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Abstract
Metasurface is a 2D metamaterial which manipulates electromagnetic wavefront by carefully designing the transmissive or reflective responses of the planar subwavelength structures. Despite various emerging new functionalities, one of the limitations of metasurfaces in practical applications is the lack of control accuracy of its local amplitude and phase responses. This is in part caused by the discrepancy between the periodic EM simulated responses of unit cells and the actual non-periodic metasurfaces when functionality-determined amplitude and phase gradients are introduced. Under such conditions, the focusing capabilities of metasurfaces can be greatly affected. In this paper, we address this problem by introducing a slotted ground plane metasurface design which reduces the above-mentioned discrepancy by limiting the mutual coupling effects of a unit cell with its surrounding elements. An offset-fed near-field focusing reflective metasurface is designed and fabricated to verify the performance of the proposed design. Both the EM simulated and measurement results demonstrate the advantages of the proposed design in terms of sidelobe level and transfer efficiency.
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1. Introduction
Metasurfaces are capable of modulating the amplitude, phase, polarization and wavefront of electromagnetic waves [1–8]. Due to the advantages of low profile, light weight and simple feed network, metasurfaces have attracted great attention and many new devices based on metasurfaces have been proposed, including polarization converters [9,10], holographic imaging [11], vortex beam generation [12,13], high gain antennas [14–16].
While many of the existing studies focus on the far-field properties, near-field focusing (NFF) can increase the electromagnetic power density in a diffraction-limited spot close to the aperture and they have been actively applied in wireless remote identification, microwave hyperthermia, microwave imaging and wireless power transmission (WPT) in recent years [17–19]. Among them, WPT has been commercialized in electronic products as well as vehicle charging. In [20], an optically transparent reflective metasurface based on indium tin oxide (ITO) material is designed for WPT, whose transfer efficiency is about 63% (if all the metal materials of the design are replaced with good conductor materials). [21] proposes a metasurface for WPT with multi-focus characteristics and high wireless power transfer efficiency of 70%. In [22], a dual-polarization and multi-focus NFF reflective metasurface is designed for WPT at 10 GHz. The low profile of the metasurface makes the WPT system applicable to more scenarios.
Similar to array-based NFF systems where mutual coupling effects must be carefully considered [23], the performances of metasurface-based NFF systems are also greatly affected by the mutual coupling among its unit cells. The reflective metasurfaces control the phase of the local reflection coefficient by discretizing the reflection surface [24,25], which is usually obtained through the local periodic (LP) approximation [25,26]. LP assumes the unit cells at the position are placed in a periodic array composed of the same elements, and the mutual coupling among identical unit cells is assumed, whereas the actual reflective metasurfaces are usually composed of different surrounding elements. To illustrate this problem, simulations are performed based on split ring (or C-shaped) metasurface [16,27–29], which is capable of both amplitude and phase controls. Two 3-by-3 arrays of unit cells are simulated with the same central element but different surrounding conditions, and the results are shown in Fig. 1. Figure 1(a) shows the scenario under the LP approximation (with identical elements), and Fig. 1(b) is an example of an actual reflective metasurface where the central element is surrounded by different element configurations. Figure 1(c)-(d) presents the current density distribution on the ground plane of the central element obtained by EM simulations of the models in Fig. 1(a) and (b) under unit cell boundary conditions, respectively. It can be seen that there is a prominent difference in the current density distributions when the same unit cell is surrounded by different elements. Another example is shown in Fig. 2, where a 0.6 m${\times}$0.6 m wide reflective metasurface is simulated. Within the metasurface, phase gradients along the x-axis is introduced to direct the beam towards 20° from boresight, while no phase gradients along the y-axis. Thus, the metasurface is periodic in one dimension and quasi-periodic in the other. The plane wave excitation is used to illuminate the metasurface at 10 GHz, and the beam patterns along both planes from full-wave EM simulations are compared with theoretical curves where isotropic elements are assumed. It is found that there is a good agreement between the theoretical and simulated results in the periodic dimension while significant discrepancies appear in the beam pattern in the quasi-periodic dimension. Both examples in Fig. 1 and Fig. 2 shows an obvious degradation of control accuracy under the conventional LP assumptions.
Fig. 1. Comparison of two 3-by-3 array of split rings with the same center element but different surrounding element conditions. (a) 3-by-3 array with identical surrounding elements. (b) 3-by-3 array with different surrounding elements. (c) The current density distribution on the ground plane of the center element in model (a). (d) The current density distribution on the ground plane of the center element in model (b).
Fig. 2. Simulation of a 0.6${\times}$0.6 m wide metasurface with phase gradients introduced along one axis (quasi-periodic) but no phase gradient along the other axis (periodic). (a) The simulated metasurface model. (b) Comparison between the full-wave EM simulated beam pattern with theoretical calculations with isotropic elements along the quasi-periodic axis (azimuth cut). (c) Comparison between the full-wave EM simulated beam pattern with theoretical calculations with isotropic elements along the periodic axis (elevation cut).
Several techniques to model the mutual coupling in practical reflective metasurfaces are proposed. The “surrounded-element” approach [30] simulates each element and its closest neighboring elements simultaneously. To get better prediction results, the simulation needs to include different variations of neighboring units. The extended LP technique [31] combines the “surrounded-element” method and the Floquet approach and the accuracy of beam prediction is improved to a certain extent. In [32], a reflective metasurface that is periodic in one dimension and aperiodic in the other is designed. The method uses one-dimension periodicity to consider the coupling between elements, and studies the elements with periodic boundary on sides only. In addition to attempting more accurate predictions, some scholars have proposed the design of elements that are not sensitive to mutual coupling effects. In [33] and [34], the uniformity of the elements is ensured by reducing the size variation of the elements during phase control, which ultimately achieves a more accurate prediction of the coupling between the elements. It is shown in [35] that the addition of an array lattice or the use of a metal cavity can reduce the mutual coupling, but the effect of the metal cavity is less effective than that of the method of increasing the array lattice. Metal vias loading is a common approach to improve isolation among elements. However, metal vias can cause fluctuations to the reflection amplitudes and nonlinear phase curves over the frequency band. Also, the sub-wavelength dimensions of meta-atoms makes it challenging to manufacture large amount of metal vias on the complete metasurfaces with thousands of elements, and can be prone to process errors, such as position deviations, inaccurate size, uneven coating, and resulting less structure stability of the metasurfaces, etc.
This paper proposes a new low-coupling design for more accurate control of amplitude and phase responses of elements within the complete metasurface. Firstly, a broadband element based on split ring is designed. Then, a method to reduce mutual coupling by cutting slots on the ground plane is presented and analyzed. Finally, near-filed focusing reflective metasurfaces with an aperture diameter of 19 times the wavelength of the center frequency is designed, simulated and measured. Experimental results are compared with simulated ones to demonstrate the effectiveness of the proposed design method.
2. Design and method
2.1 Low-coupling split ring element design
The proposed element design consists of a phased structure, two layers of dielectric substrate and a metal ground plane with surrounding slots. The phased structure adopts a split ring structure (as shown in Fig. 3), which can achieve controls of both phase and amplitude responses separately [16,27–29]. In this specific example, the split ring only involves phase control, and the orientation angle β of the split ring is fixed at 45°. Two layers of dielectric substrate are introduced to reduce the coupling between the split ring and the metal ground and increase the bandwidth of the element. In this design, the two dielectric substrates are Rogers RO4350B (εr = 3.66, tanδ = 0.0037) with a thickness of 0.254 mm and FR4 (εr = 4.3, tanδ = 0.0025) with a thickness of 3 mm, respectively. In order to limit the coupling among the elements, the metal ground plane of the element is slotted on all sides, as shown in Fig. 3(c). The selection of slot width w_slot should not be too large, it is recommended that the width of the remaining patch after the ground cut is not less than half of the wavelength at the lowest frequency in the medium. For the split ring with the orientation angle of 45°, its mirror element (as shown in Fig. 3(d)) has the same polarization properties as the original element, and the phase difference is 180°, so the two can jointly achieve 360° phase control [16]. The designed element is simulated and optimized by the frequency domain solver of CST Microwave Studio. After optimization, an element with operational bandwidth from 9 GHz to 14 GHz is achieved, whose parameters are summarized in Table 1.
Fig. 3. Geometry of split ring. (a) Top view. (b) Side view. (c) Back view. (d) Top view of the mirror element with respect to x-axis symmetry of (a).
Table 1. Parameters of designed element
Figure 4(a) shows the amplitude and phase behaviors of the designed element and its mirror element at 10 GHz. The mirror element has the same amplitude as the original element and the two phase-curves have the same shape, but differ by 180° numerically. The gap size α of the split ring varies from 28° to 198°, the original element and the mirror element can jointly achieve a 360° phase coverage. The broadband characteristics of the designed element are shown in Fig. 4(b)-(c). Frequencies range from 9 GHz to 14 GHz, the reflection amplitude keeps within -3.5 dB (with the exception of a single gap size at 14 GHz) and the reflection phase curves are linear and parallel to each other. The amplitude and phase controls of the proposed design are ideal for manipulation of electromagnetic wavefronts.
Fig. 4. (a) Reflection amplitude and phase of the original element and the mirror element at normal incidence at 10 GHz. (b),(c) The broadband characteristic of the proposed ground-slotted elements. (b) Reflection amplitudes. (c) Reflection phases.
The reflection characteristics of the elements at oblique incidence are studied, as shown in Fig. 5. It can be seen that the reflection responses of the elements are basically consistent at the normal incidence angle and the oblique incidence angles less than 20°, except for the slight decrease of the reflection amplitude at high frequency and the overall upward and downward shifts in the phase curve. The simulation results illustrate that the designed elements have relatively stable performance at oblique incidence, and therefore, it is acceptable to design the reflective metasurfaces based on the element characteristics at normal incidence.
Fig. 5. Simulated reflection amplitudes and phases at different oblique incidence angles at 10 GHz. (a) Reflection amplitudes. (b) Reflection phases.
2.2 Low-coupling analysis
In order to demonstrate the low-coupling characteristics, the same 3-by-3 array as in Fig. 1 is simulated based on the designed split ring element with slotted ground plane. The gap sizes of all split rings are consistent with those of the split rings in Fig. 1, and the specific gap size α values and models are given in Fig. 6(a)-(b) and Fig. 6(c)-(d), respectively. The EM simulation results of current distributions are shown in Fig. 6(e)-(f). It can be seen that although the current distribution changes after the slot is introduced, the differences in the current density distribution on the ground plane of the central elements when the same element are surrounded by identical and different elements decreases significantly. This indicates that the behavior of the designed elements can be more consistent when functionality-determined amplitude and phase patterns are introduced.
Fig. 6. Comparison of two 3-by-3 arrays of split rings with the same center element but different surrounding elements conditions. (a) The gap sizes of 3-by-3 array with identical surrounding elements. (b) The gap sizes of 3-by-3 array with different surrounding elements. (c) The model of 3-by-3 array with identical surrounding elements. (d) The model of 3-by-3 array with different surrounding elements. (e) The current density distribution on the ground plane of the center element in model (c) (at normal incidence). (f) The current density distribution on the ground plane of the center element in model (d) (at normal incidence).
In practical metasurfaces, the difference between the central element and its neighbors can vary in many different configurations. In order to further verify the effectiveness of the proposed method, based on the element configurations in Fig. 6(b), a set of simulations in which the gap size of the central element remains unchanged and the gap sizes of the surrounding elements increase at 10° intervals are performed. Then the structural similarity index measure (SSIM) [36] of the ground plane current density distribution of the central element surrounded by identical and different elements are calculated respectively, and the results are shown in Fig. 7(a). It can be seen that with the change of the gap sizes of the surrounding elements, the SSIM under slotted ground plane are always above 0.65, and the maximum can reach 0.95, which is 0.3-0.47 higher than the SSIM under uniform ground plane. A larger value of SSIM means that the more similar the ground plane current density distribution of the central element is when surrounded by identical and different elements.
Fig. 7. The SSIM of the current density distribution on the ground plane of the center element when the center element is surrounded with identical and different elements (at normal incidence). (a) Based on the model in Fig. 6(b), the central element remains unchanged and gap sizes of the surrounding elements increase at 10° intervals. (b) The gap size of the central element remains 100°, and the gap sizes of the surrounding eight identical elements change from 20° to 220°.
Figure 7(b) further demonstrates the variation of SSIM of current density distribution on the ground plane of the central element with the gap sizes of the surrounding elements. In this set of simulations, the gap size of the central element is 100°, and the eight surrounding elements are identical. It can be found that when the gap sizes of the surrounding elements are equal to that of the central element, which is 100°, the SSIM under both the uniform ground plane and the slotted ground plane is 1. When the surrounding elements are different from the central element, the SSIM under the uniform ground plane degrades significantly to around 0.3, while the SSIM under slotted ground plane is much more consistent under different conditions.
2.3 Effect of the slotted ground on the split ring element
Figure 8 shows the variation of the transmission power, reflection amplitude and reflection phase of the element with the width of the slot. It can be seen from Fig. 8(a) that when w_slot is zero, the transmission power of the element is 0, and with the increase of slot width, the transmission power of the element gradually increases. Figure 8(b) shows the reflection amplitude decreases with the increase of slot width, especially at low edge frequency. The reflection phase of the element is always linear in the entire frequency band under different slot widths, as shown in the Fig. 8(c).
Fig. 8. Influence of different slot widths (w_slot) on element characteristics. (a) Transmission power. (b) Reflection amplitudes. (c) Reflection phases.
It can also be seen from Fig. 8(b) that the working frequency band of the element with slotted ground plane moves to higher frequency. This behavior can be explained by the equivalent circuit model. The slot on the ground plane disturbs the field and current distribution on the ground plane. This disturbance changes characteristics of a structure such as line capacitance and inductance [37,38]. Figure 9 shows the equivalent circuit model obtained according to the electric field and surface current distribution on elements. The region where the electric field is concentrated is equivalent to the capacitor, and the region where the surface current is concentrated is equivalent to the inductor [39]. Thus, the split ring elements can be equivalent to a series of capacitors and inductors while the ground without slot can be equivalent to inductance because there is only surface current on it. As for the slotted ground, the gap of the ground plane is equivalent to capacitance, and the patch is equivalent to inductance. The split ring and the ground together form a series loop due to the coupling between the split ring and the metal ground, which is very small through the medium layer thicken and will not be considered here. When the ground is not slotted, the resonant frequency of the element f1 can be expressed as
while the resonant frequency of ground-slotted element f2 be written as where Cc is the total capacitance in seriesFig. 9. Equivalent circuit model to analyze the effect of slotted ground plane on elements. (a) Split ring. (b) Ground without slot. (c) Ground with slot.
Advanced Design System (ADS) circuit simulation software is used to fit the amplitude and phase responses of the equivalent circuit model, and the parameters in Fig. 9 is C1 = 3.44 pF, C2 = 1.13 pF, L1 = 18.92 nH, L2 = 16.2 nH, and L3 = 16.25 nH. Substituting these values into Eqs. (1)-(3), f1 is about 1.4 GHz, and f2 is about 2.9 GHz, which means that the resonant frequency of the element with slotted ground plane moves towards high frequency.
3. Simulation and measurement
3.1 Reflective metasurface design and simulation
A circular metasurface with a diameter of 575 mm (19 times the wavelength of 10 GHz) is designed to focus the electromagnetic energy at a point 600 mm in front of the center of the aperture, with a total number of 3613 elements. The linearly polarized horn antenna operating from 6 GHz to 14 GHz is chosen as the feed source. To avoid aperture blockage, offset feed is selected. After optimization and adjustment, the tilt angle (the angle between the metasurface plane and the positive direction of the z-axis in Fig. 10(a)) of the metasurface is set to 20°, and the feed antenna is set to (0, 490.36 mm, -411.46 mm), which can provide the metasurface with an amplitude taper of -10 dB. The structure of the entire reflective metasurface is shown in Fig. 10(a).
Fig. 10. (a) Geometry of the designed NFF reflective metasurface. (b) Phase distribution on the reflective metasurface.
The phase distribution of the elements on the reflective metasurface contains two parts: the phase change corresponding to the part of propagation from the feed antenna to the metasurface, and the part of phase for focusing the EM beam in the near-field. These can be expressed as
where k0 is the wavenumber at the center frequency, Ri is the distance from the phase center of the feed antenna to the ith element, $\vec{r}_i$ is position vector of the ith element, and $\hat{r}_o$ is the unit vector of the focusing direction [40]. The phase distribution on the reflective metasurface is shown at Fig. 10(b).In order to verify the effect of the slot on the ground plane of the metasurfaces, both the uniform ground plane reflective metasurface and the slotted ground plane reflective metasurface are simulated for comparison. The E-field distribution along the xz-plane through the focus point at 10 GHz are shown in Fig. 11. It can be seen from Fig. 11(a)-(b) that the sidelobes of the slotted ground plane reflective metasurface is more than 5 dB lower than that of the uniform ground plane reflective metasurface at the edge of the observed region. The Fig. 11(c)-(d) shows the distribution under 10 dB dynamic range, from which the position and size of the focus point can be observed more clearly. The focus center of the uniform ground plane reflective metasurface shifts by 1 mm and 5 mm in the horizontal and vertical directions respectively while that of the slotted ground plane reflective metasurface is right at the designed focal point.
Fig. 11. Simulated normalized E-field distribution along xz-plane through the focus point at 10 GHz from (a) the uniform ground plane reflective metasurface with 60 dB dynamic range, from (b) the slotted ground plane reflective metasurface with 60 dB dynamic range, from (c) the uniform ground plane reflective metasurface with 10 dB dynamic range, from (d) the slotted ground plane reflective metasurface with 10 dB dynamic range.
3.2 Experimental results
The pictures of the fabricated metasurface are shown in Fig. 12. A mechanical scanner is used to carry a horn antenna to scan the near-field of the metasurface and the measured near-field distribution along the plane 600 mm in front of the aperture are shown in Fig. 13. From Fig. 13(a), it is clear that the sidelobe outside the focused spot decreases quickly. Figure 13(b) shows the comparison of simulation and measured results along the vertical center line. It can be found that the sidelobes of the fabricated slotted ground plane reflective metasurface is similar to that of its simulation results, but lower than that of the reflective metasurface with uniform ground plane, especially at the edge of the observed region. The diameter of 3-dB and 10-dB focused spot of the slotted ground plane reflective metasurface is about 40 mm and 67 mm respectively as shown in Fig. 13(d), which are smaller than the simulated results.
Fig. 12. The fabricated prototype of the slotted ground plane reflective metasurface. (a) Front view. (b) Back view.
Fig. 13. Measured results of the reflective metasurface. (a) 2D E-Field distribution with 60 dB dynamic range. (b) Section along the dotted line in (a). (c) 2D E-field distribution with 10 dB dynamic range. (d) Section along the dotted line in (c).
As shown in Fig. 14(a), the transfer efficiency of the observing plane can be obtained by Poynting vector integration [19]. In an area of 150 mm ${\times}$150 mm, the transfer efficiency of the uniform ground plane reflective metasurface and the slotted ground plane reflective metasurface is 60.3% and 75.8%, respectively. In the measurement, the feed horn and the receiving antenna are coaxial connected with the vector network analyzer respectively, and the S-parameters of the system are obtained. The S-parameter directly demonstrates the transmission efficiency from the transmitter to the receiver. An area with the same square (150 mm ${\times}$150 mm) as in the simulation is chosen for integration, and the integral results are averaged in this region. The measured transfer efficiency of the reflective metasurface is 77.4%, which demonstrates the effectiveness of the NFF reflective metasurface. It should be noted that the slotted ground plane increases the transmission power, but despite this, the reflective metasurface with it can also focus a higher energy at the focused spot due to the lower sidelobes.
Fig. 14. (a) The NFF transfer efficiency calculation method of reflective metasurfaces. (b) EM-simulation and measured results of the transfer efficiency varying with frequencies.
The transfer efficiency over the entire frequency band is shown in Fig. 14(b). The dotted line indicates the positions when the transfer efficiency is reduced to half, suggesting that the relative bandwidth with 50% NFF transfer efficiency can reach 30.4% in the measured results. Due to the large size of the reflective metasurface and the form of offset-fed, the differences of the spatial phase delay from the phase center of the feed source to elements on the reflective metasurface limits the bandwidth of the reflective metasurface. Finally, the comparison of the existing state-of-the-art WPT systems is given in Table 2. The proposed design is able to achieve higher transfer efficiency under a considerable bandwidth.
Table 2. Performance comparison of the proposed design with other state-of-the-art works
4. Conclusion
In this paper, a low-coupling reflective metasurface design is proposed in order to reduce the discrepancy between the periodic EM responses and the actual non-periodic responses of elements within the complete metasurfaces. By introducing slotted ground planes behind each element, the mutual coupling effects can be significantly reduced thus improving the control accuracies of local amplitude and phase responses. A method of expanding the bandwidth of the reflective metasurface sub-wavelength elements is applied, which combines the mirror elements and double layer substrate, and a split ring element operating in the frequency band of 9-14 GHz is achieved. The designed slotted ground plane reflective metasurface with split ring elements is fabricated and measured, and the measured results are in good agreement with the simulated ones. The proposed slotted ground plane reflective metasurface achieves a transfer efficiency of more than 70% and a bandwidth with a 50% transfer efficiency of more than 30%. The proposed low-coupling design is applicable in many potential applications for metasurfaces.
Funding
National Natural Science Foundation of China (62171011); Beijing Natural Science Foundation (4232006).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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