In this paper, a wideband metasurface-loaded (MTS-L) rectenna system is proposed to capture electromagnetic (EM) energy at arbitrary azimuth angles. The radiation patterns of different modes in the original MTS configuration are analyzed using the characteristic mode theory, and potential modes with omnidirectional radiation are screened out. By the arrangement of patches, the roundness performance of the radiation pattern can be ameliorated, and the omnidirectional characteristic is obtained over a wide frequency band. Subsequently, the surface current density of the selected mode is carefully and artificially designed to facilitate probe excitation as well as refrain from introducing complex power-combining networks. A wideband rectifier circuit is designed as the load of the proposed antenna. Eventually, measured results show that it operates from 4.6 to 9.6 GHz with a fractional bandwidth of 70.4%, and the peak system efficiency is 52.2%. The proposed system demonstrates excellent potential for wireless power transmission and EM energy harvesting in indoor environments.

Energy-harvesting technology has been the focus of scholarly attention.1–3 Electromagnetic (EM) energy is widely distributed in the environment with an exceptionally high density in indoor offices and families, making it an excellent choice for the energy sources of IoT devices.4 The metasurface (MTS) evolved from artificial metamaterials and has been applied to wireless power transmission (WPT).5,6 Therefore, MTSs can be endowed with properties and functions that conventional antennas/rectennas cannot achieve. With these properties, the application of MTSs to the design of rectennas, i.e., MTS-loaded (MTS-L), can be widely and efficiently applied to modulate EM waves as well as WPT and energy harvesting (EH).7–10 

Recently, MTSs that directly output dc energy have been explored. In Ref. 11, a modified electrical-inductive-capacitive MTS unit loaded with a voltage-doubling rectifier circuit was presented. Its efficiency was maximized by improving the unit impedance and matching it to those of free space and the rectifier circuit. Eventually, a system efficiency of 76.8% was achieved in an operating frequency band of 2.45 GHz. For these narrow-band MTSs, manufacturing accuracy can easily cause the operating range to be shifted. Moreover, the frequency bands commonly operated in communication are diverse and discrete, and, therefore, there is an urgent need to expand the MTS bandwidth to adapt to multiband and multispectrum applications. To accord with this objective, a wideband MTS with an FBW of 22.4% by two resonant modes of parallel MTS resonators was presented,12 eliminating the power-combining and impedance-matching networks to up the system efficiency to 74.5%.

When constructing MTS systems, scholars generally consider only the performance in frontal or a specific azimuth orientation and rarely pay attention to others. As demonstrated in Fig. 1, in WPT and EH application scenarios, EM waves may originate from various directions. For example, different types of EM wave transmitters or IoT devices are scattered indoors and may be located anywhere in the room. As such, at the beginning of the construction, the essential properties of the system need to be estimated to determine whether it can absorb EM waves in all directions. Another aspect of this research was more complicated than dipole antennas because of the planar antenna features. Over the years, the characteristic mode (CM) theory has been developed rapidly.13 The method has been widely applied in the research of MTSs, which provides a sound theory for researchers.14,15 Therefore, the inherent pattern of the designed MTS-loaded rectenna can be screened using CMA to obtain the specific desired radiation pattern after excitation.16,17 Therefore, the CM theory is applied to explore the primitive properties of the system.

FIG. 1.

Illustrative application of an azimuth insensitivity metasurface-loaded rectenna for electromagnetic energy harvesters and wireless power transmission.

FIG. 1.

Illustrative application of an azimuth insensitivity metasurface-loaded rectenna for electromagnetic energy harvesters and wireless power transmission.

Close modal

In this paper, the proposed MTS-L construction is interpreted using CMA. The original property is calculated using this theory. The radiation pattern of each mode is derived, and the modes with omnidirectional azimuthal potential are screened for estimation and improvement. The obtained modes are investigated to boost the roundness performance of the radiation and increase its potential operating bandwidth. A probe feed structure is constructed to excite the selected mode, and the energy can be exported through the unique feed structure to a designed wideband rectifier circuit without a traditional power-combining network. This azimuth-insensitive MTS-L system maintains almost consistent absorption performances at all incident orientations in the broad band. It shows its great potential EM EH and WPT applications.

In this chapter, the CMA will be used to interpret the proposed MTS configuration to provide the assistance and recommendations for the subsequent design.

A configuration of the proposed MTS-L system is shown in Fig. 2. The system consists of two F4B substrates with a regular octagonal profile. The dielectric constants of substrates 1 and 2 are 3.5 and 3.0, respectively. The top layer is the proposed MTS patches, and after receiving the EM energy, it is transmitted through the rectifier circuit located in the bottom layer. The metal layer between the two substrates is the ground plane connected to the rectifier circuit's negative pole.

FIG. 2.

(a) Top view, (b) bottom view, and (c) side view of the proposed system framework and configuration. W = 60, H1 = 4, H2 = 0.76, D1 = 3.2, D2 = 3.8, D3 = 1.2, L1 = 14, L2 = 6.8, G1 = 1, G2 = 0.2, and S = 1. Unit: mm.

FIG. 2.

(a) Top view, (b) bottom view, and (c) side view of the proposed system framework and configuration. W = 60, H1 = 4, H2 = 0.76, D1 = 3.2, D2 = 3.8, D3 = 1.2, L1 = 14, L2 = 6.8, G1 = 1, G2 = 0.2, and S = 1. Unit: mm.

Close modal

Figure 3(a) depicts a constructed original MTS structure. The patch is arranged as a 3 × 3 configuration with the size of L1 and an intermediate gap of G1. Substrate 1 is the F4B substrate with a dielectric constant of 3.5 and a thickness of H1.

FIG. 3.

(a) Configuration and (b) MS of the original structure.

FIG. 3.

(a) Configuration and (b) MS of the original structure.

Close modal

The original MTS configuration is modeled and simulated by using CST Studio Suite. The conductor is set as a lossless perfect electrical conductor (PEC), the dielectric layer is set as a lossless substrate, and the multilayer solver is used.18,19 The first six modes of the configuration at a frequency of 5.5 GHz are calculated, as shown in Fig. 3(b). The significant and insignificant modes are differentiated by the mode significance (MS). When the MS is more than 0.707, the mode can be considered significant, and high-quality radiation can be obtained by introducing an appropriate excitation at a suitable location. In contrast, when the MS of the mode is less than 0.707, it is considered insignificant, indicating that the mode does not radiate well in the current system state. By analyzing the MS, the potential bandwidth can be preliminarily understood, which can be utilized to guide the design of the MTS in terms of structural configuration and performance enhancement.9 

Figure 4 illustrates the surface current densities and radiation patterns of the six modes calculated and plotted by the CMA. Generally, the mode's radiation patterns result from its current density distribution. The current of mode 1 is symmetrically distributed at the edge and corner patches and flows from the center to the periphery. The direction of the current and the radiation pattern are identical. It has the potential to develop into an omnidirectional radiation pattern since it is influenced by the electric field current, which likewise radiates outward. Modes 2 and 3 are a pair of orthogonal modes, which have a symmetric distribution of current densities across the diagonal outer patches with each other. These patterns cannot be omnidirectional due to their directional radiations. The current densities of modes 4 and 6 are distributed on the four diagonal patches and that of mode 5 is located at the four edge patches. A common feature is that the current is collected only on some of the patches on the periphery rather than symmetrically radiating from the center. Therefore, none of these modes have the potential to be an omnidirectional radiation pattern, except for mode 1, which will be screened out as the desired mode and analyzed to improve its performance.

FIG. 4.

Characteristic modal currents and radiation patterns of each mode for the original configuration at 5.5 GHz.

FIG. 4.

Characteristic modal currents and radiation patterns of each mode for the original configuration at 5.5 GHz.

Close modal

The top view of the radiation pattern of the desired omnidirectional radiation patterns should be a regular circle. The non-roundness (i.e., the difference between the maximum and the minimum values of the gain) should be less than 2 dB.20,21 There is a certain degree of deformation in the radiation pattern of mode 1 in the original MTS configuration. Suppose the structure is introduced directly, the final roundness performance will be inferior, and the inability to complete the intent and goal of omnidirectional radiation will not be accomplished. The mode current J1 is mainly located on the peripheral patches, with inconsistent distances from the diagonal and the edge patches to the center. These make the distribution of J1 asymmetric, which is the main reason for the distortion of the radiation pattern. Turn the middle patch circular and have the surrounding patches converge to the center. At this time, the arrangement of these patches becomes centrosymmetric, thus reducing the degree of non-roundness of the radiation pattern of the selected mode 1, as shown in Fig. 5.

FIG. 5.

(a) Configuration, (b) modal currents, and (c) radiation patterns of mode 1 for the MTS modified to be centrosymmetric.

FIG. 5.

(a) Configuration, (b) modal currents, and (c) radiation patterns of mode 1 for the MTS modified to be centrosymmetric.

Close modal

It should be noted that the simulated calculation of CMA is based on infinite substrate and ground. However, a finite-sized substrate will be applied when emulating and analyzing the performance after setting excitation. For the square outline, since the surrounding patches are not at the same distance from the edge of the finite-sized substrate and have inconsistent edge effects, the roundness of the radiation pattern is significantly affected, as depicted in Fig. 6(b). Therefore, when using an octagonal substrate shape instead of a quadrilateral one and each edge of the structure corresponds to the orientation of the internal patches, the entire MTS shape is a centrosymmetric pattern, which can maximize the roundness of the radiation pattern. It ultimately improves the MTS's capability and performance to receive EM waves in any orientation.

FIG. 6.

(a) Configuration of the excited MTS. Radiation patterns of the excited MTS of (b) the square substrate and (c) octagonal substrate.

FIG. 6.

(a) Configuration of the excited MTS. Radiation patterns of the excited MTS of (b) the square substrate and (c) octagonal substrate.

Close modal

In Sec. II B, mode 1 is identified as the MTS's primary mode, and the roundness performance is boosted. The MS of the designed MTS is obtained, as shown in Fig. 7, which is more significant than 0.707 from 4.3 to 5.9 and 7.4–10 GHz. However, the middle part of the frequency band is significantly smaller than the efficiently excited range, affecting the wideband performance of the mode. Meanwhile, although in the low-frequency part (shown at 5.5 GHz), the radiated pattern of the mode is omnidirectional with an ideal roundness performance, in the high-frequency part (shown at 8.5 GHz), J1 is mainly concentrated outside the peripheral patch. At the same time, the current direction is pointing from two sides of the patch to the center. The sidelobes are generated from this current density distribution, transforming the radiation pattern in this frequency band and deteriorating the roundness performance. Although the MS of the MTS is in the interval of easy excitation in the high-frequency bands, the radiation pattern is not the expected omnidirectional radiation pattern. There is no guarantee that the MTS will absorb EM waves with consistent performances in the desired frequency band and at all azimuths. Therefore, the following analysis and research are to ameliorate the radiation roundness performance of the high-frequency part and, at the same time, increase the MS of the MTS.

FIG. 7.

MS, modal currents, and radiation patterns of the centrosymmetric MTS at the frequency points.

FIG. 7.

MS, modal currents, and radiation patterns of the centrosymmetric MTS at the frequency points.

Close modal

In the high-frequency band, since J1 is allocated only on the outer side, the inner current is cluttered. Meanwhile, supposing that the mode of the MTS configuration is excited, a feed structure is necessary under each patch to integrate the EM energy using a power-combining network. The feed structure's complexity will be increased, and it is not conducive to the system's compactness. The operating frequency and pattern can be changed by varying the size and modifying different classes of the patches. The size of the outer patches is decreased to lessen the resonance, while the center is increased to concentrate the current. The sidelobes of the radiation pattern are gradually suppressed until eliminated, and the desired omnidirectional radiation pattern can be achieved. As shown in Fig. 8, a parametric analysis of the center and peripheral patch size is carried out. Enlarging the center patch, while decreasing the peripheral patches can obviously increase the MS of mode 1. Meanwhile, since the patch size is modified, the MS slightly shifts toward high frequencies. Ultimately, the parameter combination of L1 = 14 mm and L2 = 6.8 mm is determined. Currently, the MS has expanded to meet the system's requirements.

FIG. 8.

(a) The configuration and (b) MS of the MTS at different patch sizes.

FIG. 8.

(a) The configuration and (b) MS of the MTS at different patch sizes.

Close modal

In order to effectually excite the mode, the MS must be more than 0.707, which means that at roughly 7.5 GHz, a performance promotion is critical. The J1 at this band is computed and plotted in Fig. 9. As expected, it is mainly distributed in the center patch. However, the current direction of peripheral patches, which differs in the center, opposes each other and affects the MS in this band. A slot is cut in the peripheral patches, separating the patches into two parts so that the current is artificially cut off. Consequently, the strength of the current in the edge patches is reduced, which effectively improves the MS at 7.5 GHz by attenuating the resonance strength that are in opposition to one another with the current.

FIG. 9.

(a) The configuration of the MTS with the slot: a comparison of modal currents with and without the slot at 8 GHz. (b) A comparison of the MS of the MTS with and without the slot.

FIG. 9.

(a) The configuration of the MTS with the slot: a comparison of modal currents with and without the slot at 8 GHz. (b) A comparison of the MS of the MTS with and without the slot.

Close modal

As exhibited in Fig. 9(b), an MS of the ultimate MTS is calculated. It indicates that this MTS-L configuration has a broad potential bandwidth and will capture EM energy over a wide range of frequency bands if it is appropriately excited. Meanwhile, the surface current and radiation patterns of the proposed structure are shown in Fig. 10, where J1 is mainly distributed in the center patch and the radiation direction is center to the periphery. The currents in the peripheral patches are attenuated and no longer dominate in J1, weakening the effect on the radiation performance. In addition, the radiation pattern maintains an outstanding roundness performance over various frequency bands.

FIG. 10.

Characteristic modal currents and radiation patterns of mode 1 for the proposed MTS.

FIG. 10.

Characteristic modal currents and radiation patterns of mode 1 for the proposed MTS.

Close modal

Two structures are commonly constructed to excite a mode, as depicted in Fig. 11(a). In the first structure, a slot is cut in the ground layer and must be perpendicular to the direction of the mode currents. Then, the energy is exported by the feed structure placed in the bottom layer. Because J1 is mainly distributed in the center patch and the current direction is outward, four symmetric slots will be etched on the ground plane below the four corners of the center patch so that the modes at the corresponding positions of these slots can be efficiently excited. When this structure is introduced in the proposed MTS-L antenna, as shown in Fig. 11(b), a four-in-one power-combining network must be installed at the locations where energy is fed out. In addition, more ground slots are required to excite this mode of centralized current dispersion more effectively. This implies the need for a more complex all-in-one power-combining network, which increases the structural complexity.

FIG. 11.

(a) Two structures commonly used to excite the mode. The configuration of loading (b) the slot and (c) the probe of the proposed MTS.

FIG. 11.

(a) Two structures commonly used to excite the mode. The configuration of loading (b) the slot and (c) the probe of the proposed MTS.

Close modal

An alternative excitation structure is to place a probe at the start or end of the mode currents to feed the energy out. Because the mode current J1 of the selected Mode1 is outward from the center, a single probe construction located in the center is highly suitable here, which is a sounder way to achieve a compact structure without involving any additional structures, as shown in Fig. 11(c). At the same time, this excitation structure located at the center of the antenna can only excite the corresponding characteristic mode with the current direction from the center to the peripheries, but not others with other current directions. It is worth noting that the shape of the substrate here corresponds to that of the definitive fabricated one, which is a regular octagonal shape.

Once the mode is excited, the MTS-L antenna is ready to receive the EM energy. Then, a rectifier circuit that transforms the ac energy to dc needs to be designed as a load for the system. Because the EM energy is a weak signal, the efficiency of the rectifier circuit is mainly affected by the diode's chip built-in barrier electric field and turn-on voltage. In the recent literature, voltage-doubling rectifier circuits are more suitable for rectifying EM energy.22,23 Compared with single-diode rectification, the charge pump structure can effectively increase the output voltage, theoretically increasing the rectification efficiency and reducing the input power–level requirement. As depicted in Fig. 12(a), a wideband rectifier circuit is conceived. The basic construction is a voltage-doubling rectifier circuit consisting of two SMS7630 Schottky diodes, two capacitors, and a load. Because the impedance of the rectifier circuit is not a constant value and cannot be conjugated and matched with the impedance of the MTS-L antenna, a cross-shaped impedance-matching network is designed between them. This cross-shaped impedance-matching circuit has a wide frequency response range and is simple to adjust, making it suitable for this system. The EM energy received by the antenna needs to be transferred as efficiently as possible to the rectifier circuit, thus enhancing the overall system's efficiency.

FIG. 12.

(a) The proposed rectifier structure (all dimensions are in millimeters). (b) Rectification efficiency vs incident power and load resistance.

FIG. 12.

(a) The proposed rectifier structure (all dimensions are in millimeters). (b) Rectification efficiency vs incident power and load resistance.

Close modal

Figures 12(b) and 12(c) display the proposed rectifier circuit. It is simulated and analyzed using an Agilent electromagnetic simulation software Advanced Design System (ADS). The circuit can efficiently convert the input EM energy between −15 and 5 dBm. At the input power level of −15 dBm, it can maintain a rectification efficiency of about 30% and meet the EM EH requirement. There is a slight decrease in efficiency at the 5 dBm input power level as the output voltage has reached the breakdown voltage of the diode chip, which also fulfills the WPT requirements for low-power devices. With the features of the selected Schottky diode, the ideal input power level is optimized to 0 dBm when the efficiency is the highest.

Also, the circuit can operate at loads between 500 and 3000 Ω, and the load level is optimized to 1500 Ω for optimal operation conditions concerning the features of the rectifier circuit. The proposed rectifier circuit maintains a high system efficiency while varying power levels and loads, demonstrating functional applicability and practicality.

CST software has been used to simulate the proposed MTS-L rectenna, and it is plotted in Fig. 13 at three frequency points. There is only one major lobe and no sidelobe in the radiation pattern, indicating that the radiation has an excellent omnidirectional radiation performance. The outer contour of the mainlobe is subcircular, illustrating that the proposed MTS-L rectenna can capture the obliquely incident EM energy effectively.

FIG. 13.

Three-dimensional view of the radiation pattern of the proposed MTS-L rectenna at 5, 6.5, and 8 GHz.

FIG. 13.

Three-dimensional view of the radiation pattern of the proposed MTS-L rectenna at 5, 6.5, and 8 GHz.

Close modal
The proposed MTS-L rectenna system has been fabricated and measured. Figure 14(a) exhibits the measurement environment and the layout. A feed line is soldered on the back of the sample and connected to the VNA to obtain the required data. The gain of the sample can be calculated and obtained by way of Eq. (1). Pr refers to the received power of the sample, Pt is the transmitted power, Gt is the gain of the transmitting antenna, and R is the distance between them,
(1)
FIG. 14.

(a) The experimental platform and a fabricated sample. Inset: a layout of the manufactured sample. (b) Simulated and measured S11 and gain vs frequency of the proposed MTS-L rectenna.

FIG. 14.

(a) The experimental platform and a fabricated sample. Inset: a layout of the manufactured sample. (b) Simulated and measured S11 and gain vs frequency of the proposed MTS-L rectenna.

Close modal

The measured S11 and gain of the proposed rectenna are shown in Fig. 14(b). The system operates in a frequency band of 4.6–9.6 GHz with an FBW of 70.4%. There are some deviations between the simulated and the measured results, which may be caused by the sample fabrication and soldering accuracy. The proposed rectenna can cover the typical indoor WLAN bands (5.2–5.8 and 5.9–7.3 GHz) and the UWB bands (6–9 GHz). In the operating frequency band, the proposed rectenna has a gain of 2.3–6.8 dBi.

The radiation pattern of the system is measured. The chosen radiation pattern has only a major lobe and no sidelobes, causing the system to absorb energy at wide incidence angles with elevation planes and azimuth φ = 0°, as shown in Fig. 15(a). Figure 15(b) depicts the radiation gain of the system under the azimuth plane. Nearly perfect circles are visible at three frequency points. Although the radiation performance deteriorates slightly in the high-frequency part (at 8 GHz) in the three-dimensional view, the non-roundness is less than 2 dB, which explains that the system is almost unaffected by the EM wave's direction. This indicates that mode 1 has omnidirectional characteristics and is effectively excited.

FIG. 15.

Simulated and measured normalized radiation patterns of the proposed rectenna. Results in the (a) elevation planes of φ = 0° and (b) azimuth plane of θ = 30°.

FIG. 15.

Simulated and measured normalized radiation patterns of the proposed rectenna. Results in the (a) elevation planes of φ = 0° and (b) azimuth plane of θ = 30°.

Close modal

Eventually, the system's overall efficiency is measured in three directions, as shown in Fig. 16. Here, based on the feature of the rectifier circuit, the load resistance is 1500 Ω, and the power received by the rectenna is 0 dBm to maximize rectification efficiency. The measured peak efficiency of the system is 52.2%. The system's performances remain almost consistent at different azimuths, indicating that it can efficiently absorb EM waves at any orientation.

FIG. 16.

Measured results of system efficiency at different azimuths.

FIG. 16.

Measured results of system efficiency at different azimuths.

Close modal

A comparison of existing works on the MTS-L rectenna system is shown in Table I. Compared with the related presents, the proposed system can capture EM energy over a broader range of frequency bands. It has improved omnidirectionality as compared to directional systems with higher gain. Therefore, the system efficiency is almost unaffected by the azimuths of the EM wave, which allows it to absorb EM energy in any orientation. The system can be commonly applied for indoor localization and better satisfy indoor EM EH and transmission demand. However, the proposed system has some limitations; for example, system efficiency and input power levels need to be met for practical applications.

TABLE I.

Comparison of the proposed system with related works.

ReferenceOperating frequency (GHz)Operating FBW (each band) (%)Azimuth insensitivityMaximum system efficiencySubstrate size W × L × H (λ0)Dielectric substrate layers
11  2.45 7.9 No 76.8% @ 0 dBm 0.98 × 0.2 × 0.04 
24  2.45 7.6 Yes 71.1% @ 5 dBm 1.24 × 1.24 × 0.02 
25  1.8, 2.45 7.8, 4 No 73.0% @ 3 dBm 0.54 × 0.54 × 0.17 
26  2.4, 5.2, 5.8 0.8, 0.7, 1.1 No 38.3% @ 7 dBm 1.4 × 1.2 × 0.02 
27  1.8–2.5 32.6 No 10.0% @ −30 dBm 0.34 × 0.28 × 0.003 
28  4.8–6.1 23.9 No 71.6% @ 10 dBm 0.64 × 0.64 × 0.08 
29  5.4–8.4 42.3 No 66.6% @ 11 dBm 1.16 × 0.96 × 0.03 
12  5.32–6.66 22.4 Yes 74.5% @ 10 dBm 1.9 × 1.7 × 0.05 
This work 4.6–9.6 70.4 Yes 52.2% @ 0 dBm 0.96 × 0.96 × 0.06 
ReferenceOperating frequency (GHz)Operating FBW (each band) (%)Azimuth insensitivityMaximum system efficiencySubstrate size W × L × H (λ0)Dielectric substrate layers
11  2.45 7.9 No 76.8% @ 0 dBm 0.98 × 0.2 × 0.04 
24  2.45 7.6 Yes 71.1% @ 5 dBm 1.24 × 1.24 × 0.02 
25  1.8, 2.45 7.8, 4 No 73.0% @ 3 dBm 0.54 × 0.54 × 0.17 
26  2.4, 5.2, 5.8 0.8, 0.7, 1.1 No 38.3% @ 7 dBm 1.4 × 1.2 × 0.02 
27  1.8–2.5 32.6 No 10.0% @ −30 dBm 0.34 × 0.28 × 0.003 
28  4.8–6.1 23.9 No 71.6% @ 10 dBm 0.64 × 0.64 × 0.08 
29  5.4–8.4 42.3 No 66.6% @ 11 dBm 1.16 × 0.96 × 0.03 
12  5.32–6.66 22.4 Yes 74.5% @ 10 dBm 1.9 × 1.7 × 0.05 
This work 4.6–9.6 70.4 Yes 52.2% @ 0 dBm 0.96 × 0.96 × 0.06 

In this paper, a wideband MTS-L rectenna system is proposed with azimuth-insensitive performance and its property is analyzed by using the CM theory. The radiation roundness is ameliorated by exploring the arrangement of patches and the shape of the MTS substrate. The potential bandwidth is augmented by considering the affecting factors and artificially designing the surface current distribution. The measured results indicate that the system has an operating range of 4.6–9.6GHz with a peak system efficiency of 52.2%. It covers both 5-GHz WLAN bands and UWB bands used for indoor localization without being affected by frequency shifts and manufacturing errors. Moreover, the system's radiations under the azimuth plane maintain a near-perfect circle in the operating band with consistent characteristics, and it can receive EM energy at any orientation. The wideband and azimuth insensitivity MTS-L rectenna system can be potentially applied to WPT and indoor EH, which are EM-absorbing scenarios.

This work was supported in part by the National Natural Science Foundation of China (NNSFC) (No. 62201619), in part by the State Key Laboratory of Millimeter Waves (No. K202409), and in part by the High Performance Computing Center of Central South University. The authors would like to thank Professor Gaosheng Li from Hunan University Research Center for Antennas and EMC for providing the measurement platform.

The authors have no conflicts to disclose.

Lianwen Deng: Funding acquisition (equal); Project administration (equal); Visualization (equal). Zhe-Jia He: Data curation (equal); Formal analysis (equal); Writing – original draft (equal); Writing – review & editing (equal). Shengxiang Huang: Supervision (equal); Visualization (equal). Lei-Lei Qiu: Funding acquisition (equal); Supervision (equal); Visualization (equal); Writing – review & editing (equal). Lei Zhu: Supervision (equal); Writing – review & editing (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.

1.
H.
Xiong
,
X.
Ma
,
B.-X.
Wang
, and
H.
Zhang
, “
Design and analysis of an electromagnetic energy conversion device
,”
Sens. Actuators A
366
,
114972
(
2024
).
2.
L.
Chen
,
C.
Li
, and
J.
Fang
, “
Design of a multi-direction piezoelectric and electromagnetic hybrid energy harvester used for ocean wave energy harvesting
,”
Rev. Sci. Instrum.
94
(
12
),
125005
(
2023
).
3.
S.
Roy
,
A. N. M. W.
Azad
,
S.
Baidya
,
M. K.
Alam
, and
F.
Khan
, “
Powering solutions for biomedical sensors and implants inside the human body: A comprehensive review on energy harvesting units, energy storage, and wireless power transfer techniques
,”
IEEE Trans. Power Electron.
37
(
10
),
12237
12263
(
2022
).
4.
H.
Xiong
,
X.
Ma
,
H.
Liu
,
D.
Xiao
, and
H.
Zhang
, “
Research on electromagnetic energy absorption and conversion device with four-ring multi-resistance structure
,”
Appl. Phys. Lett.
123
(
15
),
153902
(
2023
).
5.
A. K.
Baghel
,
S. S.
Kulkarni
, and
S. K.
Nayak
, “
Linear-to-cross-polarization transmission converter using ultrathin and smaller periodicity metasurface
,”
IEEE Antennas Wireless Propag. Lett.
18
(
7
),
1433
1437
(
2019
).
6.
S.
Pearson
and
S. V.
Hum
, “
Optimization of electromagnetic metasurface parameters satisfying far-field criteria
,”
IEEE Trans. Antennas Propag.
70
(
5
),
3477
3488
(
2022
).
7.
J.
Wu
,
J.
Li
,
C.
Zhang
,
Y.
Liu
,
L.
Xu
et al, “
Frequency tunable coherent perfect absorption and lasing in radio-frequency system for ultrahigh-sensitive sensing
,”
Appl. Phys. Lett.
123
(
16
),
164102
(
2023
).
8.
J.
Cai
,
L.
Li
,
Z.
Chen
,
J.
Zhang
, and
Z.-L.
Hou
, “
High performance selective light absorber based on nickel nanopillar array for photothermal conversion
,”
J. Appl. Phys.
134
(
23
),
233104
(
2023
).
9.
E.
Liujia
,
Z.
Liu
,
J.
Zhang
,
Z.
Xu
,
Z.
Yuan
et al, “
Realization of an ultra-thin absorber with fragmented magnetic structure at L-, S-, and partial C-bands
,”
J. Appl. Phys.
134
(
22
),
223105
(
2023
).
10.
Q.
Yang
,
H.
Xiong
,
J.-H.
Deng
,
B.-X.
Wang
,
W.-X.
Peng
et al, “
Polarization-insensitive composite gradient-index metasurface array for microwave power reception
,”
Appl. Phys. Lett.
122
(
25
),
253901
(
2023
).
11.
K.
Lee
and
S. K.
Hong
, “
Rectifying metasurface with high efficiency at low power for 2.45 GHz band
,”
IEEE Antennas Wireless Propag. Lett.
19
(
12
),
2216
2220
(
2020
).
12.
Z.-J.
He
,
L.
Deng
,
P.
Zhang
,
Y.
Liu
,
T.
Yan
et al, “
Wideband high-efficiency and simple-structured rectifying metasurface
,”
IEEE Trans. Antennas Propag.
71
(
7
),
6202
6207
(
2023
).
13.
R.
Garbacz
and
R.
Turpin
, “
A generalized expansion for radiated and scattered fields
,”
IEEE Trans. Antennas Propag.
19
(
3
),
348
358
(
1971
).
14.
A.
Malekara
,
A.
Khalilzadegan
,
C.
Ghobadi
, and
J.
Nourinia
, “
Wide-angle, dual-polarized frequency selective rasorber based on the electric field coupled resonator using characteristic mode analysis
,”
J. Appl. Phys.
133
(
16
),
164504
(
2023
).
15.
C.
Ni
,
X.
Xie
, and
L.
Zhang
, “
Research on the element structure and surface current distribution of metasurface based on characteristic mode analysis
,”
J. Appl. Phys.
134
(
18
),
183104
(
2023
).
16.
D.
Zha
,
J.
Dong
,
K.
Si
,
Z.
Cao
,
R.
Li
et al, “
Characteristic mode analysis of resistor-loaded frequency selective surfaces: Theoretical research and experimental verification
,”
J. Appl. Phys.
130
(
5
),
053101
(
2021
).
17.
T.
Li
and
Z. N.
Chen
, “
Shared-surface dual-band antenna for 5G applications
,”
IEEE Trans. Antennas Propag.
68
(
2
),
1128
1133
(
2020
).
18.
L.
Qiu
and
G.
Xiao
, “
A broadband metasurface antenna array with ultrawideband RCS reduction
,”
IEEE Trans. Antennas Propag.
70
(
9
),
8620
8625
(
2022
).
19.
W.
Li
,
Y. M.
Wang
,
Y.
Hei
,
B.
Li
, and
X.
Shi
, “
A compact low-profile reconfigurable metasurface antenna with polarization and pattern diversities
,”
IEEE Antennas Wireless Propag. Lett.
20
(
7
),
1170
1174
(
2021
).
20.
X.
Yang
,
Y.
Liu
, and
S.-X.
Gong
, “
Design of a wideband omnidirectional antenna with characteristic mode analysis
,”
IEEE Antennas Wireless Propag. Lett.
17
(
6
),
993
997
(
2018
).
21.
H.
Sheng
and
Z. N.
Chen
, “
Improving radiation pattern roundness of a monopole antenna placed off-center above a circular ground plane using characteristic mode analysis
,”
IEEE Trans. Antennas Propag.
69
(
2
),
1135
1139
(
2021
).
22.
J.
Kimionis
,
A.
Collado
,
M. M.
Tentzeris
, and
A.
Georgiadis
, “
Octave and decade printed UWB rectifiers based on nonuniform transmission lines for energy harvesting
,”
IEEE Trans. Microw. Theory Technol.
65
(
11
),
4326
4334
(
2017
).
23.
W.
Liu
,
K.
Huang
,
T.
Wang
,
J.
Hou
, and
Z.
Zhang
, “
Broadband high-efficiency RF rectifier with a cross-shaped match stub of two one-eighth-wavelength transmission lines
,”
IEEE Microw. Wireless Compon. Lett.
31
(
10
),
1170
1173
(
2021
).
24.
H.-Y.
Wang
,
F.
Cheng
, and
C.
Gu
, “
A single-layer efficient polarization-insensitive electromagnetic rectifying metasurface for wireless power transfer
,”
Appl. Phys. Lett.
122
(
26
),
261703
(
2023
).
25.
H.
Takeshita
,
D.
Nita
,
Y.
Cheng
,
A. A.
Fathnan
, and
H.
Wakatsuchi
, “
Dual-band waveform-selective metasurfaces for reflection suppression
,”
Appl. Phys. Lett.
123
(
19
),
191703
(
2023
).
26.
Y.
Wei
,
J.
Duan
,
H.
Jing
,
Z.
Lyu
,
J.
Hao
et al, “
A multiband, polarization-controlled metasurface absorber for electromagnetic energy harvesting and wireless power transfer
,”
IEEE Trans. Microw. Theory Technol.
70
(
5
),
2861
2871
(
2022
).
27.
J.
Zhu
,
Z.
Hu
,
C.
Song
,
N.
Yi
,
Z.
Yu
et al, “
Stretchable wideband dipole antennas and rectennas for RF energy harvesting
,”
Mater. Today Phys.
18
,
100377
(
2021
).
28.
Y. M.
Afify
,
A.
Allam
,
G. M.
Elashry
,
M. M.
Mansour
,
A.
Tanemasa
et al, “
Compact high-efficiency broadband/multi-band stacked back-to-back high-gain rectenna based on fourth-order bandpass filter for green environment applications
,”
AEU Int. J. Electron. Commun.
170
,
154816
(
2023
).
29.
D.
Surender
,
M.
Ahsan Halimi
,
T.
Khan
,
F. A.
Talukdar
,
A. A.
Kishk
et al, “
Semi-annular-ring slots loading for broadband circularly polarized DR-rectenna for RF energy harvesting in smart city environment
,”
AEU Int. J. Electron. Commun.
147
,
154143
(
2022
).