A universal non-Hermitian platform for bound state in the continuum enhanced wireless power transfer

doi:10.1007/s11467-023-1388-x

Front. Phys.

2024, Vol. 19

Issue (4) : 43209 https://doi.org/10.1007/s11467-023-1388-x

A universal non-Hermitian platform for bound state in the continuum enhanced wireless power transfer

Haiyan Zhang¹, Zhiwei Guo¹(

), Yunhui Li², Yaping Yang¹, Yuguang Chen¹(

), Hong Chen¹

¹. School of Physics Science and Engineering, Tongji University, Shanghai 200092, China
². Department of Electrical Engineering, Tongji University, Shanghai 201804, China

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Abstract

Non-Hermitian systems with parity−time (PT)-symmetry have been extensively studied and rapidly developed in resonance wireless power transfer (WPT). The WPT system that satisfies PT-symmetry always has real eigenvalues, which promote efficient energy transfer. However, meeting the condition of PT-symmetry is one of the most puzzling issues. Stable power transfer under different transmission conditions is also a great challenge. Bound state in the continuum (BIC) supporting extreme quality-factor mode provides an opportunity for efficient WPT. Here, we propose theoretically and demonstrate experimentally that BIC widely exists in resonance-coupled systems without PT-symmetry, and it can even realize more stable and efficient power transfer than PT-symmetric systems. Importantly, BIC for efficient WPT is universal and suitable in standard second-order and even high-order WPT systems. Our results not only extend non-Hermitian physics beyond PT-symmetry, but also bridge the gap between BIC and practical application engineering, such as high-performance WPT, wireless sensing and communications.

Keywords non-Hermitian physics parity−time asymmetry bound state in the continuum wireless power transfer

Corresponding Author(s): Zhiwei Guo,Yuguang Chen

Issue Date: 19 March 2024

Cite this article:

Haiyan Zhang,Zhiwei Guo,Yunhui Li, et al. A universal non-Hermitian platform for bound state in the continuum enhanced wireless power transfer[J]. Front. Phys. , 2024, 19(4): 43209.

URL:

https://academic.hep.com.cn/fop/EN/10.1007/s11467-023-1388-x
https://academic.hep.com.cn/fop/EN/Y2024/V19/I4/43209

Fig.1 Schematic diagrams of non-Hermitian models. (a) A general non-Hermitian physical model with multiple resonators. (b) Second-order non-Hermitian systems, including the PT-symmetric model with balanced gain?loss (

g 1 = γ 2

), and PT-asymmetric model with unbalanced gain?loss (

g 1 ≠ γ 2

). (c) Third-order non-Hermitian systems, including PT-symmetric system with balanced gain?loss (

g 1 = γ 3

) and symmetric coupling (

κ 12 = κ 23

), and PT-asymmetric system with unbalanced gain?loss (

g 1 ≠ γ 3

) and/or asymmetric coupling (

κ 12 ≠ κ 23

Fig.2 BIC enabled high-efficient WPT. For the BIC condition of second-order non-Hermitian system

κ = g 1 γ 2

, the evolution of the real part (a) and imaginary part (b) of the eigenfrequencies of the system described by Eq. (4) in the two-dimensional parameter space

(g 1, γ 2)

. (c) The variation of coupling strength with gain and loss to meet the BIC condition of

κ = g 1 γ 2

. (d) The transfer efficiency of the second-order WPT system with the aid of BIC. (e?h) Same as (a?d), but for the third-order non-Hermitian WPT system. Real (e) and imaginary (f) parts of the eigenfrequencies of the system described by Eq. (10) in the parameter space of

(κ 12, κ 23)

when

g 1 = 4.8

kHz and

γ 3 = g 1 κ 232 / κ 122

. (g) The variation of loss with coupling strengths to meet the BIC condition of

γ 3 = g 1 κ 232 / κ 122

when

g 1 = 4.8

kHz. (h) The calculated transfer efficiency of the third-order WPT system with the aid of BIC when

g 1 = 4.8

kHz and

γ 3 = g 1 κ 232 / κ 122

(upper surface), and balanced gain?loss of

g 1 = γ 3 = 4.8

kHz (lower surface). The intrinsic loss is considered

Γ = 0.195

kHz to match the actual experimental system.

Fig.3 Comparison of PT-symmetry and BIC for WPT in two different non-Hermitian systems. Evolution of the real part (a) and imaginary part (b) of the eigenfrequencies in the second-order PT-symmetric system with

g 1 = 4.8

kHz and

γ 2 =

4.8

kHz. (c) The corresponding transfer efficiency versus

κ

. (d?f) Similar to (a?c), but for the BIC-assisted efficient WPT, where the asymmetric parameters are

g 1 = 4.8

kHz and

γ 2 = 7.2

kHz, respectively. (g?i) Same as (a?c), but for the third-order PT-symmetric system with

g 1 = 4.8

kHz and

γ 2 = 4.8

kHz. (j?l) Same as (d?f), but for the BIC-assisted efficient WPT in the third-order non-Hermitian system with

g 1 = 4.8

kHz and

γ 3 = g 1 κ 232 / κ 122

. The intrinsic loss is considered as

Γ = 0.195

kHz, which is consistent with the actual WPT system composed of lossy coils.

Fig.4 Third-order non-Hermitian WPT systems. (a) Third-order WPT system consisting of three resonant (transmitter, relay and receiver) coils and two non-resonant (source and load) coils. (b) The corresponding photograph of the experimental setup.

Fig.5 Flexible regulation of the BIC for efficient WPT in the third-order system. Evolution of the real part and imaginary part of the eigenfrequencies in the third-order non-Hermitian WPT system with different gain?loss ratios: (a, d)

g 1 / γ 3 = 0.5 (g 1 = 4.8

kHz and

γ 3 = 9.6

kHz); (b, e)

g 1 / γ 3 = 1

(

g 1 = 9.6

kHz and

γ 3 = 9.6

kHz); (c, f)

g 1 / γ 3 = 2

(

g 1 = 9.6

kHz and

γ 3 = 4.8

kHz). The coupling strength between the transmitter coil and relay coil is fixed, that is,

κ 12 = 13.1

kHz with

s 12 = 15

cm. The solid line and the pentagram represent the theoretical and experimental results respectively. (g?i) Similar to (a?f), but for the power transfer efficiency versus

s 23

at the fixed working frequency

ω 0

. The BIC with real eigenvalue

ω 1 = ω 0

is marked by the black arrow. The intrinsic loss of the resonant coil is

Γ = 0.195

kHz. The calculated (measured) transfer efficiency is marked by solid lines (circles).

Fig.6 Comparison of transfer efficiency between BIC-assisted systems and balanced gain?loss systems. (a) The transfer efficiency of second-order WPT systems: balanced gain?loss system (

g 1 = γ 2 = 4.8

kHz), and BIC-assisted system (

g 1 = 4.8

kHz and

γ 2 = κ 2 / g 1

). (b) Same as (a), but for the third-order WPT systems: balanced gain?loss system (

g 1 = γ 3 = 4.8

kHz), and BIC-assisted system (

g 1 = 4.8

kHz and

γ 3 = g 1 κ 232 / κ 122

). The calculated and experimental results are marked by solid lines and circles respectively.

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