In this work, we demonstrate poloidal current configuration produced by an ideal toroidal source simulated numerically in the COMSOL Multiphysics software. The Cartesian multipole decomposition with the implicit contribution of two first toroidal moments is used to demonstrate that the impact of the basic electric dipole to the radiation power is negligible.

1.
Zel'dovich
Y B
1959
Parity nonconservation in the first order in the weak-interaction constant in electron
scattering
and
other
effects
Sov. Phys. JETP
36
964
6
2.
Haxton
W C
1997
Atomic parity violation and the nuclear anapole moment
Science
275
1753
4
3.
Radescu
E E
and
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
Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top.
65
47
4.
Dubovik
V M
and
Tosunyan
L A
1981
Estimates of the effects of parity violation in quasi-nuclear systems
Pis'ma Zh. Eskp. Teor. Fiz
33
68
70
5.
Wood
C S
,
Bennett
S C
,
Cho
D
,
Masterson
B P
,
Roberts
J L
,
Tanner
C E
and
Wieman
C E
1997
Measurement of parity nonconservation and an anapole moment in cesium
Science
275
1759
63
6.
Gorbatsevich
A A
1994
Toroidal order in crystals
Ferroelectrics
161
321
34
7.
Giomi
L
and
Bowick
M J
2008
Defective ground states of toroidal crystals
Phys. Rev. E
78
1
4
8.
Krasnok
A E
,
Miroshnichenko
A E
,
Belov
P A
and
Kivshar
Y S
2012
All-dielectric optical nanoantennas
Opt. Express
20
837
42
9.
Terekhov
P D
,
Shamkhi
H K
,
Gurvitz
E A
,
Baryshnikova
K V.
,
Evlyukhin
A B
,
Shalin
A S
and
Karabchevsky
A
2019
Broadband forward scattering from dielectric cubic nanoantenna in lossless media
Opt. Express
27
10924
10.
Mirzaei
A
,
Miroshnichenko
A E
,
Shadrivov
I V
and
Kivshar
Y S
2015
All-Dielectric Multilayer Cylindrical Structures for Invisibility Cloaking
Sci. Rep.
5
1
6
11.
Alaee
R
,
Albooyeh
M
,
Rahimzadegan
A
,
Mirmoosa
M S
,
Kivshar
Y S
and
Rockstuhl
C
2015 All-dielectric reciprocal bianisotropic nanoparticles
Phys. Rev. B
92
1
6
12.
Yue
L
,
Minin
O V.
,
Wang
Z
,
Monks
J N
,
Shalin
A S
and
Minin
I V.
2018
Photonic hook: a new curved light beam
Opt. Lett.
43
771
13.
Ang
A S
,
Karabchevsky
A
,
Minin
I V.
,
Minin
O V.
,
Sukhov
S V.
and
Shalin
A S
2018
Photonic Hook” based optomechanical nanoparticle manipulator
Sci. Rep.
8
1
7
14.
Raab
R E
and O.L. D L
2005
Multipole Theory in Electromagnetism: Classical, Quantum and Symmetry Aspects, with Applications
(
Clarendon Press
Oxford
)
15.
Kuznetsov
A I
,
Miroshnichenko
A E
,
Fu
Y H
,
Zhang
J
and
Luk
B
2012
Magnetic light
Sci. Rep.
2
1
6
16.
Gurvitz
E A
,
Ladutenko
K S
,
Dergachev
P A
,
Evlyukhin
A B
,
Miroshnichenko
A E
and
Shalin
A S
2019
The High-Order Toroidal Moments and Anapole States in All-Dielectric Photonics
Laser Photonics Rev.
13
1
13
17.
Evlyukhin
A B
,
Reinhardt
C
,
Seidel
A
,
Luk'Yanchuk
B S
and
Chichkov
B N
2010
Optical response features of Si-nanoparticle arrays
Phys. Rev. B - Condens. Matter Mater. Phys.
82
1
12
18.
M.
Zhigunov
D,
B.
Evlyukhin
A,
S.
Shalin
A,
Zywietz
U
and
N.
Chichkov
B
2018
Femtosecond Laser Printing of Single Ge and SiGe Nanoparticles with Electric and Magnetic Optical Resonances
ACS Photonics
5
977
83
19.
Luk'yanchuk
B
,
Paniagua-Domínguez
R
,
Kuznetsov
A I
,
Miroshnichenko
A E
and
Kivshar
Y S
2017
Hybrid anapole modes of high-index dielectric nanoparticles
Phys. Rev. A
95
1
8
20.
Shamkhi
H K
,
Baryshnikova
K V
,
Sayanskiy
A
,
Kapitanova
P
,
Terehov
P D
,
Karabchevsky
A
,
Evlyukhin
A B
,
Belov
P
,
Kivshar
Y
and
Shalin
A S
2019
Transverse Scattering and Generalized Kerker Effects in All-Dielectric Mie-Resonant Metaoptics
Phys. Rev. Lett.
122
1
22
21.
Terekhov
P D
,
Baryshnikova
K V.
,
Artemyev
Y A
,
Karabchevsky
A
,
Shalin
A S
and
Evlyukhin
A B
2017
Multipolar response of nonspherical silicon nanoparticles in the visible and near-infrared spectral ranges
Phys. Rev. B
96
1
8
22.
Chen
J
,
Ng
J
,
Lin
Z
and
Chan
C T
2011
Optical pulling force
Nat. Photonics
5
531
4
23.
Voroshilov
P M
,
Simovski
C R
,
Belov
P A
and
Shalin
A S
2015
Light-trapping and antireflective coatings for amorphous Si-based thin film solar cells
J. Appl. Phys.
117
1
7
24.
Baryshnikova
K V.
,
Novitsky
A
,
Evlyukhin
A B
and
Shalin
A S
2017
Magnetic field concentration with coaxial silicon nanocylinders in the optical spectral range
J. Opt. Soc. Am. B
34
1
6
25.
Baryshnikova
K
,
Filonov
D
,
Simovski
C
,
Evlyukhin
A
,
Kadochkin
A
,
Nenasheva
E
,
Ginzburg
P
and
Shalin
A S
2018
Giant magnetoelectric field separation via anapole-type states in high-index dielectric structures
Phys. Rev. B
98
165419
26.
Ospanova
A K
,
Labate
G
,
Matekovits
L
and
Basharin
A A
2018
Multipolar passive cloaking by nonradiating anapole excitation
Sci. Rep.
8
1
8
27.
Totero
Gongora
J S,
Miroshnichenko
A E
,
Kivshar
Y S
and
Fratalocchi
A
2017
Anapole nanolasers for mode-locking and ultrafast pulse generation
Nat. Commun.
8
1
9
28.
Grinblat
G
,
Li
Y
,
P.
Nielsen
M,
F.
Oulton
R and
A.
Maier
S
2016
Enhanced Third Harmonic Generation in Single Germanium Nanodisks Excited at the Anapole Mode
Nano Lett.
16
4635
40
29.
Timofeeva
M
,
Lang
L
,
Timpu
F
,
Renaut
C
,
Bouravleuv
A
,
Shtrom
I
,
Cirlin
G
and
Grange
R
2018
Anapoles in Free-Standing III–V Nanodisks Enhancing Second-Harmonic Generation
Nano Lett.
18
3695
702
30.
Fernandez-Corbaton
I
,
Nanz
S
and
Rockstuhl
C
2017
On the dynamic toroidal multipoles from localized electric current distributions
Sci. Rep.
7
1
8
31.
Alaee
R
,
Rockstuhl
C
and
Fernandez-Corbaton
I
2018
An electromagnetic multipole expansion beyond the long-wavelength approximation
Opt. Commun.
407
1
21
32.
Marinov
K
,
Boardman
A D
,
Fedotov
V A
and
Zheludev
N
2007
Toroidal metamaterial
New J. Phys.
9
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