E-field Research Articles

The variation of the electric field along optic fiber for null Cartan and pseudo-null frames

In this paper, we introduce new frame and new transformation associated with combined Korteweg–de Vries–modified Korteweg–de Vries (KdV–mKdV) equation, the mKdV and the KdV equations with respect to the null Cartan frame in Minkowski 3-space. Direction of the state of polarization of monochromatic linear polarized light wave traveling in the optic fiber is given by the direction of electric field vector. We show that the electric field vector [Formula: see text] can be expressed as a linear combination of null Cartan frame apparatus using this new transformation in Minkowski 3-space. Later, we study rotation of the polarization plane along optic fiber according to null Cartan frame and Frenet frame of pseudo-null curve in Minkowski 3-space. Finally, we obtain Lorentz force equations via null and pseudo null electromagnetic curves.

Over-the-Air Array Calibration of mmWave Phased Array in Beam-Steering Mode Based on Measured Complex Signals

Accurate knowledge of initial complex excitation coefficients for phased-array elements is essential to ensure accurate array performance. In the literature, many array calibration algorithms have been proposed for this purpose, which generally requires customized phase setting for individual phase shifters connected to array elements. In this article, a new array calibration method is proposed for phased array operating in beam-steering mode only, that is, phase shifts of elements are only simultaneously set according to the beam-steering directions, and therefore, there is no need for dedicated individual element phase tuning. The proposed method requires a minimum number of complex-signal measurements in principle, which enables fast measurement. Furthermore, it is found that the performance of the proposed method is determined by the beam-steering matrix, whose condition number is mainly ruled by the beam-steering angle interval. The proposed method is numerically simulated and experimentally validated in a millimeter-wave (mmWave) phased-array antenna-in-package (AiP) platform at 28 GHz. The proposed method presents good agreement with the well-known rotating element electric field vector (REV) array calibration method, with an amplitude error and phase error within ±0.5 dB and ±5°, respectively. Furthermore, the reconstructed array pattern with the proposed method offers excellent match with the measured array pattern.

Attractive inverse-square–type interaction induced by Lorentz symmetry violation by fixed vector background

Based on a model that goes beyond the Standard Model, we study quantum effects of the violation of the Lorentz symmetry at a low-energy regime. From a background of the Lorentz symmetry violation determined by a space-like vector field and electric fields, we obtain an attractive inverse-square–type interaction. In addition, we obtain the bound-states solutions to the Schrödinger equation.

Multi-Electrode Architecture Modeling and Optimization for Homogeneous Electroporation of Large Volumes of Tissue

Electroporation is a phenomenon that consists of increasing the permeability of the cell membrane by means of high-intensity electric field application. Nowadays, its clinical application to cancer treatment is one of the most relevant branches within the many areas of electroporation. In this area, it is essential to apply homogeneous treatments to achieve complete removal of tumors and avoid relapse. It is necessary to apply an optimized transmembrane potential at each point of the tissue by means of a homogenous electric field application and appropriated electric field orientation. Nevertheless, biological tissues are composed of wide variety, heterogeneous and anisotropic structures and, consequently, predicting the applied electric field distribution is complex. Consequently, by applying the parallel-needle electrodes and single-output generators, homogeneous and predictable treatments are difficult to obtain, often requiring several repositioning/application processes that may leave untreated areas. This paper proposes the use of multi-electrode structure to apply a wide range of electric field vectors to enhance the homogeneity of the treatment. To achieve this aim, a new multi-electrode parallel-plate configuration is proposed to improve the treatment in combination with a multiple-output generator. One method for optimizing the electric field pattern application is studied, and simulation and experimental results are presented and discussed, proving the feasibility of the proposed approach.

A new radio-frequency acoustic method for remote study of liquids

In the present work, a novel study method of conductive liquids has been proposed. It is based on a discovered phenomenon of radiofrequency anisotropy of electrolyte solution, which arises in response to mechanical excitation of the solution. The phenomenon was observed during the development of a radiofrequency polarimetric contactless cardiograph. The electric field vector rotates after its transition through the pericardial region due to the acceleration changes of blood. Numerous in vitro experiments with monochromatic and impulse acoustic waves always induced the polarization rotation of the RF wave passing through an electrolyte solution. The response obtained from the solutions on acoustic excitation of the Heaviside function form demonstrates the effect of a solution “memory”. The dynamics of this process resembles the spin glasses magnetization. We hypothesized that there was a magnetic moment change within the solution, and the possible reason for it is an appearance of electromagnetic impulse caused by the same acoustic excitation. In a further experiment, we really captured a suspected electrical potential. Given that, we can declare at least three new physical effects never observed before for an electrolyte solution. The study method itself may provide broad options for remote measurement of the electrolyte solution parameters.

Method to Enhance Directional Propagation of Circularly Polarized Antennas by Making Near-Electric Field Phase More Uniform

A new approach to significantly increase the uniformity in aperture phase distribution, through time synchronization in the near-electric field, of circularly polarized (CP) antennas is presented. The method uses the phase of the CP electric field vectors, obtained through full-wave numerical simulations, and does not rely on any approximation such as ray tracing. The near-field data is post-processed to extract the relative phase difference that exists due to the unsynchronized rotations of the electric field vectors in a plane parallel to the antenna aperture. The phase delay is compensated with a thin time-synchronizing metasurface (TSM) that has a 2-D array of time-delay cells. The method is demonstrated with a prototype made of a two-port patch antenna, which is fed through a hybrid junction, and a TSM that is placed at one wavelength spacing above the patch. When TSM is used with patch antenna, its uniform phase area increases manifold thus increasing far-field directivity from 6.8 to 22 dBic.

Nanoimprinting metal-containing nanoparticle-doped gratings to enhance the polarization of light-emitting chips by induced scattering

Polarized radiative luminous semiconductor chips have huge application potential in many highly value-added fields. The integration of a subwavelength grating is recognized to be the most promising method for the development of polarized chips, but still faces the challenge of low polarized radiative performance. This paper describes a proposal for, and the development of, a scattering-induced enhanced-polarization light-emitting diode chip by directly nanoimprinting a metal-containing nanoparticle-doped grating onto the top surface of a common flip chip. The rate at which quantum-well light emission is used by the developed polarized chip is improved by more than 30%. More attractively, the doped scattering nanoparticles function as a scattering-induced polarization state converter that is sandwiched in between the top aluminum grating and the bottom silver reflector of the chips. The originally non-radiated light, with an electric-field vector parallel to the grating lines, is reflected back and forth inside the sandwich until it changes to the perpendicular vibration mode and is radiated outside the chip. Therefore, the polarization extinction ratio is greatly improved, compared to undoped samples.

Three-dimensional magnetotelluric modeling using the finite element model reduction algorithm

This study presents a fast and efficient vector finite element method, based on the model reduction algorithm, to simulate the 3-D magnetotelluric response. Firstly, we derive a finite element governing equation based on electric field vector from Maxewell's equations Then we express the electric field by a function of frequency parameter to get a transfer function that can be approximated by the Krylov subspace model reduction algorithm. The transfer function after model reduction has far lower dimensions than the original one, and it can be directly solved by the Pardiso solver. Therefore, the computational efficiency is significantly improved. For validation, we compare the proposed algorithm with the 3-D direct finite element method (3DFEM) by a three-layer model, and the results show that the computation time of the former is less than 1/10 of the latter for the same accuracy. We also compare the electromagnetic response obtained by the proposed method with that obtained by two classical models, COMMEMI 3D-2A Model and Dublin Test Model 1. These results agree well, indicating that the proposed method is feasible and efficient for 3-D magnetotelluric forward modeling.

Light refraction from a uniaxial crystal with arbitrary optic axis orientation using matrix representation

We have studied theoretically the refraction of a light beam in a uniaxial crystal plate by observing the electric field vector components, for an arbitrary orientation of optic axis with respect to plane of incidence and plane of interface. The electric field components for ordinary and extraordinary light beams are studied with varying the angle of optic axis with respect to plane of incidence and crystal surface and also with angle of incidence, in order to find the optimized position of optic axis orientation for various application prospects. We have used the matrix formulation to transform and simplify the electric field components from principal coordinate of crystal to the laboratory coordinate frame of crystal plate. It was observed that when optic axis is in the plane of incidence and optic axis is in the surface of crystal plate, ordinary and extraordinary beams have nonzero x and y components. While in other cases when optic axis is perpendicular to the plane of incidence and perpendicular to the surface of crystal plate, ordinary beam and extraordinary beams have only y and x components, respectively.

Tight focusing of the centrosymmetric shape of hybrid polarized beams by adjustable multi-vortex phases

We propose an approach for achieving various centrosymmetric shapes by employing hybrid polarized Bessel–Gaussian (HPBG) beams with multi-vortex phases, which are obtained by embedding a few first-order off-axis topological charges into vortices separated by equal arc lengths of a circle. According to the Debye–Wolf electromagnetic diffraction formula (which is routinely used to describe focusing by high numerical aperture optical systems), we investigate the evolution of tightly focused intensity profiles of the HPBG beams with multi-vortex phases (which are the vectorial electric field of radial and azimuthal polarization), by tuning the positional vectors of the embedded vortex phases, the number of vortex phases and the ratio of radial to azimuthal polarization of the hybrid polarization. The simulation results show that the number of vortex phases is equal to the number of vertices of hollow polygons, increasing the magnitude of polar vector leads to deformation of the hollow polygons, and that the ratio of the radial and azimuthal polarization magnitudes affects the edge sharpness of the hollow polygon in the focal plane, respectively. We can produce triangles, squares, pentagons, hexagons, and inner crosses in the central hollow region, and outer crosses, embedded stars and snowflakes by manipulating the numbers and sites of multi-vortex phase singularities. The focusing structures are robust to noise and maintain a limited thickness along the optical axis. These specific intensity profiles are significant for potential applications including the trapping of multiple micro-sized particles, nonlinear optics, optical beam shaping, and optical telecommunication applications.

Insight on the Coupling of Plasmonic Nanoparticles from Near-Field Spectra Determined via Discrete Dipole Approximations.

Coupling between plasmonic nanoparticles (NPs) in nanoparticle assemblies has been investigated extensively via far-field properties, such as absorption and scattering, but very rarely via near-field properties, and a quantitative investigation of near-field properties should provide great insight into the nature of the coupling. We report a numerical procedure to obtain reliable near-field spectra (Q NF) around spherical gold nanoparticles (Au NPs) using Discrete Dipole Approximation (DDA). The reliability of the method was tested by comparing Q NF from DDA calculations with exact results from the Mie theory. We then applied the method to examine Au NPs assembled in dimer, trimer, and up to pentamer in a linear arrangement. For the well-studied dimer system, we show that the Q NF enhancement, due to coupling in longitudinal mode, is much greater than the enhancement in Q ext. There is a linear correlation between the Q NF and Q ext peak positions, with the Q NF peak redshifted from the Q ext peak by an average of approximately 12 nm. In the case of the multimers, Q NF spectra from individual spheres were not always identical and become dependent on the sphere location. In the longitudinal model, the center sphere has the strongest Q NF spectra. For the transverse mode, we differentiate two different scenario, transverse-Y where both electric field (E) and light propagation vector (k) are perpendicular the chain axis, and transverse-X where k is parallel to the chain axis. In transverse-Y mode, coupling leads to reduced Q NF spectra and the center sphere has the lowest Q NF intensity. In transverse-X mode, there is retardation effect from the front sphere to the back sphere. The Q NF from the front sphere is stronger than from the back sphere. In addition, due to the phase lag in k-direction, the Q NF in transverse-X can differ quite significantly from transverse-Y for large particles. All these results could be understood when one considers how electric field from induced dipoles on neighboring NPs add on or subtract from the incident E-field. These results provide new insight into the coupling properties of Au NPs.

Plasmonic Charge Transfers in Large‐Scale Metallic and Colloidal Photonic Crystal Slabs

AbstractThe challenges in plasmonic charge transfer on a large‐scale and low losses are systematically investigated by optical designs using 1D‐plasmonic lattice structures. These plasmonic lattices are used as couplers to guide the energy in an underneath sub‐wavelength titanium dioxide layer, resulting in the photonic crystal slabs. So far, photodetection is possible at energy levels close to the semiconductor bandgap; however, with the observed hybrid plasmonic–photonic modes, other wavelengths over the broad solar spectrum can be easily accessed for energy harvesting. The photo‐enhanced current is measured locally with simple two‐point contact on the centimeter‐squared nanostructure by applying a bias voltage. As lattice couplers, interference lithographically fabricated conventional gold grating provides an advantage in fabrication; this optical concept is extended for the first time toward colloidal self‐assembled nanoparticle chains to make the charge injection accessible for large‐scale at reasonable costs with possibilities of photodetection by electric field vectors both along and perpendicular to the grating lines. To discuss the bottleneck of unavoidable isolating ligand shell of nanoparticles in contrast to the directly contacted nanobars, polarization‐dependent ultrafast characterizations are carried out to study the charge injection processes in femtosecond resolution.

High-Electric-Field-Induced Hierarchical Structure Change of Poly(vinylidene fluoride) as Studied by the Simultaneous Time-Resolved WAXD/SAXS/FTIR Measurements and Computer Simulations

A high electric field was applied cyclically to poly(vinylidene fluoride) films, during which the simultaneous and time-resolved measurements of the two-dimensional wide-angle X-ray diffraction (WAXD), small-angle X-ray scattering (SAXS), and transmission-type Fourier transform infrared (FTIR) spectra were performed using a synchrotron X-ray radiation system. The inversion of the CF2 dipole moments caused by the alternate change of the electric field vector direction was detected to occur around ±80–100 MV/m as estimated by the electric-field-strength dependence of the IR band intensity. On the other hand, the WAXD peaks were found to show the maximal intensities at 0 and ±250–300 MV/m. In these regions, the 001 reflection of the β form and the 002 reflection of the δ form changed the intensities remarkably and periodically. These experimental data were interpreted, not by the idea of a simple inversion motion of the rigid polar chains (the planar zigzag chains of the form β and the TGTG̅ chains of the α and δ forms) but by the more complicated couplings between the rotation and tilting motions of the chain segments, the cooperative T-G conformational exchanges, and the associated inversion motion of the CF2 dipoles. The idea of the cooperative chain motions was supported by the density functional theory calculations performed under the external electric field. Different from the remarkable changes of the WAXD and FTIR data, the SAXS patterns did not show the detectable changes in these processes, indicating that the above-mentioned cooperative structural changes should occur in the crystalline regions with the stacked lamellar structure kept unchanged.

Size Effects of Closed Encounter Ag Nanoshell Pairs for SERS Application

Closed encounter Ag nanoshell pairs with remarkable improved plasmonic light enhancement in their gaps have been attracting much attention in the production of sensitivity SERS substrates. This work demonstrates the size effects of Ag nanoshell pairs on obtaining higher light intensity in their gaps. It is found that very complex light intensity changes occur in the gaps of Ag nanoshell pairs with their diameter enlargements ( diameters > 100 nm). By the calculation of scattering efficiency and electric field vectors, the size-related light intensity changes in the gaps have been revealed and been concluded systematically. This work fills in the gaps of application of nanoshell pairs with larger sizes in SERS detectors and could guide the design of some other Ag nanoshell pair-based optical devices.

Coupled thermoelectroelastic analysis of thick and thin laminated piezoelectric structures by exact geometry solid‐shell elements based on the sampling surfaces method

AbstractA hybrid‐mixed exact geometry four‐node thermopiezoelectric solid‐shell element through the sampling surfaces (SaS) formulation is proposed. The SaS formulation is based on the choice of an arbitrary number of SaS within layers parallel to the middle surface and located at Chebyshev polynomial nodes in order to introduce the temperatures, displacements and electric potentials of these surfaces as basic shell unknowns. Due to the variational formulation, the outer surfaces and interfaces are also included into a set of SaS. Such choice of unknowns with the use of Lagrange polynomials in the through‐thickness approximations of temperatures, temperature gradient, displacements, strains, electric potential, and electric field leads to a very compact higher‐order thermopiezoelectric shell formulation. To implement efficient analytical integration throughout the solid‐shell element, the extended assumed natural strain method is employed for all components of the temperature gradient, strain tensor, and electric field vector. The developed hybrid‐mixed four‐node thermopiezoelectric solid‐shell element is based on the Hu–Washizu variational principle and shows a superior performance in the case of coarse meshes. It can be useful for the three‐dimensional thermoelectroelastic analysis of thick and thin doubly curved laminated piezoelectric shells under thermal loading, since the SaS formulation allows one to obtain the numerical solutions with a prescribed accuracy, which asymptotically approach exact solutions of the theory of thermopiezoelectricity as a number of SaS tends to infinity.

Study of electric field vector, angular momentum conservation and Poynting vector of nonparaxial beams

The angular momentum (AM) of light, comprising spin and orbital AMs, is conserved and produces a spin-Hall shift in this process for paraxial beams. For nonparaxial beams, the spin and orbital AMs are non-separable and produce many changes in the beams’ spatial profile contrary to paraxial beams. These changes can be manifested as polarization modulation in the transverse plane, and conversion to orbital angular momentum (OAM) structured beams in the transverse and longitudinal planes, which can be estimated by studying the electric field vector in detail. We have calculated theoretically and simulated numerically the electric field vector components in the focal plane, to study the polarization modulation and AM conservation for OAM and Gaussian light beams of circular and linear polarizations and compared the results. Further, we have calculated and simulated the Poynting vector components for the corresponding fields to study the energy flow. We have considered the focusing of light beams using a high Numerical Aperture objective lens to obtain the nonparaxial beam, and presented a detailed theoretical analysis therein. The interpretation studies presented here are new, which may have many applications in nanophotonics and help in understanding the spin–orbit interaction at the fundamental level.

Ion Adsorption at Solid/Water Interfaces: Establishing the Coupled Nature of Ion–Solid and Water–Solid Interactions

Understanding the thermodynamics of ion adsorption at solid/water interfaces is essential for all energy- and membrane-based applications involving electrolytes. At any solid/water interface, the ion–solid and water–solid interactions are intrinsically coupled through the electric fields exerted by the salt ions and the water molecules, which polarize the solid surface, yet the implications of this coupling on the adsorption behavior of ions remain unknown. In this article, we develop a theoretical framework involving all-atomistic polarizable force fields and computationally investigate the adsorption of a thiocyanate (SCN–) ion at the graphene/water interface, including comparing with available experimental data. We show that, in vacuum, the electric field exerted by the SCN– ion strongly polarizes the carbon atoms in graphene, resulting in a significantly large graphene–ion polarization energy. However, at the graphene/water interface, the interactions of the electric field vectors exerted by the interfacial water molecules with those of the SCN– ion result in a 93% screening of the graphene–ion polarization energy, thereby significantly weakening the graphene–ion interactions. Further, the free energy of SCN– adsorption predicted by our theoretical framework agrees quantitatively with the experimental result, whereas we show that an implicit modeling of the graphene–ion polarization energy using a pairwise additive potential such as the Lennard-Jones potential results in a significant overprediction by more than 10 kcal/mol. Therefore, our study highlights the critical role played by the coupled nature of the ion–solid and water–solid interactions in governing the energetics of ion adsorption at solid/water interfaces.

Kinematic modeling of Rytov's law and electromagnetic curves in the optical fiber based on elliptical quaternion algebra

In this paper, we aim a kinematic method to investigate the behavior of polarized light in an optical fiber. Geometric phase equations are obtained using elliptic quaternions. The behavior of polarized light is studied for three conditions where the angle between the polarization vector (electric field) and the Darboux frame fields are constant on the ellipsoid. For these conditions, the polarization vector experiences a homothetic motion on the ellipsoid. Moreover, this motion can be defined by the Fermi Walker parallelism rule. Also, the traced curves of the polarization vector (Rytov curves) are calculated by homothetic motions and Elliptic quaternions. Additionally, the magnetic vector field related to the polarization vector is derived. Then the characterizations of the electromagnetic curve are obtained. To reinforce the theory, the homothetic motions of the polarization vector on the ellipsoid are visualized by giving examples for each case.

Improved Flux Tracing Method Based on Parametric Curve for Calculating Ion Flow Field of HVDC Transmission Lines

An improved method for tracing electric flux lines in the vicinity of the overhead high voltage direct current (HVDC) transmission lines is developed by using parametric curves. Based on the geometric relation between the electric field vector and the derivative of the parametric curve function, the electric flux lines can be successfully traced without accumulation of the numerical error caused by the differentiation for calculating the electric potential. Considering the structural characteristics of the transmission line, the control points at both ends of the parametric curve can be easily located, and the remaining control points are modified to minimize an error function defined by the electric field vectors at nodes along the curve. Once the electric flux lines are traced, a series of flux tubes is created by bundling adjacent flux lines, and the nodal electric field vectors and space charge densities are iteratively updated. In order to consider the ionized space charge effect, new flux lines of modified electric field are traced, which in turn affects the existing space charge distribution. The process is repeated until the effect of the space charge is fully considered. The performance of the proposed algorithm is verified by comparing the resulting ground profiles of the ion flow field distribution with the result of the analytical model and the long-term measurement of the full-scale transmission line.

Pigtailed Electrooptic Sensor for Time- and Space-Resolved Dielectric Barrier Discharges Analysis

We here demonstrate the potentialities of pigtailed electrooptic probes to perform vectorial electric field characterizations of dielectric barrier discharges (DBDs). The analysis leads to the accurate determination of the breakdown voltage and the associated electric field in the vicinity of the discharge. A polarimetric analysis of the DBDs is proposed due to real-time measurement of longitudinal and radial components of the electric field vector. Moreover, the transition from capacitive to resistive behavior is characterized at the breakdown field.