Special Issue "Symmetry in Electromagnetism"

A special issue of Symmetry (ISSN 2073-8994).

Deadline for manuscript submissions: 31 October 2019.

Special Issue Editors

Guest Editor
Prof. Dr. Albert Ferrando Website E-Mail
Departamento de Óptica, C/ Dr. Moliner, 50, 46100 Burjassot, Valencia, Spain
Fax: +34 96 354 4715
Interests: electromagnetic propagation in optical waveguides; fiber devices; microwave waveguides; cavities
Guest Editor
Dr. Miguel Ángel García-March Website E-Mail
ICFO – The Institute of Photonic Sciences, Mediterranean Technology Park, Av. Carl Friedrich Gauss, 3, 08860 Castelldefels (Barcelona), Spain
Phone: (+34) 93 553 4134
Fax: (+34) 93 553 4000
Interests: expertise in quantum optics; atomic physics; nonlinear dynamics; statistical physics; quantum field theory; many body systems; disordered systems; neural networks; quantum information; foundations of quantum mechanics

Special Issue Information

Dear Collegues,

Electromagnetism plays an essential role, both in basic and applied physics research. The discovery of electromagnetism as the unifying theory for electricity and magnetism represented a cornerstone in modern physics. From the very beginning, symmetry was crucial to the concept of unification: Electromagnetism was soon formulated as a gauge theory, in which a local phase symmetry explained its mathematical formulation. This early connection between symmetry and electromagnetism shows that a symmetry approach to many electromagnetic phenomena is recurrent, even today.

Moreover, many crucial technological advances associated with electromagnetism have shaped modern civilization. The control of electromagnetic radiation in nearly all its spectra and scales is still a matter of deep interest. With the advances in material science, even at the nanoscale, the manipulation of matter–radiation interactions has reached unprecedented levels of sophistication. New generations of composite materials present effective electromagnetic properties that permit to mold electromagnetic radiation in ways that were unconceivable just a few years ago. This is a fertile field for applications and for basic understanding in which symmetry, as in the past, bridges apparently-unrelated phenomena, from condensed matter to high-energy physics.

In this Special Issue we want to pay attention to this modern view on electromagnetism, which represents both an arena for academic advance and exciting applications. This Special Issue will include contributions on electromagnetic phenomena, in which symmetry plays a significant role, such as (though not restricted to): Phase phenomena and its management  (e.g., knots of light or in singular optics); dual electromagnetism; PT-symmetry; mode classification in electromagnetic devices; photonic condensed matter (including topological photonics, synthetic gauge fields and spin-orbit effects in electromagnetism); quantum aspects of electromagnetic waves from a symmetry perspective (symmetry entanglement in optics); etc.

Prof. Dr. Albert Ferrando
Dr. Miguel Ángel García-March
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All papers will be peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Symmetry is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Topological photonics
  • Synthetic gauge fields in EM
  • Duality in EM
  • PT-symmetry in EM
  • Knots in EM
  • Symmetry and EM devices. Mode classification
  • Spin-Orbit effects in EM
  • Symmetry in complex light/singular optics
  • Symmetry in EM metamaterials
  • Symmetry entanglement in optics

Published Papers (11 papers)

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Research

Open AccessArticle
A Non-Local Action for Electrodynamics: Duality Symmetry and the Aharonov-Bohm Effect, Revisited
Symmetry 2019, 11(10), 1191; https://doi.org/10.3390/sym11101191 (registering DOI) - 21 Sep 2019
Abstract
A non-local action functional for electrodynamics depending on the electric and magnetic fields, instead of potentials, has been proposed in the literature. In this work we elaborate and improve this proposal. We also use this formalism to confront the electric-magnetic duality symmetry of [...] Read more.
A non-local action functional for electrodynamics depending on the electric and magnetic fields, instead of potentials, has been proposed in the literature. In this work we elaborate and improve this proposal. We also use this formalism to confront the electric-magnetic duality symmetry of the electromagnetic field and the Aharonov–Bohm effect, two subtle aspects of electrodynamics that we examine in a novel way. We show how the former can be derived from the simple harmonic oscillator character of vacuum electrodynamics, while also demonstrating how the magnetic version of the latter naturally arises in an explicitly non-local manner. Full article
(This article belongs to the Special Issue Symmetry in Electromagnetism)
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Open AccessArticle
Design and Analysis of a Plate Type Electrodynamic Suspension Structure for Ground High Speed Systems
Symmetry 2019, 11(9), 1117; https://doi.org/10.3390/sym11091117 - 04 Sep 2019
Abstract
The research of ground high speed systems has been popular, especially after the announcement of Hyperloop concept, and the analysis of the suspension structure is critical for the design of the system. This paper focuses on the design and analysis of a plate [...] Read more.
The research of ground high speed systems has been popular, especially after the announcement of Hyperloop concept, and the analysis of the suspension structure is critical for the design of the system. This paper focuses on the design and analysis of a plate type electrodynamic suspension (EDS) structure for the ground high speed system. The working principle of proposed whole system with functions of levitation, guidance and propulsion is presented, and the researched EDS structure is composed of permanent magnets (or superconducting magnets) and non-ferromagnetic conductive plates. Levitation and guidance are achieved by forces generated through the motion of the magnets along the plates. The plate type EDS structure is analyzed by three-dimensional (3D) finite element method (FEM) in ANSYS Maxwell. Structure parameters that affect the EDS performances are investigated, which include dimensions of magnets and plates, plate material, the relative position between magnets and plates, and arrangement of magnets. The properties of forces are discussed, especially for the levitation force, and the levitation working point is decided based on the analysis. Levitation-drag ratio of the plate type structure is investigated, and it improves with the increasing of vehicle velocity. The analysis results indicate that the plate type EDS structure is feasible for applications in ground high speed systems. The following study will focus on the dynamic research of the EDS system. Full article
(This article belongs to the Special Issue Symmetry in Electromagnetism)
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Open AccessArticle
Null Electromagnetic Fields from Dilatation and Rotation Transformations of the Hopfion
Symmetry 2019, 11(9), 1105; https://doi.org/10.3390/sym11091105 - 02 Sep 2019
Abstract
The application of topology concepts to Maxwell equations has led to the developing of the whole area of electromagnetic knots. In this paper, we apply some symmetry transformations to a particular electromagnetic knot, the hopfion field, to get a new set of knotted [...] Read more.
The application of topology concepts to Maxwell equations has led to the developing of the whole area of electromagnetic knots. In this paper, we apply some symmetry transformations to a particular electromagnetic knot, the hopfion field, to get a new set of knotted solutions with the properties of being null. The new fields are obtained by a homothetic transformation (dilatation) and a rotation of the hopfion, and we study the constraints that the transformations must fulfill in order to generate valid electromagnetic fields propagating in a vacuum. We make use of the Bateman construction and calculate the four-potentials and the electromagnetic helicities. It is observed that the topology of the field lines does not seem to be conserved as it is for the hopfion. Full article
(This article belongs to the Special Issue Symmetry in Electromagnetism)
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Open AccessArticle
Maxwell Electrodynamics in Terms of Physical Potentials
Symmetry 2019, 11(7), 915; https://doi.org/10.3390/sym11070915 - 14 Jul 2019
Abstract
A fully relativistically covariant and manifestly gauge-invariant formulation of classical Maxwell electrodynamics is presented, purely in terms of gauge-invariant potentials without entailing any gauge fixing. We show that the inhomogeneous equations satisfied by the physical scalar and vector potentials (originally discovered by Maxwell) [...] Read more.
A fully relativistically covariant and manifestly gauge-invariant formulation of classical Maxwell electrodynamics is presented, purely in terms of gauge-invariant potentials without entailing any gauge fixing. We show that the inhomogeneous equations satisfied by the physical scalar and vector potentials (originally discovered by Maxwell) have the same symmetry as the isometry of Minkowski spacetime, thereby reproducing Einstein’s incipient approach leading to his discovery of special relativity as a spacetime symmetry. To arrive at this conclusion, we show how the Maxwell equations for the potentials follow from stationary electromagnetism by replacing the Laplacian operator with the d’Alembertian operator, while making all variables dependent on space and time. We also establish consistency of these equations by deriving them from the standard Maxwell equations for the field strengths, showing that there is a unique projection operator which projects onto the physical potentials. Properties of the physical potentials are elaborated through their iterative Nöther coupling to a charged scalar field leading to the Abelian Higgs model, and through a sketch of the Aharonov–Bohm effect, where dependence of the Aharonov–Bohm phase on the physical vector potential is highlighted. Full article
(This article belongs to the Special Issue Symmetry in Electromagnetism)
Open AccessArticle
Magnetic and Structural Properties of Barium Hexaferrite Nanoparticles Doped with Titanium
Symmetry 2019, 11(6), 732; https://doi.org/10.3390/sym11060732 - 28 May 2019
Abstract
Samples of Barium Hexaferrite doped with Titanium BaFe12−xTixO19 with (x = 0.0, 0.2, 0.4, 0.6, 0.8, 1.0) were synthesized by the sol–gel auto-combustion technique. The powdered samples were divided into two parts, one sintered at 850 [...] Read more.
Samples of Barium Hexaferrite doped with Titanium BaFe12−xTixO19 with (x = 0.0, 0.2, 0.4, 0.6, 0.8, 1.0) were synthesized by the sol–gel auto-combustion technique. The powdered samples were divided into two parts, one sintered at 850 °C and another sintered 1000 °C for 1 h and samples were characterized by different experimental techniques. The XRD patterns confirmed the presence of M-type hexaferrite phase. The sizes of the crystallites were calculated by the Scherer equation, and the sizes were in the range of 27–42 nm. Using the hysteresis loops, the saturation magnetization Ms, remanence (Mr), the relative ratio (Mr/Ms), and the coercivity (Hc) were calculated. The study showed that the saturation magnetization (Ms) and remanence (Mr) decreased with increasing titanium concentration and were in the range from 44.65–17.17 emu/g and 23.1–7.7 emu/g, respectively. The coercivity (Hc) ranged between 0.583 and 4.51 (kOe). The magnetic properties of these Barium Hexaferrite doped with Titanium indicated that they could be used in the recording equipment and permanent magnets. Full article
(This article belongs to the Special Issue Symmetry in Electromagnetism)
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Open AccessArticle
On the Evolutionary Form of the Constraints in Electrodynamics
Symmetry 2019, 11(1), 10; https://doi.org/10.3390/sym11010010 - 22 Dec 2018
Cited by 1
Abstract
The constraint equations in Maxwell theory are investigated. In analogy with some recent results on the constraints of general relativity, it is shown, regardless of the signature and dimension of the ambient space, that the “divergence of a vector field”-type constraint can always [...] Read more.
The constraint equations in Maxwell theory are investigated. In analogy with some recent results on the constraints of general relativity, it is shown, regardless of the signature and dimension of the ambient space, that the “divergence of a vector field”-type constraint can always be put into linear first order hyperbolic form for which the global existence and uniqueness of solutions to an initial-boundary value problem are guaranteed. Full article
(This article belongs to the Special Issue Symmetry in Electromagnetism)
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Open AccessArticle
On the Electric-Magnetic Duality Symmetry: Quantum Anomaly, Optical Helicity, and Particle Creation
Symmetry 2018, 10(12), 763; https://doi.org/10.3390/sym10120763 - 17 Dec 2018
Abstract
It is well known that not every symmetry of a classical field theory is also a symmetry of its quantum version. When this occurs, we speak of quantum anomalies. The existence of anomalies imply that some classical Noether charges are no longer conserved [...] Read more.
It is well known that not every symmetry of a classical field theory is also a symmetry of its quantum version. When this occurs, we speak of quantum anomalies. The existence of anomalies imply that some classical Noether charges are no longer conserved in the quantum theory. In this paper, we discuss a new example for quantum electromagnetic fields propagating in the presence of gravity. We argue that the symmetry under electric-magnetic duality rotations of the source-free Maxwell action is anomalous in curved spacetimes. The classical Noether charge associated with these transformations accounts for the net circular polarization or the optical helicity of the electromagnetic field. Therefore, our results describe the way the spacetime curvature changes the helicity of photons and opens the possibility of extracting information from strong gravitational fields through the observation of the polarization of photons. We also argue that the physical consequences of this anomaly can be understood in terms of the asymmetric quantum creation of photons by the gravitational field. Full article
(This article belongs to the Special Issue Symmetry in Electromagnetism)
Open AccessArticle
Geometric Objects: A Quality Index to Electromagnetic Energy Transfer Performance in Sustainable Smart Buildings
Symmetry 2018, 10(12), 676; https://doi.org/10.3390/sym10120676 - 29 Nov 2018
Abstract
Sustainable smart buildings play an essential role in terms of more efficient energy. However, these buildings as electric loads are affected by an important distortion in the current and voltage waveforms caused by the increasing proliferation of nonlinear electronic devices. Overall, buildings all [...] Read more.
Sustainable smart buildings play an essential role in terms of more efficient energy. However, these buildings as electric loads are affected by an important distortion in the current and voltage waveforms caused by the increasing proliferation of nonlinear electronic devices. Overall, buildings all around the world consume a significant amount of energy, which is about one-third of the total primary energy resources. Optimization of the power transfer process of such amount of energy is a crucial issue that needs specific tools to integrate energy-efficient behaviour throughout the grid. When nonlinear loads are present, new capable ways of thinking are needed to consider the effects of harmonics and related power components. In this manner, technology innovations are necessary to update the power factor concept to a generalized total or a true one, where different power components involved in it calculation, properly reflect each harmonic interaction. This work addresses an innovative theory that applies the Poynting Vector philosophy via Geometric Algebra to the electromagnetic energy transfer process providing a physical foundation. In this framework, it is possible to analyse and detect the nature of disturbing loads in the exponential growth of new globalized buildings and architectures in our era. This new insight is based on the concept of geometric objects with different dimension: vector, bivector, trivector, multivector. Within this paper, these objects are correlated with the electromagnetic quantities responsible for the energy flow supplied to the most common loads in sustainable smart buildings. Besides, it must be considered that these phenomena are characterized by a quality index multivector appropriate even for detecting harmonic sources. A numerical example is used to illustrate the clear capabilities of the suggested index when it applies to industrial loads for optimization of energy control systems and enhance comfort management in smart sustainable buildings. Full article
(This article belongs to the Special Issue Symmetry in Electromagnetism)
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Open AccessFeature PaperArticle
On the Computation of the Dispersion Diagram of Symmetric One-Dimensionally Periodic Structures
Symmetry 2018, 10(8), 307; https://doi.org/10.3390/sym10080307 - 01 Aug 2018
Cited by 8
Abstract
A critical discussion on the computation of the dispersion diagram of electromagnetic guiding/radiating structures with one-dimensional periodicity using general-purpose electromagnetic simulation software is presented in this work. In these methods, full-wave simulations of finite sections of the periodic structure are combined with appropriate [...] Read more.
A critical discussion on the computation of the dispersion diagram of electromagnetic guiding/radiating structures with one-dimensional periodicity using general-purpose electromagnetic simulation software is presented in this work. In these methods, full-wave simulations of finite sections of the periodic structure are combined with appropriate simplifying network models. In particular, we analyze the advantages and limitations of two different combined methods, with emphasis on the determination of their range of validity. Our discussion is complemented with several selected numerical examples in order to show the most relevant aspects that a potential user of these methods should be aware of. Special attention is paid to the relevant role played by the high-order coupling between adjacent unit cells and between the two halves of unit cells exhibiting reflection, inversion, and glide symmetries. Full article
(This article belongs to the Special Issue Symmetry in Electromagnetism)
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Open AccessArticle
Denoising of Magnetocardiography Based on Improved Variational Mode Decomposition and Interval Thresholding Method
Symmetry 2018, 10(7), 269; https://doi.org/10.3390/sym10070269 - 09 Jul 2018
Cited by 2
Abstract
Recently, magnetocardiography (MCG) has attracted increasing attention as a non-invasive and non-contact technique for detecting electrocardioelectric functions. However, the severe background noise makes it difficult to extract information. Variational Mode Decomposition (VMD), which is an entirely non-recursive model, is used to decompose the [...] Read more.
Recently, magnetocardiography (MCG) has attracted increasing attention as a non-invasive and non-contact technique for detecting electrocardioelectric functions. However, the severe background noise makes it difficult to extract information. Variational Mode Decomposition (VMD), which is an entirely non-recursive model, is used to decompose the non-stationary signal into the intrinsic mode functions (IMFs). Traditional VMD algorithms cannot control the bandwidth of each IMF, whose quadratic penalty lacks adaptivity. As a result, baseline drift noise is still present or medical information is lost. In this paper, to overcome the unadaptable quadratic penalty problem, an improved VMD model via correlation coefficient and new update formulas are proposed to decompose MCG signals. To improve the denoising precision, this algorithm is combined with the interval threshold algorithm. First, the correlation coefficient is calculated, to determine quadratic penalty, in order to extract the first IMF made up of baseline drift. Then, the new update formulas derived from the variance that describes the noise level are used, to perform decomposition on the rest signal. Finally, the Interval thresholding algorithm is performed on each IMF. Theoretical analysis and experimental results show that this algorithm can effectively improve the output signal-to-noise ratio and has superior performance. Full article
(This article belongs to the Special Issue Symmetry in Electromagnetism)
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Open AccessFeature PaperArticle
Spin-Orbital Momentum Decomposition and Helicity Exchange in a Set of Non-Null Knotted Electromagnetic Fields
Symmetry 2018, 10(4), 88; https://doi.org/10.3390/sym10040088 - 30 Mar 2018
Cited by 3
Abstract
We calculate analytically the spin-orbital decomposition of the angular momentum using completely nonparaxial fields that have a certain degree of linkage of electric and magnetic lines. The split of the angular momentum into spin-orbital components is worked out for non-null knotted electromagnetic fields. [...] Read more.
We calculate analytically the spin-orbital decomposition of the angular momentum using completely nonparaxial fields that have a certain degree of linkage of electric and magnetic lines. The split of the angular momentum into spin-orbital components is worked out for non-null knotted electromagnetic fields. The relation between magnetic and electric helicities and spin-orbital decomposition of the angular momentum is considered. We demonstrate that even if the total angular momentum and the values of the spin and orbital momentum are the same, the behavior of the local angular momentum density is rather different. By taking cases with constant and non-constant electric and magnetic helicities, we show that the total angular momentum density presents different characteristics during time evolution. Full article
(This article belongs to the Special Issue Symmetry in Electromagnetism)
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Planned Papers

The below list represents only planned manuscripts. Some of these manuscripts have not been received by the Editorial Office yet. Papers submitted to MDPI journals are subject to peer-review.

Author: Dr. Ivan Fernandez-Corbaton
Abstract: Symmetries and conservation laws are among the most pervasive ideas in theoretical physics. In the particular setting of material systems interacting with the electromagnetic field, the use of symmetry considerations as the starting point has been recently shown to be a productive approach. Which are the symmetries that the matter has to have or break for the field to be affected in a particular way? The answers have general validity: The symmetry requirements to observe a given effect on the field constitute a universal constraint on any physical system that achieves such effect. This allows to obtain design guidelines directly from some of the most general principles in physics. In my contribution, I will give an overview of the main ideas and results of this approach, with a special emphasis on the role of the electromagnetic duality symmetry which has been shown to play a crucial role in areas as diverse as optical activity, zero back-scattering, transformation optics, and interactions involving the angular momentum of light.

Title: On the electromagnetic duality symmetry
Authors: Ivan Agullo 1,  Adrian del Rio 2 and Jose Navarro-Salas 2
Affiliations: 1 Department of Physics and Astronomy, Louisiana State University, Baton Rouge, LA 70803-4001;
2 Departamento de Fisica Teorica-IFIC. Centro Mixto
Universitat de Valencia - CSIC. Burjassot 46100, Spain
Abstract: It is well known that the source-free Maxwell equations are invariant under electric-
magnetic duality rotations. However, it is less known that Maxwell's action also remains
invariant. These transformations are therefore a symmetry of the theory in Noether's
sense. The associated constant of motion is related to the di erence of intensity between
the right and left circularly polarized components. This conservation law holds even if the
electromagnetic eld interacts with an arbitrary classical gravitational eld. After reviewing
these results, we discuss whether this symmetry is maintained when the electromagnetic eld
is quantized. The answers is in the armative in the absence of gravity, but we nd that a
non-trivial classical gravitational background can break the symmetry. As a consequence,
the net polarization of the quantum electromagnetic eld fails to be conserved in curved
spacetimes. This is a quantum e ect, and it can be understood as the generalization of the
fermionic chiral anomaly to elds of spin one.

Author: Dr. Racz Istvan
Title: On the evolutionary form of the constraints in electrodynamics
Abstract: The constraint equations in Maxwell theory are investigated. In analogy with some recent results on the constraints of general relativity it is shown, regardless of the signature and dimension of the ambient space, that the $div\vec{E}=\rho$ type constraints can always be put into the form of a linear first order hyperbolic form to which global existence and uniqueness of solutions in initial-boundary value problems are always guaranteed.

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