Special Issue "Duality Symmetry"

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

Deadline for manuscript submissions: closed (30 November 2019).

Printed Edition Available!
A printed edition of this Special Issue is available here.

Special Issue Editor

Dr. Ivan Fernandez-Corbaton
Website
Guest Editor
Karlsruhe Institute of Technology (KIT), Institute of Nanotechnology, Hermann-von-Helmholtz-Platz 1, 76344 Eggenstein-Leopoldshafen, Germany
Interests: symmetry; symmetry breaking; chirality; duality; helicity; theoretical physics and its applications

Special Issue Information

Dear Colleagues,

     Symmetry is one of the most general concepts in physics. Symmetry arguments are used to explain and predict observations at all length scales, from elementary particles to cosmology. The generality of symmetry arguments, often combined with simplicity, makes them a powerful tool for both fundamental and applied investigations. In electrodynamics, one of the symmetries is the invariance of the equations under exchange of electric and magnetic quantities. The continuous version of this symmetry is most commonly known as electromagnetic duality symmetry. It has been known for more than a century, and, throughout this time, has influenced other areas of physics, like high energy physics and gravitation. Duality symmetry is inherently attached to its generator and conserved quantity, helicity, which is yet another concept that transcends electrodynamics.

      In recent years, duality, and helicity have been receiving renewed attention in their original electrodynamic context. Their conservation law has been reconsidered, analyzed, and quantified from different points of view, and convenient numerical tools have been developed for it. Helicity is also being used in the description of chiral particles with spin, and as an alternative to the electric/magnetic description of fields and interactions. Most of the time, the material system is not symmetric under duality transformations, the symmetry is broken, and the interaction with matter mixes the two possible helicities of the electromagnetic field. Yet, material structures that, at least to good approximation, restore the breaking of the symmetry are being proposed for different applications: zero-backscattering nanoparticle arrays, artificial optical activity, enhanced circular dichroism measurements, and protected photonic edge states, among others.

       In this Special Issue, we aim to gather contributions from electrodynamics and also other fields that consolidate and enlarge the usability of duality and/or helicity with regard to both applied and fundamental questions.

Dr. Ivan Fernandez-Corbaton
Guest Editor

Manuscript Submission Information

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Keywords

  • Electromagnetic duality symmetry
  • Electromagnetic helicity
  • Conservation laws
  • Symmetry breaking

Published Papers (6 papers)

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Research

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Open AccessArticle
Role of Geometric Shape in Chiral Optics
Symmetry 2020, 12(1), 158; https://doi.org/10.3390/sym12010158 - 13 Jan 2020
Abstract
The distinction of chiral and mirror symmetric objects is straightforward from a geometrical point of view. Since the biological as well as the optical activity of molecules strongly depend on their handedness, chirality has recently attracted high interest in the field of nano-optics. [...] Read more.
The distinction of chiral and mirror symmetric objects is straightforward from a geometrical point of view. Since the biological as well as the optical activity of molecules strongly depend on their handedness, chirality has recently attracted high interest in the field of nano-optics. Various aspects of associated phenomena including the influences of internal and external degrees of freedom on the optical response have been discussed. Here, we propose a constructive method to evaluate the possibility of observing any chiral response from an optical scatterer. Based on solely the T-matrix of one enantiomer, planes of minimal chiral response are located and compared to geometric mirror planes. This provides insights into the relation of geometric and optical properties and enables identifying the potential of chiral scatterers for nano-optical experiments. Full article
(This article belongs to the Special Issue Duality Symmetry) Printed Edition available
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Open AccessArticle
A Conformally Invariant Derivation of Average Electromagnetic Helicity
Symmetry 2019, 11(11), 1427; https://doi.org/10.3390/sym11111427 - 19 Nov 2019
Abstract
The average helicity of a given electromagnetic field measures the difference between the number of left- and right-handed photons contained in the field. Here, the average helicity is derived using the conformally invariant inner product for Maxwell fields. Several equivalent integral expressions in [...] Read more.
The average helicity of a given electromagnetic field measures the difference between the number of left- and right-handed photons contained in the field. Here, the average helicity is derived using the conformally invariant inner product for Maxwell fields. Several equivalent integral expressions in momentum space, in ( r , t ) space, and in the time-harmonic ( r , ω ) space are obtained, featuring Riemann–Silberstein-like fields and potentials. The time-harmonic expressions can be directly evaluated using the outputs of common numerical solvers of Maxwell equations. The results are shown to be equivalent to the well-known volume integral for the average helicity, featuring the electric and magnetic fields and potentials. Full article
(This article belongs to the Special Issue Duality Symmetry) Printed Edition available
Open AccessArticle
Geometric Structure behind Duality and Manifestation of Self-Duality from Electrical Circuits to Metamaterials
Symmetry 2019, 11(11), 1336; https://doi.org/10.3390/sym11111336 - 28 Oct 2019
Cited by 3
Abstract
In electromagnetic systems, duality is manifested in various forms: circuit, Keller–Dykhne, electromagnetic, and Babinet dualities. These dualities have been developed individually in different research fields and frequency regimes, leading to a lack of unified perspective. In this paper, we establish a unified view [...] Read more.
In electromagnetic systems, duality is manifested in various forms: circuit, Keller–Dykhne, electromagnetic, and Babinet dualities. These dualities have been developed individually in different research fields and frequency regimes, leading to a lack of unified perspective. In this paper, we establish a unified view of these dualities in electromagnetic systems. The underlying geometrical structures behind the dualities are elucidated by using concepts from algebraic topology and differential geometry. Moreover, we show that seemingly disparate phenomena, such as frequency-independent effective response, zero backscattering, and critical response, can be considered to be emergent phenomena of self-duality. Full article
(This article belongs to the Special Issue Duality Symmetry) Printed Edition available
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Open AccessArticle
Topologically Protected Duality on The Boundary of Maxwell-BF Theory
Symmetry 2019, 11(7), 921; https://doi.org/10.3390/sym11070921 - 15 Jul 2019
Cited by 1
Abstract
The Maxwell-BF theory with a single-sided planar boundary is considered in Euclidean four-dimensional spacetime. The presence of a boundary breaks the Ward identities, which describe the gauge symmetries of the theory, and, using standard methods of quantum field theory, the most general boundary [...] Read more.
The Maxwell-BF theory with a single-sided planar boundary is considered in Euclidean four-dimensional spacetime. The presence of a boundary breaks the Ward identities, which describe the gauge symmetries of the theory, and, using standard methods of quantum field theory, the most general boundary conditions and a nontrivial current algebra on the boundary are derived. The electromagnetic structure, which characterizes the boundary, is used to identify the three-dimensional degrees of freedom, which turn out to be formed by a scalar field and a vector field, related by a duality relation. The induced three-dimensional theory shows a strong–weak coupling duality, which separates different regimes described by different covariant actions. The role of the Maxwell term in the bulk action is discussed, together with the relevance of the topological nature of the bulk action for the boundary physics. Full article
(This article belongs to the Special Issue Duality Symmetry) Printed Edition available

Review

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Open AccessReview
U-Dualities in Type II and M-Theory: A Covariant Approach
Symmetry 2019, 11(8), 993; https://doi.org/10.3390/sym11080993 - 03 Aug 2019
Abstract
In this review, a short description of exceptional field theory and its application is presented. Exceptional field theories provide a U-duality covariant description of supergravity theories, allowing addressing relevant phenomena, such as non-geometricity. Some applications of the formalism are briefly described. Full article
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Other

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Open AccessPerspective
Optical Helicity and Optical Chirality in Free Space and in the Presence of Matter
Symmetry 2019, 11(9), 1113; https://doi.org/10.3390/sym11091113 - 03 Sep 2019
Cited by 8
Abstract
The inherently weak nature of chiral light–matter interactions can be enhanced by orders of magnitude utilizing artificially-engineered nanophotonic structures. These structures enable high spatial concentration of electromagnetic fields with controlled helicity and chirality. However, the effective design and optimization of nanostructures requires defining [...] Read more.
The inherently weak nature of chiral light–matter interactions can be enhanced by orders of magnitude utilizing artificially-engineered nanophotonic structures. These structures enable high spatial concentration of electromagnetic fields with controlled helicity and chirality. However, the effective design and optimization of nanostructures requires defining physical observables which quantify the degree of electromagnetic helicity and chirality. In this perspective, we discuss optical helicity, optical chirality, and their related conservation laws, describing situations in which each provides the most meaningful physical information in free space and in the context of chiral light–matter interactions. First, an instructive comparison is drawn to the concepts of momentum, force, and energy in classical mechanics. In free space, optical helicity closely parallels momentum, whereas optical chirality parallels force. In the presence of macroscopic matter, the optical helicity finds its optimal physical application in the case of lossless, dual-symmetric media, while, in contrast, the optical chirality provides physically observable information in the presence of lossy, dispersive media. Finally, based on numerical simulations of a gold and silicon nanosphere, we discuss how metallic and dielectric nanostructures can generate chiral electromagnetic fields upon interaction with chiral light, offering guidelines for the rational design of nanostructure-enhanced electromagnetic chirality. Full article
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