2018
DOI: 10.1103/physreva.98.023858
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Electromagnetic sources beyond common multipoles

Abstract: The complete dynamic multipole expansion of electromagnetic sources contains more types of multipole terms than it is conventionally perceived. The toroidal multipoles are one of the examples of such contributions that have been widely studied in recent years. Here we inspect more closely the other type of commonly overlooked terms known as the mean-square radii. In particular, we discuss both quantitative and qualitative aspects of the mean-square radii and provide a general geometrical framework for their vi… Show more

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Cited by 40 publications
(35 citation statements)
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“…They can be deduced in a similar manner to the fundamental anapole condition but by involving higher‐order terms in the multipole expansion. The different multipolar terms can have the same far‐field radiation pattern, though their relative contributions scale differently as the wavelength changes . In particular, the lowest‐order magnetic nonradiating source is formed by a magnetic dipole and its first mean‐square radius (see Table ), while toroidal multipoles can interfere with their own mean‐square radii, leading to the anapole state formation even in the absence of electric multipoles.…”
Section: Anapole Concept In Metaopticsmentioning
confidence: 99%
“…They can be deduced in a similar manner to the fundamental anapole condition but by involving higher‐order terms in the multipole expansion. The different multipolar terms can have the same far‐field radiation pattern, though their relative contributions scale differently as the wavelength changes . In particular, the lowest‐order magnetic nonradiating source is formed by a magnetic dipole and its first mean‐square radius (see Table ), while toroidal multipoles can interfere with their own mean‐square radii, leading to the anapole state formation even in the absence of electric multipoles.…”
Section: Anapole Concept In Metaopticsmentioning
confidence: 99%
“…Hence, under illumination with an incident light, each term in a dynamic mode decomposition supports only a specific angular projection of the charge-current distribution. Moreover, in the context of mean-square radii, one can easily explore its 1st order of an electric or a magnetic dipole, as demonstrated previously in Nemkov et al [22]. By centering on the super-toroidal modes from the quantitative perspective, we first study the hierarchy of a toroidal solenoid system, in which each turn of it can be considered as another toroidal solenoid.…”
Section: The Theory Of High-order Toroidal Solenoidsmentioning
confidence: 99%
“…Nevertheless, they have a key role in the field of nanophotonics and plasmonics [4]. As indicated by Nemkov et al [22], the decomposition scheme generates high-order modes within the hierarchy of a toroidal system (i.e., toroidal solenoid), known as "mean-square radii" of the induced toroidal mode. It is noteworthy to mention that without complementing the multipole expansion with these high-order terms, the decomposition will be incorrect [23].…”
Section: The Theory Of High-order Toroidal Solenoidsmentioning
confidence: 99%
“…Based on this destructive interference, anapoles generated from high-order multipoles (electric, magnetic, and toroidal) have been studied theoretically [10]. Furthermore, it is possible to create from a single multipolar current-charge distribution other high-order multipolar sources that are denominated moments of mean-square radii (MSRs) [11]; peculiarly, the radiation pattern of a MSR source is the same as that of its parent multipole and hence the superposition of these sources gives rise to an anapole.…”
Section: Introductionmentioning
confidence: 99%