Characterization of wireless power transfer based on Fano resonant-like surface

This paper presents a new way to enhance the transmission efficiency of a dual-coils wireless power transfer system. That method is to introduce a Fano resonant-like surface in the dual-coils wireless power transfer system. This surface, positioned opposite the transmission direction of the transmitter coil in the system, adopts a four-armed helical structure. The results demonstrate that introducing the Fano resonant-like surface significantly enhances system transmission efficiency, attributed to two primary factors. First, the Fano local resonance effect in the dual-coils wireless power transfer system with Fano resonant-like surface leads to the enhance the transmission efficiency. Second, the Fano resonant-like surface shields the energy propagation of the nearby magnetic field in the direction opposite to transmission. Further, compared to a wireless power transfer system comprising only two coils, the overall improvement in transmission efficiency is 30%–40%. Owing to its simplicity, more compact size, cost-effectiveness, and ease of integration without having to be placed between the transmitting and receiving coils, the Fano resonant-like surface can lay the groundwork for practical applications in wireless charging.


Introduction
In recent years, wireless power transfer (WPT) technology has emerged as a popular method for energy transfer as it overcomes the limitations of physical transmission lines, offers Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence.Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.flexibility irrespective of environmental conditions, boasts high applicability, and presents numerous other advantages [1].WPT has broad application prospects in machinery manufacturing, power transportation, biomedicine, and household appliances [2][3][4].Since the advent of wireless power transmission, transmission efficiency and transmission distances have been important topics of research [5,6].Although research into wireless power transmission has spanned decades, the transmission efficiency remains notably lower than that of conventional wired methods.Additionally, the transmission distances realized are relatively short, among concerns about potential radiation hazards [7][8][9][10][11].Therefore, research into WPT still focuses on the improvement of transmission efficiency and transmission distance [12,13].
The Fano resonance effect is a resonant scattering phenomenon with an asymmetric linear type, originating from the quantum interference effect of resonant and nonresonant processes, which can locally locate the electromagnetic field at the resonant frequency [14].In recent years, the Fano resonance effect can be achieved in many structures, such as in structures plasmas and metasurfaces, and can be widely used in many fields, such as sensors, switches, and active devices, etc [8,[15][16][17][18][19][20].For example, in 2019, Pham et al [21] achieved dynamic tuning of electromagnetic waves by controlling the reconfigurable defective cavities formed in metamaterials and explained the physical mechanism of cavity generation using Fano interference, and experimentally characterized the transmission loss and bandwidth of various dynamically tunable metamaterial waveguides, which provide valuable references for the integration of surface wave devices and planar WPT.
Artificial magnetic conductor (AMC) have been widely used in wireless energy transmission.AMC is a kind of metamaterial that mimics the properties of a perfect magnetic conductor [22], which is an artificially designed idiosyncratic surface structure consisting of a metallic layer on the upper and lower surfaces and a dielectric layer in the middle [23,24].For example, in 2013, Wu et al [25] used AMC as a reflector in a WPT system, and the transmission efficiency was improved as measured by simulation calculations.In 2019, Shi et al [26] employed a positive hexagonal AMC structure to improve the transmission efficiency of a humbucking WPT system.
In this paper, we try to design a new special surface resonance structure, just as AMC.But, the new special surface resonance structure can combine with the dual-coils wireless energy transmission structure to realize the Fano resonance-like effect, so as to enhance the energy transmission efficiency.

Fano resonant-like surface design
Figure 1 depicts the Fano resonant-like surface discussed in this paper, comprising an upper spiral sheet clad in copper, a dielectric layer, a bottom sheet also clad in copper, and centrally positioned holes plated with copper.The upper copperclad sheet features a four-armed helical structure centered within a rectangle with a 1 mm side length and 1 mm side width.From this center, four spiral copper strips extend outward in four directions, with the entire structure on the upper surface consisting of 27 laps.The number of laps dictates the surface's operating frequency; more laps correspond to a lower working frequency.Sandwiched between the upper and lower copper sheets is a 3 mm-thick Fr-4 dielectric layer with a dielectric constant (ε) of 4.4.The surface beneath the dielectric layer is entirely copper-coated.The upper and lower surfaces are connected by copper-plated holes through the intermediate dielectric layer, with each surface and the plated holes possessing a copper thickness of 0.036 mm.After optimization, the surface's parameters, as illustrated in figure 1, reveal the four-armed helical structure on the top surface with a line width of g = 1 mm, line spacing of m = 1 mm, and diameter of the copperplated holes as d = 0.5 mm.Drawing from the theory of composite right/left-handed transmission line, the equivalent circuits are presented in figure 2. The upper spiral sheet clad in copper possesses self-capacitance (C) and selfinductance (L1).Meanwhile, the copper-plated holes linking the top and bottom copper-clad sheets offer an equivalent inductance (L2), making the surface analogous to an LC circuit.

Design and experimental results for the Fano resonance-based surface WPT system
The WPT system that incorporates the Fano resonant-like surface is based on a dual-coils system.Both the transmitter and receiver coils are circular rings made of copper, with their central axes aligned horizontally.Each coil, constructed from copper wire 2 mm in diameter, has a diameter of 100 mm.In terms of arrangement, from the topmost layer downward, the system comprises the receiver coil, the transmitter coil, and the Fano resonant-like surface, which is oriented parallel to the two coils, as illustrated in figure 3(a).For testing, the Keysight E5063A vector network analyzer was employed.The experimental setup is depicted in figure 3(b).Both the transmitting and receiving coils are fabricated from enameled round copper wires.SMA headers are soldered at their openings to enable connection to Port 1 and Port 2 of the vector network analyzer.The arrangement of the experiment was vertical for the convenience of measurement.The performance of the WPT system was experimentally evaluated based on the S-parameter, with the transmission efficiency (η) of the WPT system evaluated using the forward transmission coefficient (|S 21 |) when the network is matched at two ports; the transmission efficiency can be further expressed as [27]: To further understand the underlying mechanism of the Fano resonance-like phenomenon in this WPT system, tests were conducted on the structures shown in figures 3(c) and (d).3(d).We can see that a discernible resonance curve with a narrower line width is evident in figure 4(a), whereas figure 4(b) exhibits a spectrum with a broader line width.The S 21 curve's modulation, following the integration of the Fano resonant-like surface into the WPT system, is portrayed in figure 4(c).A clear interference between the narrowband resonance and broad-band spectral line becomes apparent upon merging the two structures from figures 3(c) and (d).This interference suppresses the amplitude near the resonance frequency of the mode exhibiting a narrower linewidth, subsequently yielding an asymmetric spectral characteristic, which results in the generation of Fano type transmission line.The significant enhancement in the transmission efficiency of the dual-coils WPT system due to the Fano resonance is marked.Simultaneous, figure 4(d) traces the variation of S 21 in relation to transmission distance within this system.Evidently, this system's transmission efficiency surpasses that of a dualcoils WPT system.Specifically, the overall efficiency of the Fano resonant-like surface-based WPT system is enhanced by approximately 30% when compared to its dual-coils counterpart.Notably, at a 10 mm distance between the transmitter and receiver coils, S 21 peaks at 72%-a marked 40% improvement over the dual-coils WPT system devoid of a Fano resonant-like surface.

Spatial electromagnetic field analysis of Fano resonance-based surface WPT system
On the basis of the above experimental results, we respectively compare the transmission efficiency of the three structures through simulation and experimental data, as shown in figure 5.The three structures are the dual-coils WPT system with Fano resonant-like surface, the dual-coils WPT system, and the dual-coils WPT system with a single copper layer.It can be seen that a significant increase in the magnitude of S 21 when the Fano resonant-like surface is introduced in the dual-coils WPT system.When the Fano resonantlike surface is introduced, the resonance frequency appears near 27 MHz, and the transmission coefficient S 21 is as high as 0.79, while S 21 is only 0.35 for the dual-coils WPT system, and S 21 is only 0.2 for the dual-coils WPT system with only a single copper layer, from simulation plots.That is to say, the transmission coefficient of the dual-coils WPT system with the Fano resonant-like surface is the strongest in the three structures, the dual-coils WPT system is second, the dual-coils WPT system with a single copper layer is the worst.The specific reasons are described below by spatial electromagnetic fields.It is worth noting that a minor shift at the Fano local resonance frequency between the simulation and experimental results, attributed to the omission of the intrinsic electromagnetic wave loss of the material in the simulation calculations.
Spatial electromagnetic fields at various positions were meticulously analyzed and compared to further understanding the underlying causes for the heightened transmission efficiency of the Fano resonant-like surface based WPT  system introduced in this study.This analysis utilized 3D electromagnetic simulation software grounded in the timedomain finite-difference analysis method.For the simulation computations, impedance-excited discrete ports were employed for the transmitting and receiving coils, with the structural parameters chosen for the simulation calculations mirroring those used in the experimental tests to obtain a clearer comparison.
Figures 6(a)-(c) give the electromagnetic field's longitudinal distribution for the above three structures.Figure 6(a) corresponds the dual-coils WPT system with Fano resonant-like surface, figure 6(b) corresponds the dual-coils WPT system, and figure 6(c) corresponds the dual-coils WPT system with a single copper layer, respectively.Compare figures 6(a) and (b), we can see that the introduction of the Fano resonant-like surface leads to a notably stronger magnetic field strength at the location of the receiving coil when compared to the dualcoils WPT system.After energizing the discrete source port at the transmitting coil's opening, a magnetic field emanates from the transmitting coil.A segment of this field is captured by the receiving coil, while another segment interacts with the opposite side of the Fano resonant-like surface.Which excites and produces the Fano resonance-like phenomenon, as discussed earlier, subsequently boosting transmission efficiency.Moreover, as visualized in figure 6(b), the Fano resonantlike surface's presence acts as a shield, hindering the energy propagation of the proximal magnetic field in the direction opposing transmission.This shielding effect further contributes to the enhanced transmission efficiency of the WPT system.Compare figures 6(b) and (c), it can be found that although the electromagnetic field is shielded, it does not enhance the electromagnetic field energy near the receiving coil.The reason is that the single copper layer cuts off the propagation loop of the near-magnetic field.
To further understand the spatial electromagnetic field distribution of the Fano resonant-like surface WPT system, simulations were conducted to observe the magnetic field strength distribution at various locations, with the results compared with that of the dual-coils WPT system.For the WPT system employing the Fano resonant-like surface, the distance set between the Fano resonant-like surface and transmitting coil is 5 mm, with a spacing of 10 mm between the transmitting and receiving coils.Simulation calculations were performed for three designated positions: position a, illustrated in figure 7, is situated between the transmitter and receiver coils at a distance of 2 mm from the transmitter coil.Comparing figures 7(a) and (b), the magnetic field strength in the Fano resonant-like surface WPT system significantly surpasses that in the dual-coils WPT system.Position b, depicted in figure 8, is nestled between the transmitting and receiving coils, 2 mm away from the receiving coil.Comparing figures 8(a) and (b), it is clear that the magnetic field strength in the vicinity of the receiving coil in the Fano resonant-like surface WPT system greatly exceeds that of the dual-coils WPT system.Position c, highlighted in figure 9, lies 3 mm beneath the surface and 12 mm from the transmitting coil.Comparing figures 9(a) and (b) reveals that the Fano resonant-like surface nearly wholly negates all the back-propagating electromagnetic field energy-a feat unattainable by the dual-coils WPT system.This shielding phenomenon arises because the lower layer of the Fano resonant-like surface consists of a fully copper-plated sheet.When electromagnetic waves encounter this low-resistivity metallic material, they induce an eddy current, which subsequently spawns a counteractive magnetic field that opposes the external field, resulting in a pronounced shielding effect.

Conclusion
In this study, a four-armed helical surface was integrated into a dual-coils WPT system to facilitate the formation of narrow-band resonance and broad-band spectrumprerequisites for manifesting the Fano resonance effect.Hence, introducing this surface into the conventional dual-coils WPT system induces the Fano resonance phenomenon, leading to a substantial improvement in transmission efficiency.Concurrently, the surface acts as a shield for electromagnetic fields within the WPT system.The straightforward and cost-effective integration of this surface offers valuable insights for advancements in wireless charging technology.

Figure 3 .
Figure 3. (a) Schematic diagram of the structure of the Fano resonant-like surface-based WPT system; (b) diagram of the experimental setup; (c) structure of the Fano resonant-like surface with transmitting coil; (d) structure of the transmitting and receiving coils.

Figure 4 (
a) displays the S 21 curve variation for the structure in figure 3(c), calculated by the S 11 curve data.Concurrently, figure 4(b) shows the S 21 curve alteration corresponding to the structure in figure

Figure 4 .
Figure 4. (a) S 21 curves corresponding to the structure of figure 3(c); (b) S 21 curves corresponding to the structure of figure 3(d); (c) S 21 curves for the Fano resonant-like surface WPT system; (d) the variation of S 21 of WPT system with transmission distance at 24.7 MHz frequency.Specifically, the black solid line indicates the presence of the Fano resonant-like surface WPT system, and the red dashed line indicates the dual-coils WPT system.

Figure 5 .
Figure 5.Comparison of experimental and simulation plots of the dual-coils WPT system with Fano resonant-like surface, without Fano resonant-like surface, and only a single copper layer.The solid line represents the WPT system with the introduction of the Fano resonance-like surface; the dotted line represents the dual-coils WPT system; and the dashed line represents the WPT system only a single copper layer.

Figure 6 .
Figure 6.The magnetic field strength distribution in a longitudinal cross-section.(a) Distribution of the magnetic field strength of the Fano resonant-like surface WPT system; (b) distribution of the magnetic field strength of the dual-coils WPT system; (c) distribution of the magnetic field strength of the dual-coils WPT system with copper layer.

Figure 7 .
Figure 7. (a) Distribution of the magnetic field strength of the Fano resonant-like surface WPT system at position a; (b) distribution of the magnetic field strength of the dual-coils WPT system at position a.

Figure 8 .
Figure 8.(a) Distribution of the magnetic field strength of the Fano resonant-like surface WPT system at position b; (b) distribution of the magnetic field strength of the dual-coils WPT system at position b.

Figure 9 .
Figure 9. (a) Distribution of the magnetic field strength of the Fano resonant-like surface WPT system at position c; (b) distribution of the magnetic field strength of the dual-coils WPT system at position c.