In recent years, resonant structures with quasi-bound states in the continuum (quasi-BICs) have significantly expanded the practical possibilities in optics and nanophotonics. A similar mode, the so-called supercavity mode, observed in single dielectric cylinders with high permittivity and low material losses, allows achieving extremely high quality (Q) factors. Resonators supporting quasi-BICs are also promising for applications in the radio frequency range. However, creating compact structures using high-permittivity materials at frequencies below 300 MHz is challenging. This study introduces a subwavelength (λ/13) volumetric structure composed of two arrays of coupled split ring resonators, with one array located inside the other, which provides a supercavity mode. The numerical Q factor of this mode is increased by approximately 100 times under lossless conditions and by about 1.5 times when accounting for material losses compared to that of non-interacting modes of the two arrays. The Q factor enhancement is confirmed experimentally by near-field measurements. The advantages of the proposed resonator include its hollow cavity, ease of fabrication, and frequency tunability within the radio frequency range.

1.
G.
Xiao
, “
Q factor of a radiator
,” in
Electromagnetic Sources and Electromagnetic Fields
(
Springer Nature
,
Singapore
,
2024
), pp.
25
32
.
2.
C. A.
Balanis
,
Antenna Theory: Analysis and Design
(
Wiley
,
Chichester, England
,
2015
).
3.
A.
Webb
,
A.
Shchelokova
,
A.
Slobozhanyuk
,
I.
Zivkovic
, and
R.
Schmidt
, “
Novel materials in magnetic resonance imaging: High permittivity ceramics, metamaterials, metasurfaces and artificial dielectrics
,”
Magn. Reson. Mater. Phys, Biol. Med.
35
,
875
894
(
2022
).
4.
F.
Costa
,
S.
Genovesi
,
M.
Borgese
,
A.
Michel
,
F. A.
Dicandia
, and
G.
Manara
, “
A review of RFID sensors, the new frontier of internet of things
,”
Sensors
21
,
3138
(
2021
).
5.
I.
Yusupov
,
D.
Dobrykh
,
P.
Terekhina
,
D.
Filonov
,
P.
Ginzburg
,
M. V.
Rybin
, and
A.
Slobozhanyuk
, “
Quasi-BIC high-index resonators for liquid characterization and analysis
,”
Appl. Phys. Lett.
123
,
244102
(
2023
).
6.
I.
Yusupov
,
D.
Filonov
,
A.
Bogdanov
,
P.
Ginzburg
,
M. V.
Rybin
, and
A.
Slobozhanyuk
, “
Chipless wireless temperature sensor based on quasi-BIC resonance
,”
Appl. Phys. Lett.
119
,
193504
(
2021
).
7.
Y.
Xie
,
Z.
Zhang
,
Y.
Lin
,
T.
Feng
, and
Y.
Xu
, “
Magnetic quasi-bound state in the continuum for wireless power transfer
,”
Phys. Rev. Appl.
15
,
044024
(
2021
).
8.
R.
Wang
,
L.
Xu
,
L.
Huang
,
X.
Zhang
,
H.
Ruan
,
X.
Yang
,
J.
Lou
,
C.
Chang
, and
X.
Du
, “
Ultrasensitive terahertz biodetection enabled by quasi-BIC-based metasensors
,”
Small
19
,
2301165
(
2023
).
9.
K.
He
,
Q.
Niu
,
Y.
Xie
,
S.
Xiao
,
Y.
Yang
, and
J.
Zhu
, “
Bound state in the continuum (BIC) excited by the metasurface breaking in-plane symmetry and quasi-BIC for terahertz sensing
,”
Appl. Phys. Lett.
124
,
231702
(
2024
).
10.
D. C.
Marinica
,
A. G.
Borisov
, and
S. V.
Shabanov
, “
Bound states in the continuum in photonics
,”
Phys. Rev. Lett.
100
,
183902
(
2008
).
11.
C. W.
Hsu
,
B.
Zhen
,
A. D.
Stone
,
J.
Joannopoulos
, and
M.
Soljačić
, “
Bound states in the continuum
,”
Nat. Rev. Mater.
1
,
16048
(
2016
).
12.
C. W.
Hsu
,
B.
Zhen
,
J.
Lee
,
S.-L.
Chua
,
S. G.
Johnson
,
J. D.
Joannopoulos
, and
M.
Soljačić
, “
Observation of trapped light within the radiation continuum
,”
Nature
499
,
188
191
(
2013
).
13.
A. F.
Sadreev
, “
Interference traps waves in an open system: Bound states in the continuum
,”
Rep. Prog. Phys.
84
,
055901
(
2021
).
14.
S.
Azzam
and
A.
Kildishev
, “
Photonic bound states in the continuum: From basics to applications
,”
Adv. Opt. Mater.
9
,
2001469
(
2021
).
15.
K.
Koshelev
,
A.
Bogdanov
, and
Y.
Kivshar
, “
Meta-optics and bound states in the continuum
,”
Sci. Bull.
64
,
836
842
(
2019
).
16.
K.
Koshelev
,
A.
Bogdanov
, and
Y.
Kivshar
, “
Engineering with bound states in the continuum
,”
Opt. Photonics News
31
,
38
45
(
2020
).
17.
E.
Bulgakov
and
A.
Sadreev
, “
Trapping of light with angular orbital momentum above the light cone
,”
Adv. Electromagn.
6
,
1
10
(
2017
).
18.
Z. F.
Sadrieva
,
M. A.
Belyakov
,
M. A.
Balezin
,
P. V.
Kapitanova
,
E. A.
Nenasheva
,
A. F.
Sadreev
, and
A. A.
Bogdanov
, “
Experimental observation of a symmetry-protected bound state in the continuum in a chain of dielectric disks
,”
Phys. Rev. A
99
,
053804
(
2019
).
19.
S.
Kim
,
K.-H.
Kim
, and
J. F.
Cahoon
, “
Optical bound states in the continuum with nanowire geometric superlattices
,”
Phys. Rev. Lett.
122
,
187402
(
2019
).
20.
A.
Gianfrate
,
H.
Sigurðsson
,
V.
Ardizzone
,
H. C.
Nguyen
,
F.
Riminucci
,
M.
Efthymiou-Tsironi
,
K. W.
Baldwin
,
L. N.
Pfeiffer
,
D.
Trypogeorgos
,
M.
De Giorgi
,
D.
Ballarini
,
H. S.
Nguyen
, and
D.
Sanvitto
, “
Reconfigurable quantum fluid molecules of bound states in the continuum
,”
Nat. Phys.
20
,
61
67
(
2024
).
21.
K.
Pichugin
,
A.
Sadreev
, and
E.
Bulgakov
, “
Ultrahigh-Q system of a few coaxial disks
,”
Nanophotonics
10
,
4341
4346
(
2021
).
22.
M. S.
Sidorenko
,
O. N.
Sergaeva
,
Z. F.
Sadrieva
,
C.
Roques-Carmes
,
P. S.
Muraev
,
D. N.
Maksimov
, and
A. A.
Bogdanov
, “
Observation of an accidental bound state in the continuum in a chain of dielectric disks
,”
Phys. Rev. Appl.
15
,
034041
(
2021
).
23.
W.
Huang
,
S.
Liu
,
Y.
Cheng
,
J.
Han
,
S.
Yin
, and
W.
Zhang
, “
Universal coupled theory for metamaterial bound states in the continuum
,”
New J. Phys.
23
,
093017
(
2021
).
24.
W.
Huang
,
S.
Liu
,
D.
Zeng
,
Q.
Yang
,
W.
Zhang
, and
S.
Yin
, “
Coupling-assisted quasi-bound states in the continuum in heterogeneous metasurfaces
,”
IEEE J. Sel. Top. Quantum Electron.
29
,
1
(
2023a
).
25.
W.
Huang
,
S.-T.
Cao
,
X.
Qu
,
W.
Zhang
,
S.
Yin
, and
J.
Han
, “
Inverse design of metamaterial bound states in the continuum device via coupled mode theory
,”
IEEE Trans. Microwave Theory Tech.
72
,
1520
1528
(
2023b
).
26.
H.-F.
Wang
,
S. K.
Gupta
,
X.-Y.
Zhu
,
M.-H.
Lu
,
X.-P.
Liu
, and
Y.-F.
Chen
, “
Bound states in the continuum in a bilayer photonic crystal with TE-TM cross coupling
,”
Phys. Rev. B
98
,
214101
(
2018
).
27.
J.
Jin
,
X.
Yin
,
L.
Ni
,
M.
Soljačić
,
B.
Zhen
, and
C.
Peng
, “
Topologically enabled ultrahigh-Q guided resonances robust to out-of-plane scattering
,”
Nature
574
,
501
504
(
2019
).
28.
Z.
Liu
,
Y.
Xu
,
Y.
Lin
,
J.
Xiang
,
T.
Feng
,
Q.
Cao
,
J.
Li
,
S.
Lan
, and
J.
Liu
, “
High-Q quasibound states in the continuum for nonlinear metasurfaces
,”
Phys. Rev. Lett.
123
,
253901
(
2019
).
29.
M. V.
Gorkunov
,
A. A.
Antonov
, and
Y. S.
Kivshar
, “
Metasurfaces with maximum chirality empowered by bound states in the continuum
,”
Phys. Rev. Lett.
125
,
093903
(
2020
).
30.
M. V.
Rybin
,
K. L.
Koshelev
,
Z. F.
Sadrieva
,
K. B.
Samusev
,
A. A.
Bogdanov
,
M. F.
Limonov
, and
Y. S.
Kivshar
, “
High-Q supercavity modes in subwavelength dielectric resonators
,”
Phys. Rev. Lett.
119
,
243901
(
2017
).
31.
M.
Odit
,
K.
Koshelev
,
S.
Gladyshev
,
K.
Ladutenko
,
Y.
Kivshar
, and
A.
Bogdanov
, “
Observation of supercavity modes in subwavelength dielectric resonators
,”
Adv. Mater.
33
,
2003804
(
2021
).
32.
A. A.
Bogdanov
,
K. L.
Koshelev
,
P. V.
Kapitanova
,
M. V.
Rybin
,
S. A.
Gladyshev
,
Z. F.
Sadrieva
,
K. B.
Samusev
,
Y. S.
Kivshar
, and
M. F.
Limonov
, “
Bound states in the continuum and Fano resonances in the strong mode coupling regime
,”
Adv. Photonics
1
(
1
),
016001
(
2019
).
33.
K. N.
Pichugin
and
A. F.
Sadreev
, “
Interaction between coaxial dielectric disks enhances the Q factor
,”
J. Appl. Phys.
126
,
093105
(
2019
).
34.
E.
Bulgakov
,
K.
Pichugin
, and
A.
Sadreev
, “
Mie resonance engineering in two disks
,”
Photonics
8
,
49
(
2021
).
35.
W.
Luo
,
J.
Guo
,
C.
Randall
, and
M.
Lanagan
, “
Effect of porosity and microstructure on the microwave dielectric properties of rutile
,”
Mater. Lett.
200
,
101
104
(
2017
).
36.
S.
Maslovski
,
P.
Ikonen
,
I.
Kolmakov
,
S.
Tretyakov
, and
M.
Kaunisto
, “
Artificial magnetic materials based on the new magnetic particle: Metasolenoid
,”
Prog. Electromagn. Res.
54
,
61
81
(
2005
).
37.
L.
Jylhä
,
S.
Maslovski
, and
S.
Tretyakov
, “
High-order resonant modes of a metasolenoid
,”
J. Electromagn. Waves Appl.
19
,
1327
1342
(
2005
).
38.
A. V.
Shchelokova
,
C. A.
van den Berg
,
D. A.
Dobrykh
,
S. B.
Glybovski
,
M. A.
Zubkov
,
E. A.
Brui
,
D. S.
Dmitriev
,
A. V.
Kozachenko
,
A. Y.
Efimtcev
,
A. V.
Sokolov
,
V. A.
Fokin
,
I. V.
Melchakova
, and
P. A.
Belov
, “
Volumetric wireless coil based on periodically coupled split-loop resonators for clinical wrist imaging
,”
Magn. Reson. Med.
80
,
1726
1737
(
2018
).
39.
A.
Jandaliyeva
,
V.
Puchnin
,
A.
Slobozhanyuk
, and
A.
Shchelokova
, “
Control of the near magnetic field pattern uniformity inside metamaterial-inspired volumetric resonators
,”
Photonics Nanostruct. Fundam. Appl.
48
,
100989
(
2022
).
40.
A.
Jandaliyeva
,
A.
Vdovenko
,
M.
Siganov
,
L.
Suleiman
,
P.
Seregin
,
M.
Udrov
,
A.
Shchelokova
, and
P.
Belov
, “
Design and demonstration of the volumetric resonator with uniform magnetic field distribution for wireless power transfer
,” in
2024 IEEE Wireless Power Technology Conference and Expo (WPTCE)
(
IEEE
,
2024
).
41.
H.
Friedrich
and
D.
Wintgen
, “
Interfering resonances and bound states in the continuum
,”
Phys. Rev. A
32
,
3231
3242
(
1985
).
42.
S. V.
Lobanov
,
W.
Langbein
, and
E. A.
Muljarov
, “
Resonant-state expansion applied to three-dimensional open optical systems: Complete set of static modes
,”
Phys. Rev. A
100
,
063811
(
2019
).
43.
K. L.
Koshelev
,
Z. F.
Sadrieva
,
A. A.
Shcherbakov
,
Y. S.
Kivshar
, and
A. A.
Bogdanov
, “
Bound states in the continuum in photonic structures
,”
Phys. Usp.
66
,
494
517
(
2023
).
44.
E. E.
Maslova
,
M. V.
Rybin
,
A. A.
Bogdanov
, and
Z. F.
Sadrieva
, “
Bound states in the continuum in periodic structures with structural disorder
,” arXiv:2108.10548v1 (
2021
).
45.
A.
Shchelokova
,
V.
Ivanov
,
A.
Mikhailovskaya
,
E.
Kretov
,
I.
Sushkov
,
S.
Serebryakova
,
E.
Nenasheva
,
I.
Melchakova
,
P.
Belov
,
A.
Slobozhanyuk
, and
A.
Andreychenko
, “
Ceramic resonators for targeted clinical magnetic resonance imaging of the breast
,”
Nat. Commun.
11
,
3840
(
2020
).
46.
H.
Zhang
,
Z.
Guo
,
Y.
Li
,
Y.
Yang
,
Y.
Chen
, and
H.
Chen
, “
A universal non-Hermitian platform for bound state in the continuum enhanced wireless power transfer
,”
Front. Phys.
19
,
43209
(
2024
).
47.
F.
Li
,
Y.
Zheng
,
C.
Hua
, and
J.
Jian
, “
Gas sensing by microwave transduction: review of progress and challenges
,”
Front. Mater.
6
,
460483
(
2019
).
48.
B.
George
,
Z.
Tan
, and
S.
Nihtianov
, “
Advances in capacitive, eddy current, and magnetic displacement sensors and corresponding interfaces
,”
IEEE Trans. Ind. Electron.
64
,
9595
9607
(
2017
).
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