To achieve omnidirectional wireless power transfer (WPT) with high efficiency, a high Q-factor transmitter generating homogeneous magnetic field is crucial. Traditionally, orthogonal coils of different shapes are used to realize transmitters. In this paper, we develop an omnidirectional magnetic resonant WPT system based on a dielectric disk resonator with colossal permittivity and low loss operating at the axial magnetic quadrupole mode. The constant power transfer efficiency of 88% at the frequency of 157 MHz over the transfer distance of 3 cm for all azimuth angles of a receiver is experimentally demonstrated. The possibility of multi-receivers charging is also studied demonstrating a total efficiency of 90% regardless of azimuth angle between two receivers with respect to the transmitting disk resonator. The minimized exposure of biological tissues to the electric and magnetic fields as well as a low specific absorption rate is observed that makes the WPT system safer for charging with higher input power.

Wireless power transfer (WPT) technologies are used to charge batteries of different electronic devices.1–4 Among different techniques, the magnetic resonant WPT has attracted great attention for its potential in safe mid-range charging.5–7 However, the power transfer efficiency (PTE) of magnetic resonant WPT systems based on metal coils still suffers from high ohmic and radiation losses and their angular instability.8–10 

To reduce the ohmic loss and enhance the PTE, the use of dielectric resonators instead of metallic coils has been recently proposed.11–13 It has been also demonstrated experimentally that dense dielectric claddings enable concentration and accumulation of electromagnetic energy from a near-field source.14 To further enhance the PTE of WPT systems, a dielectric metasurface supporting a quasi-magnetic bound state in the continuum was introduced.13 Another useful feature of the dielectric resonators is the ability to engineer the response by combination of different modes.15 Thus, nonradiating sources based on anapole states of dielectric disk resonators can be obtained,16,17 bringing a benefit for PTE enhancement of WPT systems due to the suppression of radiation losses.18 

To expand charging regions for more convenient utilization, modern WPT systems are required to be insensitive to positional misalignment.19,20 Therefore, for WPT to arbitrary spatial position devices, omnidirectional systems have been intensively investigated.21–33 Most of the proposed omnidirectional WPT systems are based on orthogonal transmitting (Tx) coils of different shapes.23,24,26,29 Such structures effectively eliminate the cross coupling effect between multiple coils and generate uniform magnetic field. However, these structures need several power sources to feed each Tx coil and dynamically control the phases and amplitudes of coil currents. Recently, Tx coils fed by a single power source generating uniform magnetic fields were implemented.22,27 One of the drawbacks of these systems is the existence of the blind zones with very small electromagnetic coupling to a receiver (Rx), resulting a low PTE. Another limitation is the safety of omnidirectional WPT systems to the biological tissues. As soon as the shielding techniques could not be applied, the level of electric and magnetic fields created by omnidirectional WPT systems must satisfy the limitations regulated by the standard.34 Thus, the allowable power transferred by an omnidirectional WPT system could be limited.

In this Letter, we propose an omnidirectional WPT system based on a dielectric hollow disk resonator operating at the axial magnetic quadrupole (AMQ) mode. We demonstrate that at this mode, the resonator produces a homogeneous magnetic field in the transverse plane, which can be potentially used to enable equivalent power transmission to Rxs at any azimuth angle and almost all polar angles around the Tx. We theoretically and experimentally study the omnidirectional WPT system with single and two Rxs in MHz frequency band. We demonstrate that the advantage of the dielectric resonator with respect to metallic coils is the confinement of the electric field. Thus, the exposure of electric and magnetic fields to biological tissues is minimized. This results in a very low specific absorption rate (SAR), making it a safer option for omnidirectional wireless charging.

A schematic view of the omnidirectional WPT system based on a dielectric hollow disk resonator is shown Fig. 1(a). The dielectric resonator with colossal permittivity excited by a copper source loop with radius R1 is used as the Tx. The Rx resonator is placed at a transfer distance d with respect to the Tx. The Rx resonator is a simple copper loop with a radius of R2 terminated by a capacitor C to provide a resonance at the same frequency as the Tx. A load copper loop with wire radius of R3 is placed at a distance of S from the Rx resonator. The Rx can rotate around the Tx with azimuthal angle θ and polar angle α. The eigenmode analysis of the dielectric resonator in CST Microwave Studio 2022 reveals three modes at the frequencies of 138, 152.5, and 150.2 MHz. They are classified as transverse magnetic dipole (TMD), transverse magnetic quadrupole (TMQ), and axial magnetic quadrupole (AMQ) (see the supplementary material for details).

FIG. 1.
(a) Schematic view of the WPT system based on the dielectric hollow disk resonator excited by a simple copper loop. The disk resonator has the outer radius R o = 62.2   mm, inner radius R i n = 50.75   mm, height h = 100   mm, permittivity ε = 1000, and loss tangent tan     δ = 4 × 10 − 4. The excitation copper loop has the radius of Rl, the wire radius of 2 mm, and placed at the position of Soff inside the dielectric resonator. The radius of the Rx resonator and load loop is set as R 2 = R 3 = 40   mm for systems operating at all three modes under study. PTE of the WPT systems operating at the TMD, TMQ, and AMQ modes extracted from the simulated S-parameters by Eq. (1), (b) as a function of azimuth angle θ for polar angle α = 0 and (c) as a function of polar angle α for θ = 0 for the transfer distance d = 3 cm. Simulated magnetic field distributions of the WPT systems operating at the TMD (d), TMQ (e), and AMQ (f) modes at the transverse and axial planes.
View largeDownload slide

(a) Schematic view of the WPT system based on the dielectric hollow disk resonator excited by a simple copper loop. The disk resonator has the outer radius R o = 62.2   mm⁠, inner radius R i n = 50.75   mm⁠, height h = 100   mm⁠, permittivity ε = 1000⁠, and loss tangent tan     δ = 4 × 10 − 4⁠. The excitation copper loop has the radius of Rl, the wire radius of 2 mm, and placed at the position of Soff inside the dielectric resonator. The radius of the Rx resonator and load loop is set as R 2 = R 3 = 40   mm for systems operating at all three modes under study. PTE of the WPT systems operating at the TMD, TMQ, and AMQ modes extracted from the simulated S-parameters by Eq. (1), (b) as a function of azimuth angle θ for polar angle α = 0 and (c) as a function of polar angle α for θ = 0 for the transfer distance d = 3 cm. Simulated magnetic field distributions of the WPT systems operating at the TMD (d), TMQ (e), and AMQ (f) modes at the transverse and axial planes.

FIG. 1.
(a) Schematic view of the WPT system based on the dielectric hollow disk resonator excited by a simple copper loop. The disk resonator has the outer radius R o = 62.2   mm, inner radius R i n = 50.75   mm, height h = 100   mm, permittivity ε = 1000, and loss tangent tan     δ = 4 × 10 − 4. The excitation copper loop has the radius of Rl, the wire radius of 2 mm, and placed at the position of Soff inside the dielectric resonator. The radius of the Rx resonator and load loop is set as R 2 = R 3 = 40   mm for systems operating at all three modes under study. PTE of the WPT systems operating at the TMD, TMQ, and AMQ modes extracted from the simulated S-parameters by Eq. (1), (b) as a function of azimuth angle θ for polar angle α = 0 and (c) as a function of polar angle α for θ = 0 for the transfer distance d = 3 cm. Simulated magnetic field distributions of the WPT systems operating at the TMD (d), TMQ (e), and AMQ (f) modes at the transverse and axial planes.
View largeDownload slide

(a) Schematic view of the WPT system based on the dielectric hollow disk resonator excited by a simple copper loop. The disk resonator has the outer radius R o = 62.2   mm⁠, inner radius R i n = 50.75   mm⁠, height h = 100   mm⁠, permittivity ε = 1000⁠, and loss tangent tan     δ = 4 × 10 − 4⁠. The excitation copper loop has the radius of Rl, the wire radius of 2 mm, and placed at the position of Soff inside the dielectric resonator. The radius of the Rx resonator and load loop is set as R 2 = R 3 = 40   mm for systems operating at all three modes under study. PTE of the WPT systems operating at the TMD, TMQ, and AMQ modes extracted from the simulated S-parameters by Eq. (1), (b) as a function of azimuth angle θ for polar angle α = 0 and (c) as a function of polar angle α for θ = 0 for the transfer distance d = 3 cm. Simulated magnetic field distributions of the WPT systems operating at the TMD (d), TMQ (e), and AMQ (f) modes at the transverse and axial planes.

Close modal
The PTE of WPT systems based on the dielectric hollow disk resonator operating at the TMD, TMQ, and AMQ modes is numerically studied with the frequency domain solver of CST Microwave Studio. At all three modes, the reflection and transmission coefficients for the different azimuth angle θ and polar angle α of the Rx are numerically obtained (see the supplementary material) and used to calculate the PTE as follows:
η = | S 21 | 2 1 − | S 11 | 2 × 100   % .
(1)
The geometrical parameters and capacitance value obtained during the numerical optimization of the WPT systems at different modes are listed in Table I of the supplementary material. The PTEs calculated by Eq. (1) as a function of Rx azimuth angle θ, for polar angle α = 0 °⁠, are shown in Fig. 1(b) for the transfer distance d = 3 cm. At the TMD mode, the PTE is zero for the angles around 90°, and the Rx cannot be charged there. The magnetic field of the system working at TMD is oscillating in the x direction and is minimum around θ = 90 ° [see Fig. 1(d)]. For the system working at the TMQ mode, there are two blind zones around 80° and 100° angles, where the PTE is about 40%. The magnetic field oscillates along both x and y axes [Fig. 1(e)]. In the system working at the AMQ mode, the PTE is over 80% for all azimuth angles. The magnetic field provides almost uniform distribution in the transverse plane, Fig. 1(f). However, the PTE is not still constant due to the asymmetric excitation of the Tx. The numerically estimated PTEs as a function of Rx polar angle α, for azimuth angle θ = 0 °⁠, and transfer distance d = 3 cm are presented in Fig. 1(c). In comparison to the WPT systems operating at TMD and TMQ modes, the system working on the AMQ mode provides higher PTE over the wider range of the polar angle α.
TABLE I.

Comparison of omnidirectional and directional magnetic resonant WPT systems based on metallic and dielectric resonators.

References Frequency Tx resonator type PTE (%) Blind zone Distance/λ Tx size/λ
5   10 MHz  Metal coil  94  Yes  0.025  0.02 
11   232 MHz  Dielectric disk  90  Yes  0.03  0.0649 
12   2.4 GHz  Dielectric sphere  80  Yes  0.05  0.8 
18   408 MHz  Dielectric disk  92  Yes  0.055  0.1142 
21   535 kHz  Orthogonal coils  78  No  0  5.35 × 10 − 4 
22   13.56 MHz  Cubic metal coil  60  No  0.0136  0.009 
25   20 kHz  Orthogonal coils  11.5  No  4 × 10 − 6  2 × 10 − 5 
27   13.56 and 27.12 MHz  Metal coil  61.6 and 65.4  No  0.004  0.0072 
30   6.78 MHz  Metal coil  74.2 (DC-DC)  No  4.5 × 10 − 4  0.0034 
This work  157 MHz  Dielectric disk  88  No  0.016  0.065 
References Frequency Tx resonator type PTE (%) Blind zone Distance/λ Tx size/λ
5   10 MHz  Metal coil  94  Yes  0.025  0.02 
11   232 MHz  Dielectric disk  90  Yes  0.03  0.0649 
12   2.4 GHz  Dielectric sphere  80  Yes  0.05  0.8 
18   408 MHz  Dielectric disk  92  Yes  0.055  0.1142 
21   535 kHz  Orthogonal coils  78  No  0  5.35 × 10 − 4 
22   13.56 MHz  Cubic metal coil  60  No  0.0136  0.009 
25   20 kHz  Orthogonal coils  11.5  No  4 × 10 − 6  2 × 10 − 5 
27   13.56 and 27.12 MHz  Metal coil  61.6 and 65.4  No  0.004  0.0072 
30   6.78 MHz  Metal coil  74.2 (DC-DC)  No  4.5 × 10 − 4  0.0034 
This work  157 MHz  Dielectric disk  88  No  0.016  0.065 
View Large

To achieve the constant PTE of the WPT system working at the AMQ mode, we come up with a symmetric source loop design, as shown in the inset of Fig. 2(c) (more details can be found in the supplementary material). With respect to the numerical predictions, the PTE can reach 90% for all azimuth angles of Rx, as shown in Fig. 2(c). Moreover, the transfer distance can be extended to 15 cm with the PTE degradation down to 60%.

FIG. 2.
(a) Photo of the omnidirectional WPT system experimental setup with one Rx. (b) Measured and simulated PTE of the omnidirectional WPT system at the frequency of 157 MHz as a function of the Rx azimuth angle θ. The inset shows the design of the Tx with symmetrical excitation shielded loop centered on the hollow disk with a radius of R 1 = 45   mm and height L = 25   mm and a 2   mm gap between its two vertical sections.
View largeDownload slide

(a) Photo of the omnidirectional WPT system experimental setup with one Rx. (b) Measured and simulated PTE of the omnidirectional WPT system at the frequency of 157 MHz as a function of the Rx azimuth angle θ. The inset shows the design of the Tx with symmetrical excitation shielded loop centered on the hollow disk with a radius of R 1 = 45   mm and height L = 25   mm and a 2   mm gap between its two vertical sections.

FIG. 2.
(a) Photo of the omnidirectional WPT system experimental setup with one Rx. (b) Measured and simulated PTE of the omnidirectional WPT system at the frequency of 157 MHz as a function of the Rx azimuth angle θ. The inset shows the design of the Tx with symmetrical excitation shielded loop centered on the hollow disk with a radius of R 1 = 45   mm and height L = 25   mm and a 2   mm gap between its two vertical sections.
View largeDownload slide

(a) Photo of the omnidirectional WPT system experimental setup with one Rx. (b) Measured and simulated PTE of the omnidirectional WPT system at the frequency of 157 MHz as a function of the Rx azimuth angle θ. The inset shows the design of the Tx with symmetrical excitation shielded loop centered on the hollow disk with a radius of R 1 = 45   mm and height L = 25   mm and a 2   mm gap between its two vertical sections.

Close modal

The experimental setup of the omnidirectional WPT system prototype for PTE investigations is shown in Fig. 2(a). The WPT system comprises a dielectric hollow disk resonator excited by a symmetric source loop as the Tx and an Rx resonator coupled to a load loop. Due to some technical limitations, we could not fabricate the disk with the parameters used in simulations. Thus, we stack it of five hollow disks with the following dimensions: the inner radius of R i n = 50.75   mm⁠, the outer radius of R o = 62.2   mm⁠, and the height of h d = 20   mm⁠. The hollow disks are made from BaSrTiO3, including Mg-containing compositions, and have the permittivity of ε = 1000 and tan   δ = 4 × 10 − 4 (at 1 MHz).35 Since the ceramic disks are fragile, several thin hollow spacers made of plexiglas with relative dielectric permittivity around 3.5 and electrical conductivity of 0.02   Sm − 1 and height of 3   mm are used between them. The symmetric source loop is a shielded loop made of a coaxial cable.36 The Rx resonator is made of copper wire with radius R 2 = 34   mm and wire diameter t = 1   mm⁠. To provide the resonance at the frequency of 157 MHz, the Rx is matched by C = 6.8   pf capacitor. The load loop radius is R 3 = 30   mm⁠. The end of the source and load loops is connected to the 50   Ω ports of a vector network analyzer by coaxial cables.

The S-parameters of the WPT system as a function of the Rx azimuth angle θ are measured and discussed in the supplementary material. The PTE is calculated using Eq. (1) and compared to the simulated PTE in Fig. 2(b). An equivalent PTE above 88% for all Rx azimuth angles is achieved.

We also study the PTE of the omnidirectional WPT system with two Rxs. An identical second Rx (Rx2) is added to the WPT system with the azimuth angle of θ2 with respect to the Rx1, as shown in Fig. 3(a). The simulated and measured S-parameters of the WPT system are presented in the supplementary material. The PTE extracted from the measured data as a function of the θ2 with the step of 20° individually for Rx1 and Rx2 as well as the total one calculated as their sum is depicted in Fig. 3(b). One can see the total PTE remains almost 90% regardless of the addition of the Rx2 or its position. Also, the PTEs of Rx1 and Rx2 remain stable and almost equal for all angles. Therefore, it is clear that the WPT system operating at AMQ can be applied to omnidirectional WPT with multi-receivers.

FIG. 3.
(a) Photo of the omnidirectional WPT system experimental setup with two Rxs separated by angle θ2. (b) Measured and simulated PTEs of Rx1 and Rx2, and total PTE of the omnidirectional WPT system at the frequency of 154 MHz as a function of θ2. Note that the angles between 0° and 50° are not feasible due to the receivers' size restrictions.
View largeDownload slide

(a) Photo of the omnidirectional WPT system experimental setup with two Rxs separated by angle θ2. (b) Measured and simulated PTEs of Rx1 and Rx2, and total PTE of the omnidirectional WPT system at the frequency of 154 MHz as a function of θ2. Note that the angles between 0° and 50° are not feasible due to the receivers' size restrictions.

FIG. 3.
(a) Photo of the omnidirectional WPT system experimental setup with two Rxs separated by angle θ2. (b) Measured and simulated PTEs of Rx1 and Rx2, and total PTE of the omnidirectional WPT system at the frequency of 154 MHz as a function of θ2. Note that the angles between 0° and 50° are not feasible due to the receivers' size restrictions.
View largeDownload slide

(a) Photo of the omnidirectional WPT system experimental setup with two Rxs separated by angle θ2. (b) Measured and simulated PTEs of Rx1 and Rx2, and total PTE of the omnidirectional WPT system at the frequency of 154 MHz as a function of θ2. Note that the angles between 0° and 50° are not feasible due to the receivers' size restrictions.

Close modal

To understand the benefits of the proposed WPT system, we compare its characteristics with other implementations reported in the literature (Table I). The proposed omnidirectional WPT system operates at the frequency of 157 MHz and achieves 88% of the PTE to a single Rx over 3 cm transfer distance. This PTE is comparable to the systems reported in Refs. 5, 11, 12, and 18 that do not offer omnidirectionality. Compared to the omnidirectional WPT systems reported in Refs. 21, 22, 25, 27, and 30, the proposed WPT system provides the highest PTE over a larger distance without any blind zone. For instance, the proposed system outperforms the metal coil-based system in Ref. 27 in both efficiency (88% vs 65.4%) and transfer distance normalized to wavelength (0.016 vs 0.004). This demonstrates the superior performance of our proposed WPT system.

To ensure the safety, it is crucial to examine the field exposure to biological tissues and SAR.35 The electric and magnetic fields of the proposed WPT system's Tx with symmetric excitation are compared with fields of the metal Txs of omnidirectional WPT systems reported in Refs. 27 and 30. The central cross sections of the electric and magnetic field distributions simulated in CST Microwave Studio are compared in Figs. 4(a) and 4(b), respectively. The magnetic field of the proposed Tx based on dielectric disk resonator has the highest amplitude at short distances d in comparison to the magnetic fields provided by the designs reported in Refs. 27 and 30 [see Fig. 4(a)]. Its magnitude decays faster as d increases, indicating strong accumulation of the magnetic field in proximity of the dielectric resonator. The electric field of the proposed Tx is negligible compared to electric fields of the metal Txs reported in Refs. 27 and 30 [see Fig. 4(b)]. Therefore, the proposed omnidirectional WPT system based on the dielectric resonator offers the strong confinement of the electric field providing less exposure of the electric field35 to surrounding biological tissues compared to WPT systems based on metal Txs.

FIG. 4.
Simulated (a) magnetic and (b) electric fields of the proposed omnidirectional WPT Tx as a function of the distance d compared to the Tx of the omnidirectional WPT systems based on metallic coils reported in Refs. 27 (square coil) and 30. To verify the correctness of our simulations with the results presented in Ref. 27, we made sure that the reflection coefficient coincides with Fig. 12(a) in Ref. 27. Magnetic field data presented in Fig. 2 of Ref. 30 are added to panel (a), which coincides with the recalculated magnetic field of the Tx. (c) Simulated SAR of the proposed omnidirectional WPT Tx.
View largeDownload slide

Simulated (a) magnetic and (b) electric fields of the proposed omnidirectional WPT Tx as a function of the distance d compared to the Tx of the omnidirectional WPT systems based on metallic coils reported in Refs. 27 (square coil) and 30. To verify the correctness of our simulations with the results presented in Ref. 27, we made sure that the reflection coefficient coincides with Fig. 12(a) in Ref. 27. Magnetic field data presented in Fig. 2 of Ref. 30 are added to panel (a), which coincides with the recalculated magnetic field of the Tx. (c) Simulated SAR of the proposed omnidirectional WPT Tx.

FIG. 4.
Simulated (a) magnetic and (b) electric fields of the proposed omnidirectional WPT Tx as a function of the distance d compared to the Tx of the omnidirectional WPT systems based on metallic coils reported in Refs. 27 (square coil) and 30. To verify the correctness of our simulations with the results presented in Ref. 27, we made sure that the reflection coefficient coincides with Fig. 12(a) in Ref. 27. Magnetic field data presented in Fig. 2 of Ref. 30 are added to panel (a), which coincides with the recalculated magnetic field of the Tx. (c) Simulated SAR of the proposed omnidirectional WPT Tx.
View largeDownload slide

Simulated (a) magnetic and (b) electric fields of the proposed omnidirectional WPT Tx as a function of the distance d compared to the Tx of the omnidirectional WPT systems based on metallic coils reported in Refs. 27 (square coil) and 30. To verify the correctness of our simulations with the results presented in Ref. 27, we made sure that the reflection coefficient coincides with Fig. 12(a) in Ref. 27. Magnetic field data presented in Fig. 2 of Ref. 30 are added to panel (a), which coincides with the recalculated magnetic field of the Tx. (c) Simulated SAR of the proposed omnidirectional WPT Tx.

Close modal

To perform SAR analysis, we employ CST Microwave Studio and a computer-aided-design model of the front part of a human arm, as depicted in Fig. 4(c). The model consists of the main biological tissues of the arm characterized by their corresponding electromagnetic properties. The distance between the Tx and the arm is 4 cm. For the input power of 0.5 W, the maximal calculated SAR is 0.034 W/kg, averaged over 1 g of tissue. There are no nonlinear effects in the WPT system, and the maximal SAR for different input powers can be obtained by scaling up these results. According to the IEEE safety regulation,34 which specifies the maximum SAR value for limbs and pinnae as 4 W/kg, a maximal input power of 117 W is allowed.

In summary, we proposed the omnidirectional WPT system based on a dielectric hollow disk resonator operating at the AMQ mode. A uniform radial magnetic field in the transverse plane of the Tx resonator is generated helping to avoid the blind zone. A symmetric excitation loop to achieve a constant PTE over all azimuth angles of the Rx is proposed. With respect to the experimental data, the omnidirectional WPT system provides 88% of PTE over all angles at the transfer distance of 3 cm to a single Rx. The possibility of charging multi-receivers is also experimentally verified. The results showed a stable and high efficiency of 90% regardless of the angle between two Rxs. Examination of the safety issues of the proposed WPT system revealed minimal exposure of the electromagnetic fields to biological tissues, resulting in a very low SAR. These findings establish the proposed WPT system as a safer option for omnidirectional wireless charging.

See the supplementary material for numerical studies of the eigenmode analysis and the WPT system as well as the numerical and experimental results of the S-parameters of the WPT system.

This work was supported by the Ministry of Science and Higher Education of the Russian Federation (Project No. 075-15-2022-1120). P.K. acknowledges the Priority 2030 Federal Academic Leadership Program. E.Z. acknowledges Dr. Alena Shchelokova for sharing the ceramic hollow disk resonators.

The authors have no conflicts to disclose.

Esmaeel Zanganeh: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Funding acquisition (equal); Investigation (equal); Methodology (equal); Visualization (equal); Writing – original draft (equal). Elizaveta Nenasheva: Resources (equal); Visualization (equal); Writing – original draft (equal). Polina Kapitanova: Conceptualization (equal); Project administration (equal); Resources (equal); Software (equal); Supervision (equal); Visualization (equal); Writing – original draft (equal).

The data that support the findings of this study are available within the article.

1.
M.
Song
,
P.
Jayathurathnage
,
E.
Zanganeh
,
M.
Krasikova
,
P.
Smirnov
,
P.
Belov
,
P.
Kapitanova
,
C.
Simovski
,
S.
Tretyakov
, and
A.
Krasnok
,
Nat. Electron.
4
,
707
(
2021
).
https://doi.org/10.1038/s41928-021-00658-x
Crossref
Search ADS
 
2.
A.
Mahesh
,
B.
Chokkalingam
, and
L.
Mihet-Popa
,
IEEE Access
9
,
137667
(
2021
).
https://doi.org/10.1109/ACCESS.2021.3116678
Crossref
Search ADS
 
3.
Z.
Zhang
,
H.
Pang
,
A.
Georgiadis
, and
C.
Cecati
,
IEEE Trans. Ind. Electron.
66
,
1044
(
2019
).
https://doi.org/10.1109/TIE.2018.2835378
Crossref
Search ADS
 
4.
M.
Song
,
P.
Belov
, and
P.
Kapitanova
,
Appl. Phys. Rev.
4
,
021102
(
2017
).
https://doi.org/10.1063/1.4981396
Crossref
Search ADS
 
5.
A.
Kurs
,
A.
Karalis
,
R.
Moffatt
,
J. D.
Joannopoulos
,
P.
Fisher
, and
M.
Soljačić
,
Science
317
,
83
(
2007
).
https://doi.org/10.1126/science.1143254
Crossref
Search ADS
PubMed
 
6.
M.
Dionigi
,
A.
Costanzo
,
F.
Mastri
, and
M.
Mongiardo
,
Wireless Power Transfer
(
River Publishers
,
2022
), pp.
157
–
197
.
Google Scholar
Crossref
Search ADS
 
7.
M.
Song
,
P.
Smirnov
,
E.
Puhtina
,
E.
Zanganeh
,
S.
Glybovski
,
P.
Belov
, and
P.
Kapitanova
,
Appl. Phys. Lett.
117
,
083501
(
2020
).
https://doi.org/10.1063/5.0012006
Crossref
Search ADS
 
8.
F.
Liu
,
Y.
Yang
,
D.
Jiang
,
X.
Ruan
, and
X.
Chen
,
IEEE Trans. Power Electron.
32
,
3240
(
2017
).
https://doi.org/10.1109/TPEL.2016.2581840
Crossref
Search ADS
 
9.
E.
Shamonina
,
L.
Solymar
, and
V.
Kalinin
,
J. Phys. D: Appl. Phys.
54
,
405502
(
2021
).
https://doi.org/10.1088/1361-6463/ac0c4f
Crossref
Search ADS
 
10.
T.
Sasatani
,
A. P.
Sample
, and
Y.
Kawahara
,
Nat. Electron.
4
,
689
(
2021
).
https://doi.org/10.1038/s41928-021-00636-3
Crossref
Search ADS
 
11.
M.
Song
,
P.
Belov
, and
P.
Kapitanova
,
Appl. Phys. Lett.
109
,
223902
(
2016
).
https://doi.org/10.1063/1.4971185
Crossref
Search ADS
 
12.
M.
Song
,
I.
Iorsh
,
P.
Kapitanova
,
E.
Nenasheva
, and
P.
Belov
,
Appl. Phys. Lett.
108
,
023902
(
2016
).
https://doi.org/10.1063/1.4939789
Crossref
Search ADS
 
13.
Y.
Xie
,
Z.
Zhang
,
Y.
Lin
,
T.
Feng
, and
Y.
Xu
,
Phys. Rev. Appl.
15
,
044024
(
2021
).
https://doi.org/10.1103/PhysRevApplied.15.044024
Crossref
Search ADS
 
14.
A.
Koshkimbay
,
I.
Yusupov
,
B.
Orazbayev
,
A.
Slobozhanyuk
, and
C.
Valagiannopoulos
, “Trapping EM Power by Hollow Cylinders,” in IEEE Transactions on Microwave Theory and Techniques,
IEEE Trans. Microwave Theory Tech.
(
IEEE
,
2023
).
https://doi.org/10.1109/TMTT.2023.3298199
15.
Y.
Yang
 and
S. I.
Bozhevolnyi
,
Nanotechnology
30
,
204001
(
2019
).
https://doi.org/10.1088/1361-6528/ab02b0
Crossref
Search ADS
PubMed
 
16.
P.
Kapitanova
,
E.
Zanganeh
,
N.
Pavlov
,
M.
Song
,
P.
Belov
,
A.
Evlyukhin
, and
A.
Miroshnichenko
,
Ann. Phys.
532
,
2000293
(
2020
).
https://doi.org/10.1002/andp.202000293
Crossref
Search ADS
 
17.
E.
Zanganeh
,
A.
Evlyukhin
,
A.
Miroshnichenko
,
M.
Song
,
E.
Nenasheva
, and
P.
Kapitanova
,
Phys. Rev. Lett.
127
,
096804
(
2021
).
https://doi.org/10.1103/PhysRevLett.127.096804
Crossref
Search ADS
PubMed
 
18.
E.
Zanganeh
,
M.
Song
,
A. C.
Valero
,
A. S.
Shalin
,
E.
Nenasheva
,
A.
Miroshnichenko
,
A.
Evlyukhin
, and
P.
Kapitanova
,
Nanophotonics
10
,
4399
(
2021
).
https://doi.org/10.1515/nanoph-2021-0378
Crossref
Search ADS
 
19.
J.
Kim
,
D.-H.
Kim
, and
Y.-J.
Park
,
IEEE Trans. Microwave Theory Tech.
64
,
3714
(
2016
).
https://doi.org/10.1109/TMTT.2016.2608802
Crossref
Search ADS
 
20.
E.
Zanganeh
,
A.
Sayanskiy
,
S.
Kosulnikov
, and
P.
Kapitanova
,
Adv. Mater. Technol.
8
,
2202133
(
2023
).
https://doi.org/10.1002/admt.202202133
Crossref
Search ADS
 
21.
D.
Lin
,
C.
Zhang
, and
S. R.
Hui
,
IEEE Trans. Power Electron.
32
,
613
(
2017
).
https://doi.org/10.1109/TPEL.2016.2523506
Crossref
Search ADS
 
22.
N.
Ha-Van
 and
C.
Seo
,
IEEE Trans. Ind. Electron.
65
,
1358
(
2018
).
https://doi.org/10.1109/TIE.2017.2733470
Crossref
Search ADS
 
23.
Z.
Ye
,
Y.
Sun
,
X.
Liu
,
P.
Wang
,
C.
Tang
, and
H.
Tian
,
Energies
11
,
2159
(
2018
).
https://doi.org/10.3390/en11082159
Crossref
Search ADS
 
24.
J.
Feng
,
Q.
Li
,
F. C.
Lee
, and
M.
Fu
,
IEEE Trans. Ind. Inf.
15
,
4656
(
2019
).
https://doi.org/10.1109/TII.2019.2908217
Crossref
Search ADS
 
25.
H.
Han
,
Z.
Mao
,
Q.
Zhu
,
M.
Su
, and
A. P.
Hu
,
IEEE Access
7
,
35981
(
2019
).
https://doi.org/10.1109/ACCESS.2019.2903831
Crossref
Search ADS
 
26.
Z.
Zhang
 and
B.
Zhang
,
IEEE Trans. Ind. Electron.
67
,
2755
(
2020
).
https://doi.org/10.1109/TIE.2019.2908604
Crossref
Search ADS
 
27.
C.
Lu
,
X.
Huang
,
X.
Tao
,
X.
Liu
,
C.
Rong
,
Y.
Zeng
, and
M.
Liu
,
IEEE Trans. Antennas Propag.
69
,
3493
(
2021
).
https://doi.org/10.1109/TAP.2020.3037713
Crossref
Search ADS
 
28.
J.
Li
,
Y.
Yang
,
H.
Yan
,
C.
Liu
,
L.
Dong
, and
G.
Wang
,
IEEE Sens. J.
20
,
6148
(
2020
).
https://doi.org/10.1109/JSEN.2020.2972618
Crossref
Search ADS
 
29.
J.
Feng
,
Q.
Li
, and
F. C.
Lee
,
IEEE Trans. Ind. Electron.
69
,
1422
(
2022
).
https://doi.org/10.1109/TIE.2021.3063981
Crossref
Search ADS
 
30.
N.
Ha-Van
,
Y.
Liu
,
P.
Jayathurathnage
,
C. R.
Simovski
, and
S. A.
Tretyakov
,
IEEE Trans. Ind. Electron.
69
,
10045
(
2022
).
https://doi.org/10.1109/TIE.2022.3151961
Crossref
Search ADS
 
31.
X.
Dang
,
P.
Jayathurathnage
,
F.
Liu
,
S. A.
Al Mahmud
,
C. R.
Simovski
, and
S. A.
Tretyakov
,
IEEE J. Emerging Sel. Top. Ind. Electron.
3
,
403
(
2022
).
https://doi.org/10.1109/JESTIE.2022.3155365
Crossref
Search ADS
 
32.
T.
Feng
,
Z.
Zuo
,
Y.
Sun
,
X.
Dai
,
X.
Wu
, and
L.
Zhu
,
IEEE Trans. Power Electron.
37
,
9999
(
2022
).
https://doi.org/10.1109/TPEL.2022.3155251
Crossref
Search ADS
 
33.
P.
Jayathurathnage
,
X.
Dang
,
C. R.
Simovski
, and
S. A.
Tretyakov
,
IEEE Trans. Ind. Electron.
69
,
6828
(
2022
).
https://doi.org/10.1109/TIE.2021.3097663
Crossref
Search ADS
 
34.
“IEEE Standard for Safety Levels with Respect to Human Exposure to Electric, Magnetic, and Electromagnetic Fields, 0 Hz to 300 GHz – Redline,” in IEEE Std C95.1-2019 (Revision of IEEE Std C95.1-2005/ Incorporates IEEE Std C95.1-2019/Cor 1-2019) – Redline, vol., no., pp.1–679, 4 Oct. 2019.
35.
E.
Nenasheva
,
N.
Kartenko
,
I.
Gaidamaka
,
O.
Trubitsyna
,
S.
Redozubov
,
A.
Dedyk
, and
A.
Kanareykin
,
J. Eur. Ceram. Soc.
30
,
395
(
2010
).
https://doi.org/10.1016/j.jeurceramsoc.2009.04.008
Crossref
Search ADS
 
36.
C. F.
Carobbi
 and
L. M.
Millanta
,
IEEE Trans. Instrum. Meas.
53
,
514
(
2004
).
https://doi.org/10.1109/TIM.2004.823297
Crossref
Search ADS
 
© 2023 Author(s). Published under an exclusive license by AIP Publishing.
2023
Author(s)

Supplementary Material

Supplementary materials- zip file