Electric Dipole Radiation Research Articles

On numerical and approximate analytical modeling of single- and two-photon Young's experiment using the photon coordinate wave function

In modern areas of photonics, the physical description of the interaction of photons with matter in the control, transmission and registration of single-photon and two-photon states implemented in practice is of great importance. An appropriate acceptable description may be faced with the need to take into account various kinds of interference effects associated with these states. Meanwhile, even the most “simple” case of single-photon interference in Young's experiment requires the use of a rather complex apparatus of quantum electrodynamics. This article explains one- and two-photon interference in Young's thought experiment based on the photon wave function (PWF) in coordinate representation. This explanation is illustrated by two examples of wavelengths: 10.6 μm and 1.5 cm. For both examples, two approaches to PWF modeling are used: “purely quantum-mechanical” and “quasi-classical”. In the first approach, a 6-component coordinate PWF is constructed using a spherically symmetric momentum distribution in a wave packet, followed by numerical and approximate analytical calculations. In the second approach, a one-component “quasi-classical” PWF is constructed, which corresponds to either electric dipole radiation or simulated spherically symmetric radiation. In all cases, the same pronounced interference pattern was obtained, which allows us to conclude that not only the quantum-mechanical coordinate PWF is able to explain the phenomena of one- and two-photon interference, but also a much simpler “quasi-classical” PWF. This conclusion sheds light on the theoretical interpretation of the measurement of the coordinate PWF in some recent experiments.

Multipole mixing effects on the angular distribution and polarization of dielectronic hypersatellite lines from highly charged helium-like ions

The angular distribution and the degree of linear polarization of the dielectronic hypersatellite lines of highly charged helium-like ions are studied by using the multiconfiguration Dirac-Fock method and density matrix theory with a focus on the multipole mixing effects. Detailed calculations have been carried out for the emission of characteristic X-rays from the (2s2p)P1,23 and P11 resonant states decay to the (1s2s)S13 state following the KLL dielectronic recombination of initial hydrogen-like ions with atomic nuclear charge from Z=22 to Z=100. It is shown that the mixing of electric dipole (E1) and magnetic quadrupole (M2) radiations significantly alters the angular distribution and the degree of linear polarization, in which the shifts are dependent on the resonant capture states and the atomic nuclear charges. The E1+M2 mixing has opposite effects for the (2s2p)P23 and (2s2p)P11 resonant states, except for the (2s2p)P11 resonance of the heavy ions with Z≳90, where the profile of angular distribution is reversed by strong mixing effects due to the contribution of the M2 term and its interference with the E1 radiative channel. The results should be of particular interest to the diagnosis of anisotropic plasmas and the test of fundamental physics in few-electron heavy ions.

Characteristic Mode Inspired Single-Plate Unidirectional Antenna Using Complementary Characteristic Radiation

Based on characteristic mode theory (CMT), a novel single-plate complementary antenna with a unidirectional radiation pattern is proposed in this communication. The proposed antenna is composed of an isosceles right triangular conductive slab (IRTCS), three inductive coupling elements (ICEs), and a feeding network. By exciting two complementary current modes of IRTCS simultaneously, the radiation of IRTCS can be tailored. More specifically, ICEs can stimulate the electric dipole and magnetic dipole current modes of IRTCS concurrently through appropriate excitation, thereby realizing an endfire radiation pattern by combining the two complementary characteristic fields with suitable modal weighting coefficients (MWC). For proof of concept, a prototype is fabricated, and the measured results demonstrate that a good unidirectional radiation pattern is achieved with a front-to-back ratio (FBR) larger than 20 dB, which verifies the feasibility and reliability of the proposed method. Compared with the conventional complementary antennas or Huygens source antennas which need two different radiating sources to realize the electric and magnetic dipole radiations individually, the proposed method reuses the radiating aperture and achieves the unidirectional radiation by a single radiating aperture.

Perfect magnetic mirror based on magnetic dipole scattering in all-dielectric resonators

Perfect magnetic mirrors are important optical devices for the development of novel optical detectors, solar cells, and imaging devices. They have the property of only reversing the magnetic field of a light wave upon reflection, for instance, in functional optical metasurfaces. To design an optical magnetic mirror, high-refractive-index dielectric nanostructures that support strong magnetic dipole (MD) response in the optical wavelength range are used. However, the spectral overlap between the MD and electric dipole in dielectric resonators degrades the magnetic mirror reflection. Here, we propose and demonstrate a perfect optical magnetic mirror metasurface that totally reflects an incident wave without electric field phase change. In this perfect magnetic mirror, the electric dipole radiation is completely suppressed by the radiation of the anapole mode in the spectral range where the destructive interference between the electric dipole and toroidal dipole occurs. By fine-tuning the size parameters of the dielectric resonators, we show near-perfect MD scattering as a result of the spectral overlap between MD resonance and anapole mode. The optical magnetic mirror can be tuned from the visible to near-infrared range by scaling the sizes of the resonators. The MD scattering resonators promote the perfect magnetic mirror, a promising platform for designing photodetectors, biological sensors, and reflected waveplates.

A Wideband Circularly Polarized Complementary Antenna for Millimeter-Wave Applications

This work presents a design of an aperture-coupled complementary antenna for realizing circularly polarized (CP) broadside radiation at millimeter-wave (mm-wave) frequencies. The proposed antenna constructively combines a patch dipole (electric dipole radiation) and a folded loop antenna (magnetic dipole radiation), which are differentially excited by a longitudinal slot etched on the top layer of the substrate integrated waveguide (SIW). The combination of the proposed patch dipole and the folded loop antenna results in a paralleled electric dipole and magnetic dipole which can generate two orthogonal electric field components and 90° phase difference in the far-field radiation when they are in-phase excited. The proposed antenna achieves a wide impedance bandwidth of 46% from 48.47 to 77.46 GHz and a wide 3 dB axial ratio bandwidth (ARBW) of 47.3% from 51.64 to 83.61 GHz with an overlapped bandwidth of 40%. To further enhance the antenna gain, sequential rotation technique is adopted to construct a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2 \times 2$ </tex-math></inline-formula> subarray, which is further employed in a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$4 \times 4$ </tex-math></inline-formula> subarray. The <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$4 \times 4$ </tex-math></inline-formula> subarray is then used to construct an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$8 \times 8$ </tex-math></inline-formula> antenna array, which achieves a wide impedance bandwidth of 33.8% from 56.11 to 78.95 GHz and a wide 3 dB ARBW of 38.8% from 53.57 to 79.32 GHz, with a maximum antenna gain of around 25.2 dBic. The proposed antenna element and array design would be a competitive candidate for future wireless applications operating at mm-wave spectrum.

A Non‐Singular, Field‐Only Surface Integral Method for Interactions between Electric and Magnetic Dipoles and Nano‐Structures

AbstractWith the development of condensed‐matter physics and nanotechnology, attention has turned to the fields near and on surfaces that result from interactions between electric dipole radiation and mesoscale structures. It is hoped that studying these fields will further the understanding of optical phenomena in nano‐optics, quantum mechanics, electromagnetics, and sensing using solid‐state photon emitters. Here, a method for implementing dynamic electric and magnetic dipoles in the frequency domain into a non‐singular field‐only surface integral method is described. It is shown that the effect of dipoles can conveniently be described as a relatively simple term in the integral equations, which fully represents how they drive the fields and interactions. Also, due to the non‐singularity, this method can calculate the electric and magnetic fields on the surfaces of objects in both near and far fields with the same accuracy, which makes it an ideal tool to investigate nano‐optical phenomena. The derivation of the framework is given and tested against a Mie theory alike formula. Some interesting examples are shown involving the interaction of dipoles with different types of mesoscale structures including parabolic nano‐antennas and gold probes.

Goal-Oriented 3-D Time-Domain Marine CSEM Modeling With Anisotropy and Topography

We have proposed a goal-oriented iteration algorithm with adaptive error estimation for the 3-D modeling of the time-domain marine controlled-source electromagnetic (CSEM) method. The algorithm is based on finite-element time-domain (FETD) formulations, and it updates both the time step and the mesh size in a staggered manner. With this scheme, the computational error is well suppressed, and the efficiency of the FETD simulation is guaranteed by adaptive time-stepping within each iteration. The verification results of an electric dipole radiation model and a synthetic 1-D marine CSEM model have shown that the proposed algorithm achieves a fine balance between computational accuracy and efficiency. Through numerical examples incorporated with stratum anisotropy and seafloor topography, we further conclude that both background anisotropy and topography impede the identification of submarine high-resistivity bodies with the electric field response. Contrarily, the time derivative of the magnetic field is sensitive to high-resistivity reservoirs over an extensive period of time in both anisotropic and topographic models. Based on this, we suggest that the magnetic field should be collected along with the electric field over the whole target area to reveal the anisotropic structure of submarine sediments and the existence of oil and gas reservoirs.

Analytic Solution of Surface–Volume–Surface Electric Field Integral Equation on Dielectric Sphere and Analysis of Its Spectral Properties

The exact solution of the surface–volume–surface electric field integral equation (SVS-EFIE) is presented for the problem of radiation in the vicinity of the homogeneous dielectric sphere. The solution is obtained via the Galerkin method of moments (MoM) utilizing rotational and irrotational complete sets of orthogonal vector spherical harmonics as basis and test functions according to the Helmholtz decomposition. In the case of radial or tangential electric dipole radiation, the electric field throughout the sphere evaluated via the analytic MoM solution of the SVS-EFIE is compared against the exact classical Mie series solution. The two are shown to agree to 12 digits of accuracy upon a sufficient number of basis/test functions taken in the MoM solution and the Mie series expansion. The exact solution confirms and validates the rigorous nature of the SVS-EFIE formulation. It also reveals the spectral properties of its individual operators, their products, and their linear combination, as well as the spectrum of the MoM impedance matrix. It is shown that, upon choosing basis and test functions in the Sobolev space <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{div}^{1/2}(S)$ </tex-math></inline-formula> and performing testing inner products evaluation in the space <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{div}^{-1/2}(S)$ </tex-math></inline-formula> , with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$S$ </tex-math></inline-formula> being the surface of the sphere, the MoM impedance matrix features bounded condition number with increasing order of discretization similar with analogous exact MoM solution of the surface EFIE (S-EFIE) on the perfectly electrically conducting (PEC) sphere.

Magnetic excitation of high-Q resonance with split-ring resonators

Planar split-ring resonators (SRRs) with broken symmetry, excited by the electric field of incident wave, have been widely used to realize the high-Q resonance. In this paper, we report by theory and experiment an alternative scheme to induce the SRR-based high-Q resonance. The proposed scheme utilizes a two-dimensional array of vertical SRRs with vertical air gaps, which enables the excitation of narrow resonance with magnetic field and strong enhancement of local electromagnetic fields. The working mechanism correlates with the strong directional dependence of the dipole radiation (i.e., the elimination of electric-dipole radiation of the SRRs in the propagation direction), rather than the destructive interference due to the structural symmetry breaking. The dependence of Q factor on the structural parameters has also been studied theoretically, suggesting that a Q factor more than 2000 can be achieved. The results may be useful for designing narrow-band filters and sensors in the microwave or THz regime.

DES map shows a smoother distribution of matter than expected: a possible explanation

The largest and most detailed map of the distribution of dark matter in the Universe has been recently created by the Dark Energy Survey (DES) team. The distribution was found to be slightly (by a few percent) smoother and less clumpy than predicted by general relativity. This result was considered as a hint of some new physical laws. In the present paper we offer a relatively simple model that could explain the above result without resorting to any new physical laws. The model deals with the dynamics of a system consisting of a large number of gravitating neutral particles, whose mass is equal to the mass of hydrogen atoms. The central point of the model is a partial inhibition of the gravitation for a relatively small subsystem of the entire system. It would be sufficient for this subsystem to constitute just about a few percent of the total ensemble of particles for explaining the few percent more smooth distribution of dark matter (observed by the DES team) compared to the prediction of general relativity. The most viable candidate for the dark matter particles in this model is the second flavor of hydrogen atoms (SFHA) that has only S-states and therefore does not couple to the electric dipole radiation or even to higher multipole radiation, so that the SFHA is practically dark. The SFHA has experimental confirmation from atomic experiments, it does not go beyond the Standard Model, it is based on standard quantum mechanics and it explains puzzling astrophysical observations of the redshifted line 21 cm from the early Universe. Thus, our model explaining the DES result of a little too smooth distribution of dark matter without resorting to any new physical laws seems to be self-consistent.

Quadrupole radiation and e+e− pair production in the collision of nonrelativistic nuclei

We analyze the one-photon mechanism of e+e− pair production in the collision of nonrelativistic nuclei. The contribution of electric quadrupole radiation of virtual photon to the corresponding cross section is found. The effect of the finite nuclear size is considered in detail. A comparison is made with the contribution of electric dipole radiation of virtual photon and with the contribution of the two-photon pair production mechanism. It is shown that the contribution of electric quadrupole radiation is dominant in a wide range of relative velocities. The cross section for the production of e+e− pair with the capture of an electron by one of the nuclei is also analyzed.

Charging and Electromagnetic Radiation during the Inspiral of a Black Hole–Neutron Star Binary

Abstract Because mergers of black hole–neutron star (BH–NS) binaries are widely argued to produce both gravitational and electromagnetic waves, these binaries are among the most attractive systems in the era of multi-messenger astronomy. In this paper we explore the charging processes of a moving BH in two types of charged surroundings and propose a new charging scenario differing from the elegant mechanism of Wald. During the inspiral of such a binary, the NS is strongly magnetized and the BH is moving inward. By considering this moving BH charging scenario, we find that the BH will increasingly accumulate enough net charge to light up the binary system at the inspiral stage. This charging process is universal no matter whether the BH spins or not. We show that our BH charging scenario can physically explain the BH’s unipolar inductor mechanism in a BH–NS binary system. We calculate electromagnetic emission luminosities due to various energy dissipation mechanisms and find that the electric dipole radiation of the BH makes a dominant contribution to electromagnetic emission at the final stage of inspiral if the BH spins slowly.

Penetration of dipole radiation into an ENZ medium

We consider electric dipole radiation emitted near an interface with an epsilon-near-zero (ENZ) material. Such a medium is nearly impenetrable for electromagnetic plane waves, but we show that dipole radiation can penetrate deep into the medium. The radiation is represented by an angular spectrum of plane waves, and each partial wave transmits as an evanescent wave. The sum of these waves, however, is not evanescent, but decays algebraically with the distance to the interface. We have evaluated the electric and magnetic fields inside the material, and we have constructed the Poynting vector. We found that energy flows through the material, and not only in a small region near the interface. For the case of a perpendicular dipole, the magnetic field is zero, and the electric field can be obtained in closed form. We show that the electric field decays as the third power of the distance to the interface.

Modification of a Projection Method for Analysis of Radiation of a Radial Dipole in the Presence of an Inhomogeneous Body of Revolution

The problem of radiation of a radial electric dipole located on the axis of rotation of an axisymmetric body consisting of a homogeneous dielectric sphere and an external inhomogeneous dielectric layer is considered. The new numerical algorithm developed to solve the problem is based on a projection method that includes the projection of fields to transverse spherical harmonics in combination with a one-dimensional finite element method in a projection form along the radial coordinate. The algorithm is also generalized to the case in which the inner sphere is perfectly conducting. Numerical results, which characterize both the efficiency of the method and the effect of various parameters of the body on the directional pattern of the dipole, are presented.

Two Flavors of Hydrogen Atoms: A Possible Explanation of Dark Matter

In one of our previous papers, it was shown that for the ground state of hydrogenic atoms/ions, it is possible to match the interior (inside the nucleus) solution of the Dirac equation with the singular exterior solution of the Dirac equation, so that the singular solution should not be rejected for the ground state of hydrogenic atoms/ions. In that paper, there was presented also the first experimental proof of the existence of this Alternative Kind of Hydrogen Atoms (AKHA)—by showing that the presence of the AKHA solves a long-standing mystery of the huge discrepancy between the experimental and previous theoretical results concerning the high-energy tail of the linear momentum distribution in the ground state of hydrogen atoms. In another paper, we showed that for hydrogen atoms, the singular solution of the Dirac equation outside the proton is legitimate not just for the ground state 12S1/2, but also for the states 22S1/2, 32S1/2 and so on: it is legitimate for all the discrete states n2S1/2. Moreover, the singular exterior solution is legitimate also for the l = 0 states of the continuous spectrum. In that paper, we demonstrated that the AKHA can be the basis for explaining the recent puzzling astrophysical observational results concerning the redshifted radio line 21 cm from the early Universe. Thus, there seems to be the astrophysical evidence of the existence of the AKHA—in addition to the already available observational proof of their existence from atomic experiments. In the present paper, we point out that the AKHA provide an alternative view on dark matter—without resorting to new subatomic particles or dramatically changing the existing physical laws. This is because due to the selection rules, the AKHA do not have state that can be coupled by the electric dipole radiation. We also reformulate the above theoretical results in terms that hydrogen atoms can have two flavors: one flavor corresponding to the regular solution outside the proton, another—to the singular solution outside the proton, both solutions corresponding to the same energy. Since this means the additional degeneracy, then according to the fundamental theorem of quantum mechanics, there should be an additional conserved quantity, which we call isohydrogen spin (isohyspin). Further atomic experiments for accurately measuring the high-energy tail of the linear momentum distribution in the ground state of hydrogen atoms, as well as further observational studies of the redshifted 21 cm radio line from the early Universe, could provide a further proof that dark matter or a part of it is the AKHA.

On the reflection, diffraction and refraction of a spherical wave of parallel polarization by a sphere of electrically long radius

A novel mathematical approach is proposed for the analysis of the reflection, diffraction and refraction of spherical waves from curved material interfaces. As a paradigm, this approach is applied to the radiation of a vertical electric dipole over an electrically homogenous sphere. The material of the sphere can be dielectric or conducting. The radius of the sphere is assumed to be much greater than the wavelength in its less dense exterior. The formulation is developed for any height of the dipole above the sphere and for any radial distance of the point of observation from the center of the sphere. Novel expansions are applied to the integral representations of the resulting fields. It is shown that contributions to the value of the fields can be produced either from stationary-phase points of the integrands that are generated by such expansions or from any of the two strings of poles of these integrands. Contributions from rapidly converging residue series, as opposed to those coming from stationary-phase points, correspond to wave trajectories containing a curved path in addition to rectilinear paths. For the sake of demonstration, approximate analytical formulas for computation are derived for a number of select cases. The method yields leading-order approximations for the reflected and refracted fields. The affinity with the reflection from a planar interface is analysed.

On the wave-particle duality within the framework of modeling single-photon interference

The general results of constructing and modeling the photon wave function in the coordinate representation in the framework of quantum mechanics are presented in order to explain single-photon interference phenomena, in particular Young’s experiment. The relevance of this function is emphasized in connection with modern single-photon and two-photon experiments. The necessity of replacing the explanation of obtaining coherent light sources using the concept of a train of supposedly real electromagnetic waves emitted by one atom, by the conditional emission by this atom of the photon wave function in the coordinate representation, which then experiences diffraction and interference, is substantiated. A single-photon wave function is simulated based on the consideration of the electric dipole radiation of an atom in classical electrodynamics, and a conclusion is drawn on the possibility to explain Young’s experiment. It is argued that although the photon wave function (as well as of particles having mass) is not a physical object, the application of this function significantly weakens the problem of wave-particle duality of light. It is assumed the “nature” of this function reflects the properties of a physical vacuum, but new experiments are required to clarify it.

Toroidal Dipole Mode Observation In Situ

Besides classical dipole moments, the metaparticles are characterized by toroidal dipole moments that are important for numerous applications ranging from strong field localizations to anapole modes and the dynamic Aharonov–Bohm effect. On the other hand, the toroidal and electric dipole radiation are undistinguished by external observers due to identical radiation patterns. Therefore, the importance of toroidal dipole moments in multipole expansion is questioned by many researchers. However, a long‐awaited unanswered question is—what is going on inside a toroidal metamolecule and is its near‐field distribution distinct from the electric dipole field? Herein, the toroidal dipole mode is experimentally confirmed in situ by proof‐of‐concept measurements of electric and magnetic fields inside properly fabricated water metamolecules with toroidal topology in the microwave frequency range.

Staggered H-shaped metamaterial based on electromagnetically induced transparency effect and its refractive index sensing performance

In this work, we report numerical research concerning a planar electromagnetically induced transparency (EIT) terahertz metamaterial capable of exhibiting refractive index sensing with high sensitivity. The unit cell of the proposed EIT metamaterial is consisted by metal cut wires with staggered H-shaped arrangement, and can display a sharply narrow transmission transparency peak at 2.653 THz with high quality-factor (Q-factor) valued 48.3. Through analysis of the extracted surface current distributions on metallic structures, it is confirmed that the EIT-like resonance results from the destructive interference of the electric quadrupole excited by the strong radiation of electric dipole. Furthermore, the EIT-like effect shows highly sensitive response to the refractive index of the covered layer. When it covered by 3μm-thickness analyte layer, the EIT metamaterial can yield a sensitivity of 0.2695 THz/refractive index unit (RIU) and a figure of merit (FOM) of 5.39. Meanwhile, it is also found that the sensitivity S is inversely proportional to the dielectric constant of the substrate material, and effective sensing capability maintains when the coverage thickness within 15μm. The proposed EIT metamaterial design provides great potential application for refractive index sensing performance.

Inspiral of a Spinning Black Hole–Magnetized Neutron Star Binary: Increasing Charge and Electromagnetic Emission

Abstract The mergers of black hole (BH)–neutron star (NS) binaries have been one of the most interesting topics in astrophysics, because such events have been thought to possibly produce multimessenger signals including gravitational waves and broadband electromagnetic (EM) waves. In this paper, we investigate EM emission from the inspiral of a binary composed of a spinning BH and a magnetized NS. Observationally, the BH is usually more massive than ∼7 M ⊙ and the NS has a mass ≃1.4 M ⊙. During the inspiral of such a binary, the BH will accumulate more and more charges based on the charging scenario of Wald, even though the BH will eventually swallow the NS whole inevitably. We calculate the emission luminosities and energies through three energy dissipation mechanisms: magnetic dipole radiation, electric dipole radiation, and magnetic reconnection. We show that magnetic dipole radiation due to the spin of the increasingly charged BH and magnetic reconnection in between the BH and the NS could be most significant at the final inspiral stage. We find that if the BH is rapidly spinning and the NS is strongly magnetized, these mechanisms would lead to a detectable EM signal (e.g., a short-duration X-ray transient).