Cartesian Multipole Expansions and Tensorial Identities

Rǎdescu, E.E.; Vaman, G.

doi:10.2528/pierb11090702

Cited by 12 publications

(23 citation statements)

References 12 publications

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“…For the spherical multipole expansion 35 up to electric and magnetic quadrupoles terms only 36,37 . The corresponding expressions for the Cartesian multipoles contributions are presented in Table 1.…”

Section: Vertically Standing Disk Configuration Horizontally Lying DImentioning

confidence: 99%

“…The corresponding expressions for the Cartesian multipoles contributions are presented in Table 1. The total scattering power and corresponding scattering cross section ( ), where is the free-space impedance 36,37 is given by:…”

Section: Vertically Standing Disk Configuration Horizontally Lying DImentioning

confidence: 99%

“…This technique offers unique opportunities to fabricate high-quality structures with variable radii, longitudinal heterostructures from lattice-mismatched materials with different refractive indexes 30 and in crystal phases that are not available in bulk III-V materials [31][32][33][34] .We experimentally show the lack of radiation in the near-infrared domain and the strong secondharmonic generation (SHG) enhancement due to an efficient electromagnetic field confinement. The multipole expansion of the electromagnetic field, performed in both spherical 6,35 and Cartesian coordinates 36,37 , shows that the fabricated standing disks have anapole-type nonradiating current distributions. The proposed novel geometry of vertically free-standing disks has a lower aspect ratio between diameter and height compared with previous horizontally lying disk designs 6,7 and results in significant decrease in the substrate influence.…”

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confidence: 99%

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Anapoles in Free-Standing III–V Nanodisks Enhancing Second-Harmonic Generation

et al. 2018

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Nonradiating electromagnetic configurations in nanostructures open new horizons for applications due to two essential features: a lack of energy losses and invisibility to the propagating electromagnetic field. Such radiationless configurations form a basis for new types of nanophotonic devices, in which a strong electromagnetic field confinement can be achieved together with lossless interactions between nearby components. In our work, we present a new design of free-standing disk nanoantennas with nonradiating current distributions for the optical near-infrared range. We show a novel approach to creating nanoantennas by slicing III-V nanowires into standing disks using focused ion-beam milling. We experimentally demonstrate the suppression of the far-field radiation and the associated strong enhancement of the second-harmonic generation from the disk nanoantennas. With a theoretical analysis of the electromagnetic field distribution using multipole expansions in both spherical and Cartesian coordinates, we confirm that the demonstrated nonradiating configurations are anapoles. We expect that the presented procedure of designing and producing disk nanoantennas from nanowires becomes one of the standard approaches to fabricating controlled chains of standing nanodisks with different designs and configurations. These chains can be essential building blocks for new types of lasers and sensors with low power consumption.

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Section: Vertically Standing Disk Configuration Horizontally Lying DImentioning

confidence: 99%

Section: Vertically Standing Disk Configuration Horizontally Lying DImentioning

confidence: 99%

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confidence: 99%

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Anapoles in Free-Standing III–V Nanodisks Enhancing Second-Harmonic Generation

et al. 2018

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“…The scattering properties of the dielectric nanocuboids are investigated by decomposing the fields inside the nanoparticles into Cartesian multipole moments. This widely employed method permits the calculation of the contributions stemming from toroidal moments and hence the identification of the conditions for the excitation of anapole modes [32,33,34,35,36]. Assuming the ejωt convention for the harmonic electromagnetic fields, the induced polarization current density boldJ(boldr) boldJ(r)=jω()εp−εbboldE(r), where boldE(boldr) is the electric field, ω is the angular frequency, and εp=εr,pε0 and εb=εr,bε0 are the permittivities of the nanocuboid and the background medium, respectively, while ε0 is the vacuum permittivity.…”

Section: Methodsmentioning

confidence: 99%

Anapole Modes in Hollow Nanocuboid Dielectric Metasurfaces for Refractometric Sensing

et al. 2018

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This work proposes the use of the refractive index sensitivity of non-radiating anapole modes of high-refractive-index nanoparticles arranged in planar metasurfaces as a novel sensing principle. The spectral position of anapole modes excited in hollow silicon nanocuboids is first investigated as a function of the nanocuboid geometry. Then, nanostructured metasurfaces of periodic arrays of nanocuboids on a glass substrate are designed. The metasurface parameters are properly selected such that a resonance with ultrahigh Q-factor, above one million, is excited at the target infrared wavelength of 1.55 µm. The anapole-induced resonant wavelength depends on the refractive index of the analyte superstratum, exhibiting a sensitivity of up to 180 nm/RIU. Such values, combined with the ultrahigh Q-factor, allow for refractometric sensing with very low detection limits in a broad range of refractive indices. Besides the sensing applications, the proposed device can also open new venues in other research fields, such as non-linear optics, optical switches, and optical communications.

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“…We have proved in Ref. [3] the following formula for the Cartesian multipole expansion of an arbitrary charge distribution:…”

Section: General Mathematical Formalismmentioning

confidence: 99%