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Electromagnetic energy around Hertzian dipoles
Abstract
This paper considers the behavior of electromagnetic energy around
Hertzian dipoles. The method of “causal surfaces” (surfaces
through which there is no net flow of electromagnetic energy) is used to
partition and track the energy. A variety of examples, involving both
transient and harmonic time dependence, are presented, to illustrate the
way in which static and/or reactive energy is converted to outgoing,
uncoupled, “radiated” energy around a Hertzian or point
dipole. The principal conclusion is that although accelerating charge
may be thought of as the source of the radiation fields, the source of
the radiated energy lies in the static and/or reactive field energy near
an antenna, and not “in” or “on” an antenna
itself
... The time-domain electromagnetic fields of TM antenna in free space can be found in [31] E θ (t, r, θ) = ηdl 4πr ...
... In free space (or lossless medium), the timedomain normalized radial EFV within one wavelength is shown in Fig. 4 (a) and (b) for TE and TM respectively. Our TM result of Fig. 4 (a) repeated the pattern in [31]. We recognize EFV is highly related to radiation efficiency. ...
... Comparing to Poynting power (19) and (20) to the Ohmic losses (31) and ( ...
We investigate dipoles generated by electric current line (TM), electric loop (TE), and mechanically spinning of electret and magnet. While far-zone |HE| of the TE and TM dipole are identical, their near-zone behaviors are drastically different. We present closed form expressions of the Ohmic loss in a spherical lossy shell (SLS) for the first time, which leads to accurate computations and discussions of the article. For electrically small dipole of normalized half dipole-length |ka| ≪1, analytic results show that the radiation efficiency ηr is proportional to |ka| 3 for TM dipole, and |ka| for TE dipole, respectively. Consequently, ηr of TE can be better than TM in two to three orders of magnitude for under seawater communication. The time-domain energy flow velocity (EFV) pattern shows that TM dipole in lossy media is cavity-dominating, while TE/TM in lossless and TE in lossy medium are all radiation-dominating. Numerical results reveal that mechanically spinning dipole is smaller in size and weight but it requires more operation power, compared to its electromagnetic counter-partners. Finally, design, tuning and impedance matching of low-profile TE dipole antenna are outlined.
... We are usually more concerned for the far fields because of the notion of antennas as the radiating devices. The study of near fields for the hertz dipole in past has revealed interesting features such as the presence of causal surfaces (the surfaces with equal and opposite power flow) around the dipole Schantz [2001] Schantz et al. [2002. These surfaces have been called as the source of the radiation. ...
... These surfaces doesn't have a net outward power flux and exists at the very vicinity of an antenna beyond which an electromagnetic wave is said to be radiated. In this paper Schantz [2001], Schantz has reported the existence of such surfaces and have analysed the near field region of a hertzian dipole in time domain. This region has been regarded as the seat of reactive energy which is the actual source of radiation. ...
This paper investigates the propagation and radiation of spin waves in gyroelectric waveguides within the terahertz (THz) frequency range. With applications in imaging, spectroscopy, and integrated circuits, THz radiation has garnered significant interest, but the two-way propagation of traditional plasmonic waveguides limits their potential in nonreciprocal devices like isolators and switches. We explore the use of magnetically biased semiconductors, particularly InSb, which exhibit gyroelectric behavior at THz frequencies, offering promising alternatives to ferrites that face limitations at higher frequencies. Through the analysis of the near field region of a dipole antenna and a loop antenna, we examine the coupling between magnons and photons and the formation of reactive modes with imaginary impedance. We demonstrate how gyrotropy breaks spin-momentum locking, leading to unidirectional propagation of waves, and investigate the emergence of breathing and hyperbolic modes, along with cut-off modes, in these media. Our findings provide a deeper understanding of the underlying physics of THz waveguides and their potential for the development of advanced radiating and guiding structures.
... It should be finally noticed that, in [66][67][68], indications of the possibility of defining the near-field region boundary for elementary sources were given. In particular, in [66][67][68], an elementary electric dipole was considered, and the phase shift ∆φ between the transverse components of electric and magnetic fields was examined against the distance r from the source, obtaining ...
... It should be finally noticed that, in [66][67][68], indications of the possibility of defining the near-field region boundary for elementary sources were given. In particular, in [66][67][68], an elementary electric dipole was considered, and the phase shift ∆φ between the transverse components of electric and magnetic fields was examined against the distance r from the source, obtaining ...
We review the field regions and their boundaries around an electromagnetic source. We consider the cases of sources whose dimensions are comparable or larger than the wavelength, of planar sources/apertures, and of sources whose dimensions are small with respect to the wavelength and the criteria involving the strength of the reactive components of the electromagnetic field with respect to the radiative ones. The Fraunhofer and the Fresnel Regions are detailed, along with references to the paraxial approximation for planar apertures. The near-field and intermediate regions are also discussed. We review the standard boundaries between the regions. However, the standard boundaries are not clearly marked, nor are the regions uniquely defined. Accordingly, we also discuss different criteria that have been proposed during the years, which depend on the application and typically rely on numerical arguments, but are not necessarily universally accepted.
... The time-domain electromagnetic fields of TM antenna in free space can be found in [30] Similarly, for TE case ...
... In free space (or lossless medium), the time-domain normalized radial EFV within one wavelength is shown in Fig. 4a and b for TE and TM respectively. Our TM result of Fig. 4a repeated the pattern in [30]. We recognize EFV is highly related to radiation efficiency. ...
In this paper we present the results of a study of electronically and mechanically generated transverse magnetic (TM) and transverse electric (TE) dipoles in a lossy environment, so that antenna design guidelines may be established at the system level. At far-zone, the ratio is the intrinsic impedance, and they are identical for the TM and its dual TE dipoles. Nonetheless, the ratio in near-zone behaves drastically different between the TM and dual TE. We derived closed form expressions of the antenna Ohmic loss in a spherical lossy shell (SLS) for the first time, yielding precise radiation efficiency and accurate computations. For electrically small dipole of normalized half dipole-length , analytic results show that is proportional to for TM dipole, and |ka| for TE dipole, respectively. Consequently, efficiency of TE can be better than TM in two to three orders of magnitude for under seawater communication. The time-domain energy flow velocity (EFV) patterns show that the TE dipoles are always radiation-dominating, in either lossless or lossy medium. Numerical results reveal that mechanically spinning dipole is smaller in size and weight but it requires more operation power, compared to its electromagnetic counter-partners. Finally, design, tuning and impedance matching of low-profile TE dipole antenna are outlined.
... mhcdias@ime.eb.br. central [3][4]. Calcular a distribuição de campo próximo de uma antena não é simples. ...
... Em primeiro lugar, observando a Fig. 1, percebe-se que cada dipolo infinitesimal considerado na integração apresenta contribuições em ambas as direções fixas R e q. O outro cuidado diz respeito ao aspecto vetorial da integração. Com isso, tomando-se a componente E q como exemplo, a integração necessária para seu cálculo é dada por: [3][4]. ...
... An radiated power approach, including near and fare (kr ≪ 1 to kr ≫ 1) field, we find at Balanis [1]. The fields of the Hertzian dipole and in particular the reactant field were considered in the work of Schantz [10]. A system theoretical approach with isotropic antennas in Uniform Linear Array ULA configuration is given in [12]. ...
We investigate the theoretical impedance equations for several near-field antenna positions. In the standard model one computes the currents at the antennas for given voltages using the impedance matrix of the antennas, which is only possible if the determinant of the impedance matrix is non-zero. We consider Hertzian group antennas, its relative corresponding impedance and two approximations (mid and far) of it. For the approximations we show that for many situations the determinant is zero. We find three antenna configurations for three antennas, i.e., on a line, on a right triangle, and an isosceles triangle, which result in a zero determinant of the impedance for the far-field approximation. This means that with existing methods, one cannot determine the behavior of this antenna system. For the better mid approximation, we find a configuration of 15 triangular-positioned antennas resulting in a singular impedance matrix. Furthermore, we investigate grid placed antennas in the more accurate Hertzian impedance model and find that for wavelengths of grid distance for n=2, ..., 8 the absolute value of the determinant of the corresponding impedance matrix decreases by an order of magnitude with each increased grid size.
... or "stored" energy around resonant ESAs with its IBW, radiated power and peak gain. However, while the "stored energy" is well-defined in the limit for static cases as well as for pure guided-wave systems or lumped circuits, evaluation of total "stored" energy around any radiator, which is fundamentally an unbounded system, is inherently problematic [8], [11], [13]. Therefore, it is not possible to have a unique definition of "stored energy" around radiators valid for all cases [11], [13]. ...
p>In this paper, we present an electromagnetic (EM) Lagrangian approach to quantify the reactive energy density distribution around generic antenna systems operating in the time-harmonic regime. First, we introduce the `period-averaged EM Lagrangian density' for radiating EM fields and present its intrinsic relations with the complex Poynting vector, total EM energy density, complex Helicity density, antenna reactive energy and radiation Q-factor. Furthermore, utilising full-wave MoM (method-of-moments) based MATLAB Antenna Toolbox, we compute contour plots of period-averaged EM Lagrangian density around thin-strip dipoles as well as printed microstrip patch antennas. It is demonstrated that such contour plots can not only distinguish between the capacitive and inductive nature of reactive energy density around multiple antenna systems, but also assist in the visualization of the links of inter-element mutual coupling via reactive fields. Such spatial maps of period-averaged EM Lagrangian density can be potentially useful for engineers working in the design of antenna arrays, MIMO (multiple-input multiple-output) and full-duplex systems, as well as EMI/EMC (Electromagnetic Interference/Compatibility) compliant devices.</p
... The antenna Q-factor connects the total reactive or "stored" energy around resonant ESAs with its IBW, radiated power and peak gain. However, while the "stored energy" D. Sarkar is well-defined in the limit for static cases as well as for pure guided-wave systems or lumped circuits, evaluation of total "stored" energy around any radiator, which is fundamentally an unbounded system, is inherently problematic [8], [11], [13]. Therefore, it is not possible to have a unique definition of "stored energy" around radiators valid for all cases [11], [13]. ...
p>In this paper, we present an electromagnetic (EM) Lagrangian approach to quantify the reactive energy density distribution around generic antenna systems operating in the time-harmonic regime. First, we introduce the `period-averaged EM Lagrangian density' for radiating EM fields and present its intrinsic relations with the complex Poynting vector, total EM energy density, complex Helicity density, antenna reactive energy and radiation Q-factor. Furthermore, utilising full-wave MoM (method-of-moments) based MATLAB Antenna Toolbox, we compute contour plots of period-averaged EM Lagrangian density around thin-strip dipoles as well as printed microstrip patch antennas. It is demonstrated that such contour plots can not only distinguish between the capacitive and inductive nature of reactive energy density around multiple antenna systems, but also assist in the visualization of the links of inter-element mutual coupling via reactive fields. Such spatial maps of period-averaged EM Lagrangian density can be potentially useful for engineers working in the design of antenna arrays, MIMO (multiple-input multiple-output) and full-duplex systems, as well as EMI/EMC (Electromagnetic Interference/Compatibility) compliant devices.</p
In antenna theory, a full understanding of both transmitting and receiving characteristics is essential. While many studies have investigated field energy propagation and flow velocity near transmitting antennas, there is a distinct lack of similar studies on receiving antennas. The Poynting streamline method can be used to visually plot the field energy trajectory of a receiving antenna from the far field to the near field region. The visual representation distinguishes between Poynting streamlines absorbed by the antenna load and Poynting streamlines bypassing the antenna, allowing analysis of the trajectory, propagation time, and velocity of field energy flow near the antenna. In this work, it is found that due to the reactive field near the receiving dipole antenna, the velocity of the field energy flow near the antenna is slower than the speed of light. Despite the variation in trajectory length, the propagation time of the field energy flowing along the Poynting streamline, all of which terminates at the antenna load, exhibits approximate uniformity.
Citation
L. MANDEL, "Energy Flow from an Atomic Dipole in Classical Electrodynamics," J. Opt. Soc. Am. 62, 1011-1012 (1972)
http://www.opticsinfobase.org/josa/abstract.cfm?URI=josa-62-8-1011
In a typical dipole decay, the induction magnetic field and the radiation magnetic field are in opposing directions. The former is dominant close to the decay, and the latter is dominant far away. Thus, there exists a surface on which these two components cancel each other, so that the magnetic field reverses direction. Because the magnetic field changes direction, so also will the Poynting vector field, provided the electric field is reasonably well behaved. This defines a "causal surface," within which electromagnetic energy will collapse, and outside which the electromagnetic energy will radiate away. I present a simple example, the decay of a point electric dipole, to argue that the radiated energy comes, not necessarily from the accelerating charges themselves, but from the energy stored in the far field.
J. B. Marion New York: Academic Press. 1965. Pp. xv + 479. Price 86s.
As the author says, there exists a vast literature of general works on electricity and magnetism. This book extracts and organizes the topics most relevant to radiation theory, and presents them to the student who is equipped with the basic physical facts and the basic mathematical techniques, but who may need some guidance through the morass of analysis found in the more exhaustive works.
Described by Einstein as “the most important event in physics since Newton's time,” the discovery by James Clerk Maxwell that a vast array of phenomena could be united by four elegant formulas remains one of the greatest successes of modern physics. This book, based on the third originally published in 1891, presents the original work which underpins the electronic revolution in the 20th century and which inspired both Lorentz’s theories on the electron and Einstein's theory of relativity. Volume II covers magnetism and electromagnetism.
MAXWELL, James Clerk. A treatise on electricity and magnetism.Vol. I. Oxford: Clarenton Press Series, 1873. Preface, p.V-XIV. [Le texte intégral A treatise on electricity and magnetism est disponible en mode image sur Gallica]