Dynamic toroidal dipole

Last updated

In classical electrodynamics, the dynamic toroidal dipole arises from time-dependent currents flowing along the poloidal direction on the surface of a torus. [1] In relativistic quantum mechanics, spin contributions to the toroidal dipole needs to be taken into account. [2] Toroidal dipole moments are odd under parity and time-reversal symmetries. Dynamic toroidal dipole is distinguished from the static toroidal dipole introduced by Zeldovich in 1957 under the name of static anapole. [3]

Schematic illustrations of static electric, magnetic, and toroidal dipoles in classical electrodynamics. In relativistic quantum physics, apart from magnetic and toroidal moments induced by charge currents, spin must be considered because it can also contribute to the toroidal dipole moment. Image created by Diego P. Araujo (Biosteam) ElectromagneticDipolesInclToroidal.jpg
Schematic illustrations of static electric, magnetic, and toroidal dipoles in classical electrodynamics. In relativistic quantum physics, apart from magnetic and toroidal moments induced by charge currents, spin must be considered because it can also contribute to the toroidal dipole moment. Image created by Diego P. Araujo (Biosteam)

The dynamic toroidal multipoles were theoretically introduced in the 1970s in the context of a complete multipole expansion in electrodynamics [3] [4] and their radiation properties were studied in a series of theoretical works. [5] [6] The experimental study of dynamic toroidal multipoles, however, became possible only with advances in artificial electromagnetic materials (metamaterials), [7] leading to the first experimental observation of the toroidal dipole, in 2010 in an array of microwave resonators with elements of toroidal symmetry. [8]

The far-field radiation properties of the dynamic toroidal dipole are identical to those of the conventional electric dipole. [1] Hence combining a dynamic toroidal dipole with an electric dipole can result in a non-radiating charge-current configuration (termed dynamic anapole), in which the electromagnetic fields vanish outside the source, whereas the vector potential persists. [9] Non-radiating anapoles were observed experimentally for the first time in 2013 as peak of transmission of structured matter at microwave frequencies [10] and in 2015 at optical wavelengths in nanoparticles. [11] Electrodynamics of dynamic toroidal dipole and anapoles is now massively influencing research in metamaterials, nanoparticles, plasmonics, sensors, lasers and spectroscopy [1] [12]

Note: The terminology of dynamic "electric" and "magnetic" toroidal multipoles has also been introduced. The latter is already part of the standard multipole expansion in the form of the mean square radii of the magnetic multipoles. [5]

See also

Related Research Articles

<span class="mw-page-title-main">Dipole</span> Electromagnetic phenomenon

In physics, a dipole is an electromagnetic phenomenon which occurs in two ways:

<span class="mw-page-title-main">Near and far field</span> Regions of an electromagnetic field

The near field and far field are regions of the electromagnetic (EM) field around an object, such as a transmitting antenna, or the result of radiation scattering off an object. Non-radiative near-field behaviors dominate close to the antenna or scatterer, while electromagnetic radiation far-field behaviors predominate at greater distances.

<span class="mw-page-title-main">Metamaterial</span> Materials engineered to have properties that have not yet been found in nature

A metamaterial is any material engineered to have a property that is rarely observed in naturally occurring materials. They are made from assemblies of multiple elements fashioned from composite materials such as metals and plastics. These materials are usually arranged in repeating patterns, at scales that are smaller than the wavelengths of the phenomena they influence. Metamaterials derive their properties not from the properties of the base materials, but from their newly designed structures. Their precise shape, geometry, size, orientation and arrangement gives them their smart properties capable of manipulating electromagnetic waves: by blocking, absorbing, enhancing, or bending waves, to achieve benefits that go beyond what is possible with conventional materials.

A quadrupole or quadrapole is one of a sequence of configurations of things like electric charge or current, or gravitational mass that can exist in ideal form, but it is usually just part of a multipole expansion of a more complex structure reflecting various orders of complexity.

Planar chirality, also known as 2D chirality, is the special case of chirality for two dimensions.

Negative refraction is the electromagnetic phenomenon where light rays become refracted at an interface that is opposite to their more commonly observed positive refractive properties. Negative refraction can be obtained by using a metamaterial which has been designed to achieve a negative value for (electric) permittivity (ε) and (magnetic) permeability (μ); in such cases the material can be assigned a negative refractive index. Such materials are sometimes called "double negative" materials.

Asım Orhan Barut was a Turkish-American theoretical physicist.

The toroidal ring model, known originally as the Parson magneton or magnetic electron, is a physical model of subatomic particles. It is also known as the plasmoid ring, vortex ring, or helicon ring. This physical model treated electrons and protons as elementary particles, and was first proposed by Alfred Lauck Parson in 1915.

<span class="mw-page-title-main">Negative-index metamaterial</span> Material with a negative refractive index

Negative-index metamaterial or negative-index material (NIM) is a metamaterial whose refractive index for an electromagnetic wave has a negative value over some frequency range.

A nonlinear metamaterial is an artificially constructed material that can exhibit properties not yet found in nature. Its response to electromagnetic radiation can be characterized by its permittivity and material permeability. The product of the permittivity and permeability results in the refractive index. Unlike natural materials, nonlinear metamaterials can produce a negative refractive index. These can also produce a more pronounced nonlinear response than naturally occurring materials.

<span class="mw-page-title-main">Chiral media</span> Applied to electromagnetism

The term chiral describes an object, especially a molecule, which has or produces a non-superposable mirror image of itself. In chemistry, such a molecule is called an enantiomer or is said to exhibit chirality or enantiomerism. The term "chiral" comes from the Greek word for the human hand, which itself exhibits such non-superimposeability of the left hand precisely over the right. Due to the opposition of the fingers and thumbs, no matter how the two hands are oriented, it is impossible for both hands to exactly coincide. Helices, chiral characteristics (properties), chiral media, order, and symmetry all relate to the concept of left- and right-handedness.

<span class="mw-page-title-main">Metamaterial cloaking</span> Shielding an object from view using materials made to redirect light

Metamaterial cloaking is the usage of metamaterials in an invisibility cloak. This is accomplished by manipulating the paths traversed by light through a novel optical material. Metamaterials direct and control the propagation and transmission of specified parts of the light spectrum and demonstrate the potential to render an object seemingly invisible. Metamaterial cloaking, based on transformation optics, describes the process of shielding something from view by controlling electromagnetic radiation. Objects in the defined location are still present, but incident waves are guided around them without being affected by the object itself.

<span class="mw-page-title-main">History of metamaterials</span>

The history of metamaterials begins with artificial dielectrics in microwave engineering as it developed just after World War II. Yet, there are seminal explorations of artificial materials for manipulating electromagnetic waves at the end of the 19th century. Hence, the history of metamaterials is essentially a history of developing certain types of manufactured materials, which interact at radio frequency, microwave, and later optical frequencies.

<span class="mw-page-title-main">Electric dipole moment</span> Measure of positive and negative charges

The electric dipole moment is a measure of the separation of positive and negative electrical charges within a system, that is, a measure of the system's overall polarity. The SI unit for electric dipole moment is the coulomb-meter (C⋅m). The debye (D) is another unit of measurement used in atomic physics and chemistry.

Multipole radiation is a theoretical framework for the description of electromagnetic or gravitational radiation from time-dependent distributions of distant sources. These tools are applied to physical phenomena which occur at a variety of length scales - from gravitational waves due to galaxy collisions to gamma radiation resulting from nuclear decay. Multipole radiation is analyzed using similar multipole expansion techniques that describe fields from static sources, however there are important differences in the details of the analysis because multipole radiation fields behave quite differently from static fields. This article is primarily concerned with electromagnetic multipole radiation, although the treatment of gravitational waves is similar.

In electromagnetism, a toroidal moment is an independent term in the multipole expansion of electromagnetic fields besides magnetic and electric multipoles. In the electrostatic multipole expansion, all charge and current distributions can be expanded into a complete set of electric and magnetic multipole coefficients. However, additional terms arise in an electrodynamic multipole expansion. The coefficients of these terms are given by the toroidal multipole moments as well as time derivatives of the electric and magnetic multipole moments. While electric dipoles can be understood as separated charges and magnetic dipoles as circular currents, axial toroidal dipoles describes toroidal (donut-shaped) charge arrangements whereas polar toroidal dipole correspond to the field of a solenoid bent into a torus.

Quantum metamaterials extend the science of metamaterials to the quantum level. They can control electromagnetic radiation by applying the rules of quantum mechanics. In the broad sense, a quantum metamaterial is a metamaterial in which certain quantum properties of the medium must be taken into account and whose behaviour is thus described by both Maxwell's equations and the Schrödinger equation. Its behaviour reflects the existence of both EM waves and matter waves. The constituents can be at nanoscopic or microscopic scales, depending on the frequency range .

In physics, an anapole is a system of currents which does not radiate into the far field. The term "anapole" firstly appears in the work of Zel'dovich, where he thanks A. S. Kompaneets, who first proposed the name.

<span class="mw-page-title-main">Nikolay Zheludev</span> British scientist

Nikolay Zheludev is a British scientist specializing in nanophotonics, metamaterials, nanotechnology, electrodynamics, and nonlinear optics. Nikolay Zheludev is one of the founding members of the closely interlinked fields of metamaterials and nanophotonics that emerged at the dawn of the 21st century on the crossroads of optics and nanotechnology. Nikolay’s work focus on developing new concepts in which nanoscale structuring of matter enhance and radically change its optical properties.

Classical Electrodynamics is a textbook written by theoretical particle and nuclear physicist John David Jackson. The book originated as lecture notes that Jackson prepared for teaching graduate-level electromagnetism first at McGill University and then at the University of Illinois at Urbana-Champaign. Intended for graduate students, and often known as Jackson for short, it has been a standard reference on its subject since its first publication in 1962.

References

  1. 1 2 3 Papasimakis, N.; Fedotov, V. A.; Savinov, V.; Raybould, T. A.; Zheludev, N. I. (2016). "Electromagnetic toroidal excitations in matter and free space". Nature Materials. 15: 263–271. doi:10.1038/nmat4563.
  2. 1 2 Kuprov, I.; Wilkowski, D.; Zheludev, N. I. (2022). "Toroidal optical transitions in hydrogen-like atoms". Science Advances. 8 (45): eabq6751. arXiv: 2205.01412 . doi: 10.1126/sciadv.abq6751 .
  3. 1 2 Dubovik, V. M.; Cheshkov, A. A.; Zheludev, N. I. (1974). "Multipole expansion in classic and quantum field theory and radiation". Soviet Journal of Particles and Nuclei. 5 (3): 318–337.
  4. Dubovik, V. M.; Tosunyan, L. A.; Tugushev, V. V. (1986). "Axial toroidal moments in electrodynamics and solid-state physics". Soviet Physics - JETP. 63 (2): 344–351.
  5. 1 2 Afanasiev, G. N. (1990). "The electromagnetic field of solenoids with time-dependent currents". Journal of Physics A: Mathematical and General. 23: 5755–5764. doi:10.1088/0305-4470/23/24/017.
  6. Radescu, E. E.; Vaman, G. (2002). "Exact calculation of the angular momentum loss, recoil force, and radiation intensity for an arbitrary source in terms of electric, magnetic, and toroid multipoles". Physical Review E. 65 (2): 046609. doi:10.1103/PhysRevE.65.046609.
  7. Papasimakis, N.; Fedotov, V. A.; Marinov, K.; Zheludev, N. I. (2009). "Gyrotropy of a metamolecule: wire on a torus". Physical Review Letters. 103: 093901. arXiv: 0810.3539 . doi:10.1103/PhysRevLett.103.093901.
  8. Kaelberer, T.; Fedotov, V. A.; Papasimakis, N.; Tsai, D. P.; Zheludev, N. I. (2010). "Toroidal dipolar response in a metamaterial". Science. 330: 1510–1512. doi: 10.1126/science.1197172 .
  9. Afanasiev, G. N.; Stepanovsky, Y. P. (1995). "The electromagnetic field of elementary time-dependent toroidal sources". Journal of Physics A: Mathematical and General. 28: 4565–4580. doi:10.1088/0305-4470/28/16/014.
  10. Fedotov, V. A.; Rogacheva, A. V.; Savinov, V.; Tsai, D. P.; Zheludev, N. I. (2013). "Resonant transparency and non-trivial non-radiating excitations in toroidal metamaterials". Scientific Reports. 3: 2967. arXiv: 1211.3840 . doi: 10.1038/srep02967 .
  11. Miroshnichenko, A. E.; Evlyukhin, A. B.; Yu, Y. F.; Bakker, R. M.; Chipouline, A.; Kuznetsov, A. I.; Luk’yanchuk, B.; Chichkov, B. N.; Kivshar, Y. S. (2015). "Nonradiating anapole modes in dielectric nanoparticles". Nature Communications. 6: 8069. doi: 10.1038/ncomms9069 . hdl: 1885/15019 .
  12. Zheludev, N. I.; Wilkowski, D. (2023). "The Rise of Toroidal Electrodynamics and Spectroscopy". ACS Photonics. 10: 556. doi: 10.1021/acsphotonics.2c01953 . PMC   10021009 .