Dynamic augmentation of scattering cross‐section by a conducting polycylinder coated with varactor‐loaded metasurface

National Natural Science Foundation of China, Grant/Award Number: 61601379; National Natural Science Foundation of China, Grant/Award Number: 61771407; Fundamental Research Funds for the Central Universities, Grant/Award Number: 2682018CX41 Abstract Through reconfigurable scattering pattern assisted by a varactor‐loaded polycylindrical metasurface, augmentation of backscattering as well as bistatic scattering cross‐section of a conducting polycylinder is presented in this study. The tunable reflection phase gradient and the resultant redirection of the dominant scattering that are enabled by the direct‐ current‐biased varactors serve as the basis of the agile scattering pattern reconfiguration of the polycylindrical metasurface. To achieve compactness and facilitate biasing, the metasurface unit cell comprises an outer conducting grid frame and an inner rectangular conducting patch grounded with a via hole, while a surface‐mounted varactor is soldered across the gap between them. It is demonstrated that the polycylinder coated with the designed reconfigurable metasurface can generate scattering behaviour very similar to a conducting plate with specific dimensions and orientation towards the plane's electromagnetic wave incidence. As a result, augmentation relative to the polycylinder without coating is observed for both backscattering and bistatic scattering cross‐section. The agreement between simulated and measured scattering cross‐section results validates the observations.


| INTRODUCTION
As many radar targets involve cylinder-like component parts, electromagnetic scattering of cylinders has received persistent attention. In the past, analytical solutions to the scattering of conducting cylinders with or without surrounding dielectric materials [1,2] were derived. While various approaches including impedance loading [3], plasma coating [4], cloaking [5,6], and hard surfaces [7] were extensively studied with the purpose of reducing the scattering from conducting cylinders, relatively limited measures, such as random rough surfaces [8], complementary media [9], and phase gradient metasurface [10,11], were emphasized for the sake of enhancing the scattering. Besides, the reported scattering enhancement of cylinders mainly concentrates on passive and static techniques, which indicates that the angular range of the enhancement effect is probably narrow and their application thus suffers from certain restrictions. Considering the changeable angle of incidence towards the target cylinder, the wide angular range and agility of the enhancement effect is desirable. Reconfiguration is an effective technique for the problem of wide-angle operation and agile enhancement.
With regard to reconfiguration, tunable or switchable features have been reported in literature for antennas [12], absorbers [13], polarization converters [14], and so on. Recently, the reconfigurable metasurface with dynamically adjustable characteristic draws a growing interest in the fields of microwave, terahertz [15,16], optics [17,18], and acoustics [19,20]. It is noted that the majority of reconfigurable metasurfaces reported are designed with flat geometry. Through modifying the equivalent capacitance or inductance, the tunable phase gradient of the reconfigurable metasurface is usually accomplished by the tuning of lumped elements loaded onto the unit cell, unit cell geometry, or material properties. The lumped elements mainly involve varactor diode [21][22][23][24][25][26][27][28] and PIN diode [29,30] to tune the equivalent capacitance of the metasurface. Tuning the shape or orientation of the unit cell alters the equivalent capacitance and inductance of the metasurface. Examples are the microfluid metasurface of which the unit cell contains liquid metal or dielectric [31,32] and physical dimensions changed by the external strain or field [33]. In addition, permittivity, permeability, and conductivity of certain materials [34,35] are tuned by external biasing for the sake of the reconfigurable metasurface.
In the interest of backscattering cross-section enhancement of cylinders, passive and conformal metasurfaces have been previously studied [10,11]. In this study, a reconfigurable metasurface based on the varactor-loaded unit cell is presented to achieve a reconfigurable and conformal design with an agile enhancement of electromagnetic scattering from cylinders. During the design of the unit cell geometry of the tunable metasurface, embedded bias structure is incorporated so as to achieve the tunability without obviously increased complexity [36]. The local reflection phase is dynamically modified and reconfigured through the direct-current-biased varactors which are loaded into each unit cell of the metasurface. In addition, varactors on the unit cells along the axial direction of the cylinder are provided with a same direct-current voltage and the reflection phase gradient necessary for the metasurface to redirect the dominant scattering is assisted by the voltage gradient along the circumferential direction of the cylinder. A multichannel programmable voltage source is utilized to produce the voltage gradient and its real-time adjustment. As a result of the dominant scattering redirected with the active design, effectively enhanced backscattering cross-section is observed. Besides, it is demonstrated that the scattering pattern can be reconfigurable and therefore the bistatic scattering cross-section can be augmented with a changeable bistatic angle through the cylinder coated with the designed metasurface. Section 2 of the presentation formulates the operating principle of the enhancement design. A numerical example, design, and tuning principle of the metasurface are presented in Section 3. The scattering pattern and experimental verification are discussed in Section 4. Section 5 summarizes the work of this study. Figure 1 displays the cross-sectional view of a cylinder geometry. Considering that the involved metasurface coating is loaded with lumped elements, the polycylinder with a profile formed by N polyline segments is chosen to facilitate loading. Along the increasing direction of the central angle α, the polyline segment is numbered with n ranging from 0 to N -1. The axis of the polycylinder lies in z-axis of the coordinate system and a plane electromagnetic wave coming from the aspect angle φ illuminates the polycylindrical geometry. The bistatic angle χ is subtended by the direction of incidence and the desired direction of scattering enhancement. The radius of the circumcircle of the polycylinder is represented with r and the length of each polyline segment is then p c = 2r � sin(π/N ).

| OPERATING PRINCIPLE OF RECONFIGURABLE SCATTERING PATTERN
Based on the scattering redirection expressed by the generalized law of reflection [37], the formulation of the involved metasurface starts from the profile polyline segment j with the minimum local angle of incidence, where the braces {} indicate rounding. For a given φ, the illuminated polycylindrical surface corresponds to the range of (φ -π/2) ≤ α ≤ (φ + π/2), as indicated by the arc AB in blue colour in Figure 1. On the other hand, it can be noted that only the unit cells of the metasurface within the range of (φ -π/2) ≤ α ≤ (φ + π/2 -χ), where χ ≥ 0, contributes to the enhancement of scattering towards the bistatic angle of interest, as implied by the arc AC. To establish the reflection phase gradient for the unit cells contributing to the enhancement, the local angle of incidence is determined for each polyline within the range of (φ -π/2) ≤ α ≤ (φ + π/2 -χ) as In order to redirect the scattering towards the direction of the bistatic angle χ, the angle of reflection is found to be Thus, by inserting the angles of incidence and reflection into the generalized law of reflection, the reflection phase gradient can be established for the metasurface coating along the anticlockwise and clockwise directions of segment j as where k 0 is the free-space wavenumber and h is the thickness of the dielectric substrate which closely surrounds the F I G U R E 1 A polycylindrical profile illuminated by a plane wave coming from the aspect angle φ. It is stipulated that α and φ increase for clockwise rotation, while χ increases for counterclockwise rotation polycylindrical surface and supports the metasurface unit cells. This reflection phase gradient determinable for a specified bistatic angle χ serves as a basis for operation of the reconfigurable scattering pattern of the polycylinder coated with metasurface. Since arc AC denoting the effective operation surface in Figure 1 gradually diminishes as the increase of χ, χ is practically less than π for any φ. It may be pointed out that arc AC denoting the effective operation surface coincides with arc AB indicating the illuminated surface when χ = 0, which expresses the backscattering cross-section enhancement.

| NUMERICAL ANALYSIS AND METASURFACE DESIGN
As a numerical example, a polycylinder with N = 182 and r = 136.15 mm (≈4.54 λ 0 , where λ 0 is the free-space wavelength at 10 GHz) is employed. The angular interval between adjacent polylines as well as unit cells depicted in Figure 1 is thus δ = dα = 2π/N. With h = 0.635 mm and φ = 0, the segment j = 0 is under normal incidence. Besides, the reflection phase gradient dΦ n is calculated for χ = 0, π/6, and π/3 at 10 GHz and shown in Figure 2 with respect to α n corresponding to the middle point of each involved polyline segment.
Furthermore, based on the calculated gradient, the reflection phases Φ n can be obtained for the unit cells situated in left and right sides of the segment j, Figure 3 illustrates the obtained reflection phase distribution for each polyline segment involved in the three bistatic angle examples. The initial phase for segment j = 0 is selected as Φ 0 = -160°, -30°, and -130°for χ = 0, π/6, and π/3, respectively. Other values can also be selected for the initial phase with the similar effect.
The obtained reflection phases are then mapped onto the polycylindrical surface through physical unit cells. Along the circumferential direction of the polycylinder, the unit cell carries a period p c equal to the length of the polyline segment, which is calculated as 4.7 mm (≈0.157 λ 0 ) in this example. The unit cell geometry, which is constructed in the form of a rectangular conducting patch enclosed with a conducting grid frame and shown in Figure 4 loss tangent 0.0023, and thickness of h = 0.635 mm. This kind of geometry is selected mainly by taking into consideration the unit cell compactness and convenience of embedding elements as well as their biasing wires. The rectangular patch is connected to the ground through a plated via hole at the unit cell centre. With the aim of a tunable reflection phase, a varactor is loaded across the gap between the patch and frame. An applied voltage can therefore be conveniently supplied to the varactor through wires connected with the frame and ground for the sake of biasing. Other dimensions of the unit cell are p a = 4.5 mm (0.15 λ 0 ), l 1 = 3.7 mm, a = 3.25 mm, b = 3.4 mm, and d 1 = 0.3 mm. In order to gain an insight into this varactorbased tunability, Figure 4(b) estimates an equivalent circuit model of the proposed metasurface geometry under normal incidence. The series L 1 C 1 circuit branch represents the grid frame, while the L 2 C 2 branch denotes the rectangular patch [38]. The inductance L 3 and impedance Z 0 represent the plated via hole [39,40] and free space, respectively. The grounded dielectric substrate is expressed as a short-circuited transmission line segment. On account of the asynchronous influence of the varactor capacitance indicated by C v on both the L 1 C 1 and L 2 C 2 branches, a scale factor k is simply introduced and determined in combination with other component values through simulation. It is noted that the input impedance Z in of this model can be written as where ω = 2πf with f indicating the frequency, and β ¼ ω ffi ffi ffi ffi ε r p =c with c implying the speed of light in free-space. Therefore, the reflection coefficient Γ of this model can be derived and its phase is extracted as It then can be deduced from (10) that the phase of the reflection coefficient decreases as the increase of the varactor capacitance C v , since B exists in the denominator.
By using the periodic boundaries, the planar array of the unit cell geometry in Figure 4(a) can be simulated in high frequency structure simulator for the incident angles φ i(n) to examine its reflection phase. Taking xz-plane as the incident plane, an example of reflection phase varying as the capacitance C v of the varactor is shown in Figure 5 for normal incidence of transverse electric (TE) polarization at 10 GHz. It is seen that the reflection phase can be arbitrarily modified within the range of almost ±180°by the change of the capacitance. Besides, the full-wave and circuit simulations agree and both results illustrate the operating principle of the varactor-based tuning implied by (10). As a result, using the unit cells with different capacitance values to construct an array could achieve the phase gradient along the circumferential direction of the polycylinder.
Full-wave simulations of the unit cell are then conducted so as to ascertain the capacitance values which can attain the objective phases in Figure 3 for the corresponding local angles of incidence and polyline segments which imply the positions of the unit cells on the polycylindrical surface. For each illustrated bistatic angle χ, the varactor capacitance values necessary for involved unit cells to generate the corresponding reflection phase gradient are shown in Figure 6. along the axial direction of the polycylinder. One row consisting of seven unit cells along the axial direction is also shown in the inset of Figure 7 for details of the direct-current bias. Anode of the voltage source is connected to the frame of each cell in a same row through a short stub with dimensions 2.5 mm � 1.0 mm, which ensures that the unit cells in a same row share a same biasing voltage. By virtue of the via holes, all rows of the unit cells attached on the polycylindrical surface can jointly use only one conducting wire for the cathode of the voltage source through the conducting polycylinder. Hence, different capacitance values shown in Figure 6 can be independently applied to different rows to provide the required reflection phase gradient of the reconfigurable metasurface.
In the interest of augmenting the scattering cross-section for the directions of 0, π/6, and π/3 bistatic angles, Figure 8 plots the simulated scattering cross-section by the conducting polycylinder coated with the metasurface. Meanwhile, the scattering cross-section results of the corresponding conducting polycylinder without any coating and that of the flat conducting plates are also shown in Figure 8 for a comparison. It should be mentioned that dimensions of the flat conducting plates are AC � l p , since the chord AC is perpendicular to the angle bisector of the bistatic angle χ and it represents the projection area of the polycylindrical surface with effectively operating unit cells. For the monostatic case of χ = 0, chord AC coincides with chord AB. In this case, dimensions of the flat conducting plate become AB � l p and are perpendicular to the incident direction. Compared with the conducting polycylinder without any coating, obvious enhancement of backscattering and bistatic scattering cross-section is observed around the design frequency of the metasurface.
Besides, the scattering cross-section values at 10 GHz are summarized in Table 1 to inspect the enhancement. Relative to the polycylinder without any coating, a 13.49 dB augmentation of the backscattering cross-section is obtained through the coated polycylinder for the bistatic angle χ = 0. In contrast with the conducting plate, the enhancement efficiency [10] is calculated as 81.47%. As seen in Figure 1, the increase of χ leads to the decrease in the polycylindrical surface area for the effective operation of the metasurface unit cells, which  -839 accounts for the reduced enhancement magnitude and efficiency for the π/6 and π/3 bistatic angles. However, the reduction of the enhancement magnitude is maintained within 3 dB till at least π/3 bistatic angle.

| DISCUSSION AND EXPERIMENTAL VERIFICATION
In order to further understand the effective redirection of scattering through the reconfigurable metasurface coating, the bistatic scattering pattern at 10 GHz is investigated in Figure 9 for 0, π/6, and π/3 bistatic angles. For the monostatic case, the reflection phase gradient is symmetrical with respect to x-axis. As a result, the bistatic scattering from the polycylinder is symmetrically suppressed by the metasurface coating, which devotes to the apparent scattering lobe towards the incident direction. Due to the asymmetrical reflection phase gradient for left and rights sides of x-axis, different suppression effect is noticed with a scattering lobe pointing at the design angle of enhancement for π/6 and π/3 bistatic angles. The observation of a scattering lobe aiming at the design angle of enhancement implies that the scattering pattern of the coated polycylinder can be dynamically reconfigurable by tuning the capacitance values of varactors loaded on different rows of the metasurface coating. Therefore, backscattering cross-section enhancement can occur for an arbitrary aspect angle φ in Figure 1 by applying the necessary reflection phase gradient for unit cells in effective operation. For a specific φ, the scattering lobe dedicated to enhancement can be reconfigured in a wide angular range towards a bistatic angle of interest. A brief comparison of the main features between this proposed design and existing work on scattering cross-section enhancement of cylinder is listed in Table 2. As a result of the scattering pattern reconfiguration capability of the designed active metasurface, additional power supply becomes necessary, while agility and flexibility in scattering cross-section enhancement effect can be obtained.
In order to verify the simulation-based observations, a polycylinder is fabricated and coated with the designed metasurface for measurement. Aluminium and commercial laminate Taconic radio-frequency (RF)-10 are used for the polycylinder and the dielectric substrate of the metasurface, respectively. A photo of this prototype is provided in Figure 10. For the purpose of verification, the metasurface coating covers only half of the polycylindrical surface from -π/2 ≤ α ≤ π/2. One conducting wire is soldered to the short stub of each row of the metasurface for the sake of connection to the anode of the voltage source. According to the needed capacitance range shown in Figures 5 and 6, the flip-chip M/A-COM varactor MAVR0001201411 is adopted to provide the capacitance values with the reverse-biasing voltages varying between 15 and 0 V. The multiplex channel voltage output amplifier Analog Devices AD5535B is used to supply those biasing voltages for each row of the metasurface coating. A 47-kΩ surface-mounted resistor, which connects the cathode of the direct-current power supply and the conducting polycylinder, is employed as an RF choke for the metasurface coating, as seen in Figure 10.
The measurement is conducted in a microwave anechoic chamber. Two horn antennas connected to a vector network analyser are responsible for transmitting and receiving. The prototype under test and the calibration plate are in the far-field of the horn antennas. The measured scattering cross-section results are already compared with the simulated ones in Figure 8. A frequency shift is observed between the simulation and measurement. The factors causing the difference from simulation mainly include the assembly tolerance and the tuning accuracy of the varactors which cause divergence of actual reflection phases from the objective ones. Overall, those measured results are comparable with simulations. Due to the frequency shift, the scattering cross-section values of the coated polycylinder at 10 GHz are -2.93, -3.13, and -6.10 dBsm for the bistatic angles of 0, π/6 and π/3, respectively. Compared with the measured results of the polycylinder without coating (-13.41, -16.68, and -15.66 dBsm at 10 GHz for three bistatic angles), the scattering cross-section is then enhanced by 10.48, 13.55, and 9.56 dB for three bistatic angles, respectively.

| CONCLUSION
By virtue of the tunable reflection phase gradient, agile reconfiguration of the scattering pattern from a polycylindrical metasurface has been demonstrated and employed to augment the backscattering as well as bistatic scattering cross-section of a conducting polycylinder. For specific illumination and enhancement directions, the unit cells required to be in effective operation and the variable reflection phase gradient have been formulated. By soldering a surface-mounted varactor across the gap between the conducting grid and the inner conducting patch with a grounding via, the tunable capacitance of the directcurrent-biased varactor loaded onto each unit cell of the array accounts for the phase gradient tunability and therefore redirection-based scattering pattern agility. As a result, a dominant scattering lobe can be efficiently generated around the desired aspect angle of enhancement. Besides, wide-angle stability of the dominant scattering lobe scanning has been observed during bistatic scene. Through this reconfigurable scattering pattern, the presented low-profile metasurface may serve as a potential design basis for dynamic control of scattering cross-section from the cylinder-like main body of a certain airborne decoys or friendly tracking of physically small targets. As this design operates with TE polarization, dual-polarized geometry of the tunable unit cell is an objective of a future study.