the direction of light’s SAM density using the right-hand rule with reference to the electric and magnetic polarisation ellipses. Using Maxwell’s equations, this vector equation can be decomposed into a sum of two distinct terms, akin to the well-known Poynting vector decomposition into orbital and spin currents. We present the first general study of this spin decomposition, showing that the two terms, which we call canonical and Poynting spin, are chiral analogies to the canonical and spin momenta of light in its interaction with matter. Like canonical momentum, canonical spin is directly measurable. Both canonical and Poynting spin incorporate spatial variation of the electric and magnetic fields and are influenced by optical vortices. The decomposition allows us to show that a linearly polarised vortex beam, which has no total SAM, can nevertheless exert longitudinal chiral pressure due to equal and opposite canonical and Poynting spins.

Harmonic power flow under non-sinusoidal conditions

This article aims to analyze the electric field and the flow of electromagnetic energy in power cables with copper and aluminum cores, without considering the implicit physics of the coating that surrounds the conductor, which is generally composed of XLPE. Computational simulations were carried out with two models of alternating electrical current (AC) intensities, with a frequency of 60 HZ, electrical voltage of 1 kV, in a transient regime, with a phase difference of 120° and considering the lengths of the cables at a value of L = 30 m. Applying a Fourier series expansion to a sinusoidal electric current and expanding to the third term of the series, resulting in a new formulation of the electric current that was called modified electric current. The peculiarity of this research lies in the fact that, through the Fourier series expansion of conventional alternating current, a transformation to a modified current was observed, presenting behavior analogous to that of a Rectifying Diode. The improvements provided by this method include increased efficiency in the transmission of electrical energy, reduction of voltage drops, reduction of losses associated with the Joule-Lenz effect and extension of the useful life of the cable. The results demonstrated that, by modifying the electric current, the electric fields and Poynting vectors were calculated and approached the solutions of Maxwell's equation for conventional electric current, in both types of power cables. In addition, this approach has been observed to be particularly effective for power cables with a length of 30 m, and using the modified current in Maxwell's equations to compare the electric and Poynting fields with those calculated using conventional electric current. Therefore, the results obtained are satisfactory for both power cables.

Effective method for photonic jet shaping in reflection mode.

We report an effective method to shape a photonic jet (PJ) generated by a dielectric cuboid scatterer on a hollow reflection screen. The study focuses on the shaping of PJ by hollow and cuboid geometries, including side length, depth, and position. The results show that all the geometric parameters can effectively shape the PJ in characteristic parameters of intensity, focal length (FL), and lateral size. The comparison shows that the present shaping method is much superior to the previously reported one based on a change of cuboid height, characterized by three times larger of the varying ranges of the PJ characteristic parameters. The shaping by the side length and depth of hollow and cuboid is explained from viewpoints of ray optics and electromagnetic field theory in terms of hollow-induced phase singularity in Poynting vector distribution. The hollow position mainly shapes the propagation trajectory of PJ. The deviation of the hollow position results in the curvature of the propagation trajectory of PJ, and the curvature is correlated with the asymmetric extent of the scattering system.

Nonlinear electrodynamics for the vacuum of Dirac materials: Photon magnetic properties and radiation pressures

We investigate the magnetic properties of photons propagating through Dirac materials in a magnetic field, considering both vacuum and medium contributions. Photon propagation properties are obtained through a second-order expansion of nonlinear Euler-Heisenberg electrodynamics at finite density and temperature considering Dirac material parameters (Dirac fine structure constant, band gap, and Fermi velocity). Total magnetization (including electron and photon contributions) and photon-effective magnetic moment are computed. Observables such as photon energy density, radiation pressure, and Poynting vector are obtained by an average of components of the energy-momentum tensor. All quantities are expressed in terms of Lagrangian derivatives. Those related to the vacuum are valid for any value of the external magnetic field, and both the weak- and strong-field limits are recovered. We discuss some ideas of experiments that may contribute to testing in Dirac materials the phenomenology of the strong magnetic field in the quantum electrodynamic (QED) vacuum and how nonlinear corrections on the magnetization, radiation pressure, and birefringence are amplified up to 103 times QED corrections. Published by the American Physical Society 2024

Elastic reverse time migration based on first-order velocity-dilatation-rotation equations using the optical flow vector

The determination of the P- and S-wave propagation directions is crucial for wavefield decomposition, polarity reversal correction, and noise suppression in elastic reverse time migration (RTM). Compared with the conventional decoupled elastic wave equation, the first-order velocity-dilatation-rotation equations enable more accurate computation of propagation directions for P and S waves. Moreover, compared with the Poynting vector, the optical flow vector signifies the wavefield propagation directions more accurately. To effectively enhance the accuracy of elastic wave imaging, we develop an elastic RTM based on first-order velocity-dilatation-rotation equations using the optical flow vector. Numerical tests illustrate that our method, with or without noise, can better eliminate migration artifacts and improve the imaging accuracy of the elastic RTM than conventional methods, achieving more accurate wavefield decomposition and superior S-wave polarity reversal correction.

Revisiting optical absorption power density of inhomogeneous plane waves

We review the analytical expressions for the complex Poynting’s vector in the case of arbitrary plane-waves in a lossy isotropic medium. We demonstrate how these expressions can be used to recover the optical absorption power density Q, considering the divergence of the time-averaged Poynting vector. This quantity, proportional to the imaginary part of the dielectric function and the field intensity, i.e. Q∝|E|2ɛ”, is usually established for harmonic fields, using the Poynting’s identity. The derivation from the complex Poynting vector expression is more direct for TE-polarized homogeneous waves, but the derivation encompasses the other cases like inhomogeneous TM plane waves. As an application, the optical absorption profile Q(x) within 1D multilayers is detailed using matrix transfer method for both TE and TM plane waves, including the evanescent case.

A new stress tensor approach for application to the conductor surface

PurposeThe purpose of this paper is to derive a new stress tensor for calculating the Lorentz force acting on an arbitrarily shaped nonmagnetic conductive specimen moving in the field of a permanent magnet. The stress tensor allows for a transition from a volume to a surface integral for force calculation.Design/methodology/approachThis paper derives a new stress tensor which consists of two parts: the first part corresponds to the scaled Poynting vector and the second part corresponds to the velocity term. This paper converts the triple integral over the volume of the conductor to a double integral over its surface, where the subintegral functions are continuous through the different compartments of the model. Numerical results and comparison to the standard volume discretization using the finite element method are given.FindingsThis paper evaluated the performance of the new stress tensor computation on a thick and thin cuboid, a thin disk, a sphere and a thin cuboid containing a surface defect. The integrals are valid for any geometry of the specimen and the position and orientation of the magnet. The normalized root mean square errors are below 0.26% with respect to a reference finite element solution applying volume integration.Originality/valueTensor elements are continuous throughout the model, allowing integration directly over the conductor surface.

Investigation of super-resolution in microsphere-assisted microscopy with the Poynting vector of the dipole model.

In this paper, the Fourier spectrum of an image in microsphere-assisted microscopy (MAM) and the wavenumber decomposition of the Poynting vector of the dipole model are compared for the first time to study the super-resolution performance within several wavelengths in MAM. Firstly, an experiment using microsphere-assisted microscopy is performed, and the fast Fourier transformation (FFT) spectra of the images along the distance are studied. Then the Poynting vector in the point dipole field is theoretically investigated based on the spectral decomposition of dyadic Green's function. Our study finds that the result of decomposition of the Poynting vector corresponds with the propagation results of components with different transverse wavenumbers kρ in an experiment. Even when kρ reaches 1.7k0, the waves can still arrive outside one wavelength. Our work is the first effort (to our knowledge) to associate the Fourier spectrum and the decomposition of the Poynting vector together, and it may contribute to the quantitative exploration of super-resolution performance in MAM in the future.

Guided wave propagation in a three-layer functionally graded piezoelectric cylinder with graded-index effects

The paper introduces a semi-analytical method, the Legendre polynomial approach (LPA), for solving the three-dimensional axisymmetric vibrations problem induced by the piezoelectric effect in a three-layer functionally graded (FG) cylinder. While previous studies have limited the application of LPA to wave propagation in multilayer functionally graded structures without considering the piezoelectric effect, this study presents a novel approach that effectively integrates both aspects without imposing restrictions, thus preserving their overall physical properties. By enabling a comprehensive analysis of the combined effects, this approach offers valuable insights into the behavior and characteristics of piezoelectrically multilayer FGM. The study investigates the influence of configuration and piezoelectric effects on dispersion curves. Results, with a maximum error of 0.98 %, confirm the efficiency of the expanded modeling approach. Notably, the normalized frequency is found to be influenced by the piezoelectric coefficients, and the addition of a third layer in the FGP structure significantly impacts wave propagation properties. Furthermore, insights from Poynting vectors shed light on energy transfer direction and the distinct characteristics of various vibration modes. This research expands our understanding of wave behavior in complex structures, offering novel opportunities for engineering applications and materials science. By leveraging the piezoelectric effect, guided wave systems could be designed and optimized for various industries, including non-destructive testing and structural integrity assessment.

Optical flow vector of elastic waves in transversely isotropic media

The propagation direction of the wavefield is particularly important for migration imaging in the reverse-time migration (RTM) of elastic waves in transversely isotropic (TI) media. However, due to the problem of the computational instability of the Poynting vector, the wave field propagation direction estimated based on the Poynting vector method has errors and cannot accurately indicate the real propagation direction of the elastic wavefield. To solve this problem, a method for calculating the optical flow vector of elastic waves in TI media is developed to obtain the propagation direction. The optical flow vector of elastic waves in TI media is determined by applying the spatial and temporal derivatives of the wavefield at each time step under the assumption that the wavefields are almost the same at subsequent time steps and are smooth in the spatial direction. As the additional smoothing item is added and the multiple iterative algorithm is introduced in calculating the optical flow vector, the direction is calculated more accurately than the Poynting vector. Based on the optical flow vectors, we can separate the source wavefield and receiver wavefield into four directions: up-going, down-going, left-going, and right-going wavefields, respectively, and finally perform elastic reverse-time migration (ERTM) imaging based on the optical flow vector traveling-wave separation. We use a layered model and the BP model to test our method. The testing results demonstrate that the optical flow vector can overcome the Poynting vector limitations and obtain more accurate and reliable information regarding the direction of elastic wave propagation in TI media, as well as precisely separate the wavefields. The separated wavefields for migration effectively improve the quality of the ERTM.

Generation of reverse time migration dip gathers with the stabilized Poynting vector and their application in the improvement of subsalt images

Subsalt imaging is challenging with coherent noise prevalent beneath complex salt structures. The coherent noise degrades the imaging quality, making image enhancement and interpretation difficult and potentially erroneous. The dip gathers of reverse time migration (RTM) serve as an ideal domain for separating signals from coherent noise due to their distinct distributions in the dip domain. Methods utilizing the Poynting vector offer an efficient and cost-effective means to produce dip gathers. However, the presence of zero points in the Poynting vector causes instabilities in direction or angle estimation, leading to the leakage of reflection energy into false dip angles. This issue complicates the separation of desired signals from coherent noise. We address this instability by employing a stabilized Poynting vector to produce high-quality RTM dip gathers. The stabilized Poynting vector does not contain zero points within the range of wave propagation, thus mitigating the instability problem. The dip gathers generated using the stabilized Poynting vector provide a clearer and more precise depiction of signal and noise distributions, allowing us to identify the boundaries of desired signals and mute all noise outside these boundaries. Two numerical examples with a synthetic dataset and a field dataset are used to demonstrate our method's effectiveness in reducing coherent noise and improving quality of subsalt images.