Electric Hertzian Dipole Research Articles

Dipole excitation of collective modes in viscous two-dimensional electron systems

We describe the structure of the time-harmonic electromagnetic field of a vertical Hertzian electric dipole source radiating over an infinite, translation invariant two-dimensional electron system. Our model for the electron flow takes into account the effects of shear and Hall viscosities as well as an external static magnetic field perpendicular to the sheet. We identify two wave modes, namely, a surface plasmon and a diffusive mode. In the presence of an external static magnetic field, the diffusive mode combines the features of both the conventional and Hall diffusion and may exhibit a negative group velocity. In our analysis, we solve exactly a boundary value problem for the time-harmonic Maxwell equations coupled with linearized hydrodynamic equations for the flat, two-dimensional material. By numerically evaluating the integrals for the electromagnetic field on the sheet, we find that the plasmon contribution dominates in the intermediate-field region of the dipole source. In contrast, the amplitude of the diffusive mode reaches its maximum value in the near-field region, and quickly decays with the distance from the source. We demonstrate that the diffusive mode can be distinguished from the plasmon in the presence of the static magnetic field, when the highly oscillatory plasmon is gapped and tends to disappear.

Interface-Induced Near-Infrared Response of Gold-Silica Hybrid Nanoparticles Antennas.

We proposed an IR absorber hybrid nanoantenna comprise of two overlapping gold nanoparticles residing over larger a silica nanoparticle. A wet chemical route was employed to prepare the hybrid structure of nanoantenna. High-resolution transmission electron microscope was used to measure the size and morphology of the nanoantenna. The Hybrid nanoantenna was excited by electron beam to investigate the optical response over a large wavelength range using Electron Energy Loss Spectroscopy. The beam of the electron was focused and we measured the electron energy loss spectra at different point of interest, which confirmed the of Low Energy Surface Plasmon Politron resonances in the IR region. The optical response of the nanoantenna was simulated numerically by employing Electric Hertzian dipole using finite element method with frequency domain solver in CST Microwave Studio. We used the Electric Hertzian dipole approach for the first time to model the Electron Energy Loss Spectroscopy experiment. The Electron Energy Loss Spectroscopy experimental results with their numerically simulated values confirmed the plasmonic resonance at the interface of the two overlapped gold nanoparticles.

Subwavelength plasmonic nanoantenna as a Plasmonic Induced Polarization Rotator (PI-PR)

This article reports the finding of the plasmonic induced polarization rotation and propagation rotation when the plane EM wave radiates the adjacent active coated nano particle and large dielectric sphere at resonant frequency. The results investigate that the incident electromagnetic planewave excites the TM21 mode in the large size dielectric sphere at first, which affects the TM11 mode field from the coated nano particle. Consequently, when the combined active coated nano particle and large dielectric sphere are in resonant, the main E–field polarization direction becomes parallel to the propagation direction of the original planewave and main beam of the pattern becomes omnidirectional i.e. both rotates by 90°. Furthermore, the polarization and propagation rotation angle varies with different size of the dielectric sphere. Likewise, the structure of dielectric sphere clamped by two active nanoparticles is also showing plasmonic induced polarization and propagation rotation along with TM11 mode from each coated nano particle (CNP) having 180° phase difference. In addition to this, the induced polarization rotation was also verified by the Electric Hertzian Dipole (EHD). The integration of this simpler geometry with other optical devices has possible applications in polarization manipulation, nano-sensors and detectors on nanoscale.

Arbitrary shaped beam scattering from a chiral-coated conducting object with arbitrary monochromatic illumination

An exact semi-analytical method of calculating the scattered fields from a chiral-coated conducting object under arbitrary shaped beam illumination is developed. The scattered fields and the fields within the chiral coating are expanded in terms of appropriate spherical vector wave functions. The unknown expansion coefficients are determined by solving an infinite system of linear equations derived using the method of moments technique and the boundary conditions. For incidence of a Gaussian beam, circularly polarized wave, zero-order Bessel beam and Hertzian electric dipole radiation on a chiral-coated conducting spheroid and a chiral-coated conducting circular cylinder of finite length, the normalized differential scattering cross sections are evaluated and discussed briefly.

Shaped beam scattering by an object with a uniaxial anisotropic inclusion

The differential scattering characteristics of an object having a uniaxial anisotropic inclusion, for incidence of an arbitrarily shaped beam, are theoretically investigated. The scattering problem is solved in a spherical basis by using the boundary conditions, method of moments technique and Schelkunoff’s equivalence theorem, which leads to a system of linear equations for the expansion coefficients of the scattered and internal fields when the description of the incident shaped beam is known. The theoretical formulation is reviewed, and the numerical problems are discussed. As examples, for a Gaussian beam, zero-order Bessel beam and Hertzian electric dipole radiation striking a spheroid with a uniaxial anisotropic spheroid inclusion and a circular cylinder with a uniaxial anisotropic circular cylinder inclusion, the normalized differential scattering cross sections are calculated, and the scattering properties are analyzed concisely.

Scattering of electromagnetic beam by a chirally coated object

We present a semi-analytical solution to the electromagnetic scattering by a chirally coated object with arbitrary monochromatic illumination. The scattered fields and the internal fields in different regions are expanded in terms of appropriate spherical vector wave functions, and the unknown expansion coefficients are determined using the boundary conditions and the method of moments scheme. As examples, for a Gaussian beam, zero-order Bessel beam and Hertzian electric dipole radiation incident on a chirally coated spheroid and circular cylinder of finite length, numerical results of the normalized differential scattering cross section are provided to illustrate the validity and capability of the proposed method, and the scattering characteristics are discussed concisely.

Cylindrical and Spherical Active Coated Nanoparticles as Nanoantennas: Active Nanoparticles as Nanoantennas

In this article, we review the fundamental properties of several spherical and cylindrical, passive, and active coated nanoparticles (CNPs) with an emphasis on their potential for nanoantenna and nanoamplifier synthesis. For the spherical geometries, the nanoparticles are excited by an electric Hertzian dipole (EHD), which represents, e.g., a stimulated atom or molecule. The cyl indr ical nanoparticles are excited by a magnetic line source (MLS). In the active cases, gain is added to the core region of the particle. For simplicity, it is represented by a canonical, frequency-independent gain model. We demonstrate that specific CNPs can be designed to be resonant and well matched to their respective excitation sources. With active cores, these designs can lead to extremely large total radiated powers. For both configurations, insights into the effects of the nanoparticle material composition, source location, and orientation will be given on the basis of studying their near-field and power-flow density distributions, total radiated powers, and directivity properties.

Transmission of shaped beam through a rotationally uniaxial anisotropic sphere

We proposed a semi-analytical solution to the arbitrarily shaped beam scattering by a rotationally uniaxial anisotropic sphere. The scattered and internal fields are expanded in terms of appropr- iate spherical vector wave functions, and the unknown expansion coefficients are determined by virtue of the boundary conditions and the method of moments procedure. For incidence of a Gaussian beam, zero-order Bessel beam and Hertzian electric dipole radiation, numerical results are given for the normalized internal and near-surface field intensity distributions, and then their properties are discussed concisely.

Dipole excitation of surface plasmon on a conducting sheet: Finite element approximation and validation

We formulate and validate a finite element approach to the propagation of a slowly decaying electromagnetic wave, called surface plasmon–polariton, excited along a conducting sheet, e.g., a single-layer graphene sheet, by an electric Hertzian dipole. By using a suitably rescaled form of time-harmonic Maxwell's equations, we derive a variational formulation that enables a direct numerical treatment of the associated class of boundary value problems by appropriate curl-conforming finite elements. The conducting sheet is modeled as an idealized hypersurface with an effective electric conductivity. The requisite weak discontinuity for the tangential magnetic field across the hypersurface can be incorporated naturally into the variational formulation. We carry out numerical simulations for an infinite sheet with constant isotropic conductivity embedded in two spatial dimensions; and validate our numerics against the closed-form exact solution obtained by the Fourier transform in the tangential coordinate. Numerical aspects of our treatment such as an absorbing perfectly matched layer, as well as local refinement and a posteriori error control are discussed.

Time-Domain Line-Integral Representations of Physical-Optics Scattered Fields

A time-domain (TD) line-integral (LI) representation of the physical-optics (PO) radiation integral is developed for the scattering from a perfectly conducting surface illuminated by an electric Hertzian dipole. The proposed LI representation, which is valid and singularity-free for all near-field observers, is derived directly in the TD by introducing dyad potentials. This TD representation can be further expressed in terms of geometric-optics and boundary-wave components of the scattering mechanisms, as in the conventional frequency-domain LI representations. Using the proposed LI representation, the computational complexity is reduced by an order of the scatterer’s linear electric size, compared with the straightforward numerical quadrature of the PO surface integral. Simple and complicated numerical examples are presented to demonstrate the efficiency and accuracy of the proposed TD-LI algorithm.

Shaped beam scattering by an anisotropic particle

An exact semi-analytical solution to the electromagnetic scattering from an optically anisotropic particle illuminated by an arbitrarily shaped beam is proposed. The scattered fields and fields within the anisotropic particle are expanded in terms of spherical vector wave functions. The unknown expansion coefficients are determined by using the boundary conditions and the method of moments scheme. For incidence of a Gaussian beam, zero-order Bessel beam and Hertzian electric dipole radiation, numerical results of the normalized differential scattering cross section are given to a uniaxial, gyrotropic anisotropic spheroid and circular cylinder of finite length. The scattering properties are analyzed concisely.

Scattering of arbitrarily shaped beam by a chiral object

An exact semi-analytical solution to the arbitrarily shaped beam scattering by a chiral object is proposed through expanding the scattered and internal fields in terms of appropriate spherical vector wave functions. By using the boundary conditions and the method of moments technique, the unknown expansion coefficients are determined. For incidence of a Gaussian beam, zero-order Bessel beam and Hertzian electric dipole radiation, numerical results of the normalized differential scattering cross section are given to a chiral spheroid and a chiral circular cylinder of finite length, and the scattering characteristics are discussed concisely.

Scattering of shaped beam by a chiral spheroid

An exact semi-analytical solution to the scattering of an arbitrarily shaped beam by a chiral spheroidal object is constructed in a spheroidal coordinate system. The scattered fields as well as internal fields are expanded in terms of appropriate spheroidal vector wave functions, and the unknown expansion coefficients are determined by using the continuous boundary conditions and the method of moments technique. For incidence of a Gaussian beam, zero-order Bessel beam and Hertzian electric dipole radiation, numerical results of the normalized differential scattering cross section are presented, and the scattering characteristics are analyzed concisely.

Numerically Efficient Line-Integral Representation of Physical-Optics Scattered Field: The Case of Perfectly Conducting Surface Illuminated by Electric Hertzian Dipoles

This paper presents a novel line-integral representation of the physical-optics radiation integral from a perfectly conducting surface illuminated by a finite number of electric Hertzian dipoles. By introducing a new dyad potential, this novel representation guarantees the integrand free from singularities along the computational path. As such, it can be easily integrated for arbitrary positions of the source and observation points. Conversely, for certain situations of the Hertzian dipole being on the cone connecting the observation point to the scattering rim, the existing formulations exhibit a nonremovable singularity in their integrands. This will lead to invalid or inaccurate results. Meanwhile, for near-singular integration region, time-consuming computations need to be performed by utilizing a variable mesh integration. The efficiency in numerical calculation is the main objective of this kind of approach, and the time reduction performance would be improved by our singularity-free formula. The line-integral representation offers an alternative method to rapidly solve the scattering problem as it is usually more efficient than producing the same result in conventional surface-integral. Simple and complicated numerical examples are included to demonstrate the beneficial effect of the proposed expressions in terms of efficiency and accuracy.

Semi-analytical solution to arbitrarily shaped beam scattering

Based on the field expansions in terms of appropriate spherical vector wave functions and the method of moments scheme, an exact semi-analytical solution to the scattering of an arbitrarily shaped beam is given. For incidence of a Gaussian beam, zero-order Bessel beam and Hertzian electric dipole radiation, numerical results of the normalized differential scattering cross section are presented to a spheroid and a circular cylinder of finite length, and the scattering properties are analyzed concisely.

Characteristics of near field of the horizontal vibrator located above a square screen

The 3D vector problem concerned with the diffraction of the horizontal half-wave vibrator field by a perfectly conducting and infinitely thin rectangular screen is solved during observations at a finite distance from the vibrator. The technique for calculating the diffracted field, which is based on the laws of geometric diffraction theory and uniform diffraction coefficients obtained from the rigorous solution to the problem of the diffraction of the field of a Hertzian electric dipole at the edge of a perfectly conducting semiplane, is proposed. Fast-acting programs for calculating and analyzing the amplitudes and phases of the components of diffracted and complete vibrator fields in the entire space of observation angles at the set distance of the observation point from a rectangular screen and along the normal to the screen under changes in the distance between the screen and the observation point are developed. The character of the transformation of the spatial amplitude distribution of three field components depending on removal of observation point from an antenna is studied. It is shown that the distance to the far field zone of the investigated radiating system exceeds two wave lengths.

Superbackscattering Antenna Arrays

This paper discusses the theory, design, and practical implementation of superbackscattering antenna arrays. In analogy with Uzkov's maximal directivity theorem, it is demonstrated that the maximal backscattering cross-section, normalized to the wavelength squared, of a linear array of N isotropic scatterers whose separation tends to zero is N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> (N+1) <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> /(4π). This analytical result is validated via numerical optimization of the excitation coefficients, and the same procedure is utilized to assess the maximal backscattering of arrays of electric Hertzian dipoles (EHDs). It is found that electrically small arrays of two and three EHDs can enhance the backscattering by factors of 6.22 and 22.01, respectively, with respect to the maximum value generated by a single element. In addition, physical realizations of arrays featuring comparable enhancement factors can be straightforwardly designed by using a simple procedure inspired by Yagi-Uda antenna concepts. The practical implementations of such arrays based on copper wires and printed circuit technologies is also addressed.

Designs and Performance Characteristics of Coated Nanotoroid Antennas

The electromagnetic properties of a toroidal coated nanoparticle (T-CNP) antenna with an active core (doped with rare earth erbium Er3+ions) are investigated. It is demonstrated that the active T-CNP acts as a strong dipole radiator at its resonance frequency when it is excited by a plane wave or an electric Hertzian dipole (EHD) radiating element. It is shown that in comparison to being a passive structure, the plane wave scattering cross section of the T-CNP can be increased by nearly 108 dBsm at its resonance frequency when it is active. Moreover, it is further demonstrated that the maximum peak of the power radiated by an EHD element in the presence of a properly designed active T-CNP is more than 120 dB over its value when radiating in free space; that is, its Purcell factor is 1012.

Transmitted fields of a directional antenna in proximity of a wall

Transmission of a directional antenna in near proximity of a building wall modelled by a semi-finite dielectric slab above a perfectly conducting ground is investigated and an accurate and fast method to predict wall penetration loss (PL) once the source/observation points are in proximity of the wall is proposed. First, the antenna is replaced by an array of electric Hertzian dipoles with approximately the same half power beamwidth. Second, the dipole array radiation is calculated both numerically and asymptotically. They are based on computation of Sommerfeld integrals using Filon quadrature (FQ) technique and the steepest descent method, respectively. Third, PL of a typical x -polarised and y -polarised horn and a z -polarised wire antenna, simulated in FEKO using the method of moments (MoM) is compared with that of, respectively, the x -, y - and z -directed dipole arrays calculated using FQ technique. A good agreement between MoM and the dipole model results are obtained for relatively short stand-off distances for which estimation based on slab transmission coefficient is not an accurate approximation. The proposed dipole array model with FQ technique makes calculation at least 7.5 times faster than FEKO. Fourth, PL for different wall permittivity and conductivity is studied.

Nano-sensing of the orientation of fluorescing molecules with active coated nano-particles

The potential of using active coated nano-particles to determine the orientation of fluorescing molecules is reported. By treating each fluorescing molecule as an electric Hertzian dipole, single and multiple fluorescing molecules emitting coherently and incoherently in various orientations are considered in the presence of active coated nano-particles. It is demonstrated that in addition to offering a means to determine the orientation of a single molecule or the over-all orientation of the molecules surrounding it, the nature of the far-field response from the active coated nano-particles provides insight into the degree of phase coherence between emitters in specific molecular environments.