The dynamic and integrated control of near- and far-field electromagnetic waves is essential for advancing emerging intelligent information technology. Metasurfaces, distinguished by their low-profile design, cost-effectiveness, and ease of fabrication, have successfully revolutionized various electromagnetic functions. However, current research on the dynamic integrated manipulation of near-field and far-field electromagnetic waves using a single metasurface remains relatively constrained, due to the complexity of element-level control, restricted dynamic tuning range, and tuning speed. Herein, we propose an element-level controlled, versatile, compact, and broadband platform allowing for the real-time electronic reconstruction of desired near/far-field electromagnetic wavefronts. This concept is achieved by precisely regulating the 1-bit amplitude coding pattern across a guided-wave-excited metasurface aperture loaded with PIN diodes, following our binary-amplitude holographic theory and modified Gerchberg–Saxton (G–S) algorithm. Consistent findings across calculations, simulations, and experiments highlight the metasurface’s robust performance in 2D beam scanning, frequency scanning, dynamic focusing lens, dynamic holography display, and 3D multiplexing holography, even under 1-bit control. This simplified and innovative metasurface architecture holds the promise of substantially propelling forthcoming investigations and applications of highly integrated, multifunctional, and intelligent platforms.
【AIGC One Sentence Reading】:The proposed metasurface, controlled at the element level, enables real-time electronic reconstruction of desired electromagnetic wavefronts, demonstrating robust performance in various applications, including beam scanning and dynamic holography.
【AIGC Short Abstract】:In this study, we introduce a metasurface platform that enables dynamic and integrated control of near- and far-field electromagnetic waves. The platform, featuring element-level control, versatility, compactness, and broadband capability, allows real-time electronic reconstruction of desired wavefronts. Through precise 1-bit amplitude coding, it demonstrates robust performance in beam scanning, dynamic focusing, holography, and multiplexing, paving the way for highly integrated and intelligent electromagnetic applications.
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1. INTRODUCTION
As modern information technology advances toward greater intelligence, flexible manipulation of near- and far-field electromagnetic (EM) waves is important. Traditional antenna arrays for controlling near/far-field EM waves often rely on intricate feed networks, resulting in high costs and cumbersome devices. In contrast, metasurfaces, characterized by their periodic or quasi-periodic two-dimensional structures, have brought functional innovations including flat lenses [1], stealth materials [2], and holographic imaging [3–5]. Recently, the proposal of programmable metasurfaces bridges EM space and the digital information domain, greatly expanding the diversity of EM characteristics control [6,7].
Research on metasurfaces has thrived in exploring EM manipulation through polarization [8–10], frequency [8,11], incident angle [12], and reflection/transmission [13–18]. Intelligent algorithms based on deep neural networks have also been employed to design and expand metasurface functionalities [18–20]. While antennas and metasurfaces have unlocked myriad capabilities for far-field EM wave manipulation, near-field EM waves also offer a rich spatial spectrum. Therefore, some recent studies have emerged to simultaneously control the near-field (amplitude) and far-field (phase) of EM waves to increase information density and encryption, opening a new degree of freedom of metasurface [21–25]. However, research on dynamically controlling both near-field and far-field EM characteristics across various function scenarios using a single metasurface is relatively scarce in the literature [26–29]. This complexity can be attributed to the requirement for element-level control flexibility to precisely tailor near/far-field EM waves. In addition, achieving fast 360° dynamic phase tunability remains a challenging task, hampered by limited tuning range and speed, the interdependence of element amplitude and phase, and trade-offs among various metrics including the working bandwidth and power efficiency of meta-atoms. Decoupling the amplitude and phase correlation by careful geometric design of particles [30,31] and differences in polarization responses [32,33], metasurfaces with complex amplitude have been developed, but primarily in passive configurations. Active metasurfaces with multibit elements increase flexibility by using more active components, albeit at the cost of increased control complexity, especially for 2D arrays with element-level control at millimeter-wave bands [34,35].
Unlike the traditional transmissive and reflective metasurface architectures, generating a uniform excitation wavefront in the near-field achieves a subwavelength scale of metasurface thickness [36]. Furthermore, researchers have innovatively integrated metasurfaces directly on transmission lines to couple guided waves into free space [37]. These approaches provide effective avenues for realizing highly integrated applications of multifunctional meta-devices by eliminating the longitudinal path required for an outside feed. The latter one is known as guided-wave-excited metasurfaces (GWEMs). Although this GWEM has succeeded in far-field beam scanning and multibeam generation based on holographic theory, its multifunctional characteristics and flexibility in controlling EM waves still need further development [38–43]. For instance, a guided-wave-excited reconfigurable aperture for near-field focusing was only demonstrated by simulation, and there is no dynamic holographic imaging investigation [44]. In contrast to the commonly used Pancharatnam–Berry (PB) phase gradient metasurfaces, we have previously developed a metasurface excited by a parallel-plate waveguide, offering a potential integrated platform for rapid switching of vortex beams [45]. However, the phase modulation range of this metasurface is limited by Lorentz resonance, which prevents it from exceeding 180°. Amplitude control metasurfaces provide a valuable complement to EM wave control, yielding favorable outcomes [43,46]. In this paper, an interesting finding reveals that the GWEM enables spatial harmonics suppression in the focused scene, especially with 1-bit quantization and a limited number of elements (see Appendix B for details). Moreover, GWEMs require the capacity to individually control each metasurface element and incorporate specific holographic algorithms to realize dynamic holographic imaging.
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Here, a reprogrammable guided-wave-excited metasurface (RGWEM) is proposed to achieve both dynamic near-field hologram and far-field radiation manipulation, advancing the process of multifunctional and intelligent EM wave control. The RGWEM employs a high-efficiency round complementary electric-LC-coupled (CELC) structure [47], embedded with a PIN diode to create meta-atoms characterized by two states of “ON” and “OFF,” represented as the binary digits “1” or “0” while maintaining the phase constant. Consequently, reprogrammable and real-time control over EM waves can be achieved through field programmable gate array (FPGA) technology. Each meta-atom can be individually addressed in both near-field and far-field scenarios. To ensure accurate tailoring of the far-field and near-field radiation, we establish a binary-amplitude holographic theory and a modified Gerchberg–Saxton (G–S) algorithm, both grounded in the dipole-radiation model of the guided-wave-excited meta-atom. As a proof-of-concept, an RGWEM prototype is designed, fabricated, and measured. Distinguished from the previously demonstrated near-field and far-field EM manipulation metasurfaces, this compact and broadband RGWEM architecture establishes dynamic connections between guided modes and near/far-field free-space waves, and it can realize functions of 2D beam scanning, frequency scanning, dynamic focusing lenses, dynamic holography display, and 3D multiplexing holography in a single device. We firmly believe that this multifunctional and integrated platform holds significant potential for future intelligent application scenarios.
2. GEOMETRY DESIGN OF RGWEM
Figure 1 illustrates a visual representation of the real-time RGWEM that integrates various functions by manipulating near-field and far-field EM radiation. In this system, each meta-atom is integrated with one PIN diode and excited by the guided waves in the substrate-integrated waveguide (SIW). The RGWEM is expected to have switching speeds in the GHz range. A control circuit predominantly composed of surrounding amplifier drive circuits and FPGA chips is designed to provide 240 channels of non-interfering bias voltages. Thus, the 1-bit encoding sequences of different near-/far-field manipulations can be dynamically switched by addressing each local unit and can be calculated by the carefully built binary-amplitude holographic theory and the modified G–S algorithm. For far-field applications, the system’s performance is demonstrated through 2D beam scanning and frequency scanning. For near-field control, it successfully achieves a dynamic focusing lens, dynamic holography display, and 3D multiplexing holography, further exemplifying the proposed RGWEM’s ability to manipulate EM waves with accuracy and efficiency.
Figure 1.Conceptual illustration of the RGWEM for near-field and far-field radiation control with binary-amplitude round CELC meta-atoms and the FPGA-based control circuit. This compact platform can support functions including dynamic focusing lens, dynamic holography display, 3D multiplexing holography by manipulating near-field radiation, 2D beam scanning, and frequency scanning by manipulating far-field radiation.
As shown in Figs. 2(a) and 2(b), the meta-atom consists of two substrates (Rogers 4003C, dielectric constant , loss tangent , thicknesses and ) and four metal layers (copper, thickness ). A bonding layer Rogers 4450F (dielectric constant of 3.52, loss tangent of 0.004) with a thickness of 0.102 mm is applied. The round CELC pattern is etched on the top layer and connects to the DC bias line on the bottom layer by a metalized via. To ensure effective electrical isolation among elements, two round holes of identical size are opened on the two middle layers. As depicted in Fig. 2(c), the PIN diode (MACOM, MADP-000907-14020) bridges the gap between the center patch and the ground, and a fan-shaped capacitor is set on the bias layer for RF isolation (see Appendix C for isolation performance). Linearly polarized radiation in the -direction is observed in Fig. 2(d), and the predominant contribution to the meta-atom’s radiation originates from the left iris, as the electric fields on the right iris are small and obscured due to the presence of the PIN diode. Figure 2(e) displays the E-plane radiation patterns of the meta-atom under “ON” and “OFF” states, demonstrating that substantial isolation exceeding 20 dB is obtained between the “ON” and “OFF” states, even with the utilization of a single PIN diode. Therefore, this design significantly enhances the radiation efficiency of the element by reducing both ohmic loss and active component loss. As depicted in Fig. 2(f), compared with the rectangle CELC structure, the round CELC element exhibits a clear increase in radiation efficiency, which keeps above 40% from 25 to 27 GHz. The amplitude and phase responses of the meta-atom are shown in Fig. 2(g), illustrating the weak coupling between the meta-atom and the guided wave, with phase perturbations of less than 10° introduced to the guided wave in both the “ON” and “OFF” states.
Figure 2.Structure and properties of the meta-atom. (a) 3D view, (b) side view, (c) top and bottom views of the radiating meta-atom. Simulated (d) electric field distributions and (e) E-plane radiation patterns of the meta-atom under “ON” and “OFF” states when the rotating angle . (f) Simulated radiation efficiencies of the round CELC and rectangle CELC elements. (g) Simulated amplitude and phase responses of the two-state meta-atom. The diagrams of the round CELC (blue solid line) and rectangle CELC (red dotted line) elements are displayed. Both are loaded with the same PIN diode (black) and are designed to resonate at the same frequency. , , , , , , , , .
Utilizing the above binary-amplitude meta-atoms, a 2D RGWEM prototype is constructed, comprising eight SIW channels and a 240-element array, as exemplified in Fig. 3. These elements are arranged in a triangular grid pattern, reducing their number while ensuring optimal performance. As the metasurface elements gradually radiate the guided wave, its rapid amplitude attenuation leads to an uneven radiation intensity distribution along the transmission line. To address this issue, the coupling strength of the element is decreased by increasing the rotating angle of the PIN diode, as shown in Fig. 2(c). Notably, on each SIW channel, PIN diodes are rotated outwardly in 1° intervals, progressing from right () to left (). At each end of the SIW channel, two triangular gradient gaps convert the SIW line into a grounded coplanar waveguide (GCPW). An eight-way power divider is used to excite the eight SIW channels in the experiment. The 240 independent voltage channels, crucial for facilitating real-time control, are efficiently established by an FPGA-based control circuit.
Figure 3.2D RGWEM prototype layout. (a) Top and (b) back views. Each SIW channel is marked by green Arabic numerals, and green circles on the back view represent the solder mask.
3. THEORY AND EM PROPERTIES OF FAR-FIELD BEAMFORMING
The implementation of dynamic 2D beam scanning enables swift orientation and adjustment of EM waves in azimuth and elevation, facilitating target tracking and precise beam control. As a result, 2D beam scanning technology has garnered broad applications across diverse fields, including communication systems, radar technology, imaging devices, and unmanned driving. However, most metasurface-based beam scanning designs still focus on 1D cases. In the first demonstration, we directed our efforts toward achieving 2D beam scanning in both azimuth and elevation using amplitude sampling instead of the conventional gradient phase.
A. Binary-Amplitude Holographic Theory
According to holographic modulation theory [48], achieving a far-field pencil beam directed toward (, ) necessitates the establishment of the following phase distribution across the metasurface aperture, where represents the propagation constant within the SIW channel, (, ) is the position of the th meta-atom, and is the free-space propagation constant. Further, to convert phase modulation into binary amplitude modulation, the sinusoidal portion of the complex amplitude is selected and quantized to the binary amplitude,
The state of each PIN diode is determined based on the obtained binary matrix. By selecting various (, ) values and repeating the calculation, it becomes possible to obtain the desired amplitude mask for any spatial beam pointing. Subsequently, this instruction is assigned to the FPGAs and implemented by the metasurface, enabling two-dimensional dynamic reconfigurability of the beam.
B. Far-Field 2D Beam Scanning
Figure 4(a) illustrates the experimental setup in the microwave anechoic chamber for the far-field radiation pattern measurement. The transmitting horn antenna is located at a distance of from the RGWEM, ensuring compliance with far-field conditions. As depicted in Fig. 4(b), it is evident that the metasurface prototype effectively encompasses a impedance bandwidth within the frequency range of 25–28 GHz under almost all the scanning angles. For the broadside beam, as displayed in Figs. 5(a) and 5(d), the measured radiation patterns align well with the simulated ones. The radiation patterns with scanning angles of in azimuth and elevation show a similar overall trend between the measured and simulated patterns in Figs. 5(b), 5(c), 5(e), and 5(f). Additionally, Figs. 5(g) and 5(h) reveal the frequency scanning performance of the RGWEM, showcasing a scanning range of approximately 20° for the broadside beam and 15° for the azimuth directional beam. The realized gains (the dB value representing the ratio of power radiated by the RGWEM in the maximum gain direction to the input power) varying with frequency are also investigated in Fig. 5(i).
Figure 4.(a) Far-field experiment setup in the microwave anechoic chamber and top view of the fabricated RGWEM prototype. An enlarged image of a through-wall sub-miniature push-on (SMP) connector is shown in the lower right corner. (b) Measured reflection coefficients of channel 4 under the azimuth angle varying from to 60°, and the elevation angle varying from −30° to 30°. The reflection coefficients of other channels are almost the same.
Figure 5.Simulated and measured normalized far-field patterns with corresponding 1-bit amplitude coding patterns at 26 GHz. (a) E-plane ( plane) and (d) H-plane ( plane) patterns of the broadside beam. (b), (e) The beam directed at (, 0°), and (c), (f) the beam directed at (, ). Measured normalized far-field patterns for (g) the broadside beam and (h) the beam directed at (, 0°), and (i) measured realized gains of these two beams, with frequencies varying from 25 to 28 GHz.
Then the overall radiation performance of the proposed RGWEM is analyzed. As shown in Figs. 6(a) and 6(b), the far-field 2D beam scanning capability is verified to exceed in azimuth and a minimum of in elevation. Figures 6(c) and 6(f) depict the steering accuracy of the beam direction, illustrating that the measured beam directions closely match the target angles within in azimuth and in elevation, and a maximum angle deviation of 7° is found at a target angle of 60° in azimuth. From the results in Figs. 6(d) and 6(g), the gain fluctuation of the azimuth scanning beam remains below 3 dB, with the maximum radiation efficiency reaching 18.5% at the scanning angle of , while the gain fluctuation in elevation is less than 4 dB, with the maximum radiation efficiency being 14.7% at the scanning angle of 10°. As presented in Figs. 6(e) and 6(h), the sidelobe level of the RGWEM is less than at the broadside.
Figure 6.Measured far-field 2D beam scanning results. Normalized radiation patterns of the RGWEM scanning from to 60° in (a) azimuth and to 30° in (b) elevation. (c), (f) Steering accuracy, (d), (g) realized gain and radiation efficiency, (e), (h) 3 dB beamwidth and sidelobe level of the directional beam at different scanning angles in azimuth and elevation, respectively.
Indeed, the far-field radiation performance in azimuth exhibits superior characteristics compared to elevation, primarily arising from two key factors. First, the azimuth direction boasts approximately twice as many elements as that in elevation. This discrepancy in element count has a significant influence on the maximum achievable scanning angle. It is important to note that the effectiveness of amplitude holographic modulation theory relies on the presence of adequate elements. Furthermore, the larger metasurface aperture results in a narrower beam width, consequently affording greater tolerance for beam distortion at large scanning angles. Second, the sampling interval for the guided wave in elevation, which stands at ( is the waveguide wavelength of SIW), is notably larger than that in azimuth, where it is . This disparity contributes to an elevation in sidelobe levels and a decrease in the aperture utilization rate, impacting the overall gain and radiation efficiency.
4. OPERATION PRINCIPLES AND NEAR-FIELD REAL-TIME HOLOGRAM
In different application scenarios reliant on holographic technology, such as data storage and security, 3D virtual reality technology, and biomedical imaging, the necessity of real-time image switching creates a pressing demand for compact and electronically dynamic reconfigurable metasurface holograms. In the second demonstration, we accomplished various functionalities through dynamic near-field manipulation. The same prototype is measured in a near-field microwave anechoic chamber as shown in Fig. 7. The waveguide probe is placed at various distances from the RGWEM under test (specifically, at , , , , ), scanning the imaging plane with 5 mm intervals in both dimensions, guided by instructions from a PC. Following each scanning, the field distribution results obtained through a comparison measurement conducted by the VNA are collected and visualized on the PC for further analysis.
Figure 7.Diagram of the near-field experiment setup. The measuring system consists of five parts: waveguide probe, RGWEM under test, vector network analyzer (VNA), scanning controller, and personal computer (PC).
Considering the guided-wave-excited mechanism of the metasurface, we have developed the modified G–S algorithm with three key enhancements, as illustrated in Fig. 8. First, instead of employing Green’s function, we incorporate the radiation pattern of a dipole to describe the transmission relationship, which is a practical approach applicable in both near-field and far-field regions. Second, it is crucial to emphasize that the metasurface is not exposed to plane waves, but interacts with guided waves, so an attenuation factor of the wavefront amplitude as the guided waves propagate forward is introduced. Third, phase distribution on the metasurface is converted into binary amplitude control.
Figure 8.Flowchart of the modified G-S algorithm. The forward propagation and backward projection operation based on the dipole radiation pattern establishes an iterative process between the hologram plane and the imaging plane to get the binary hologram mask.
We discretize the hologram plane into dipole sources and the imaging plane into pixels. The reconstructed image on the target plane results from the superposition of electromagnetic fields radiated from these dipole sources. Conversely, the phase distribution of the dipole sources needed to form the target image can be retrieved through the backward projection of the target image. The iterative process between the hologram plane and the imaging plane aims to ensure that the reconstructed image produced by these dipole sources progressively approximates the target image. As previously mentioned, the propagation kernel of fields is directly related to the radiation pattern of a dipole. Therefore, the forward propagation from the hologram plane to the image plane can be described as where and are the th pixel strength on the imaging plane and the th dipole electric field strength on the metasurface aperture in the th iteration, represents the amplitude of the guided wave at position and can be retrieved from simulation, is the elevation angle parameter in the spherical coordinate system, and corresponds to the propagation distance from the center of the th dipole to the th pixel.
Then, the backward projection from the image plane to the hologram plane can be deduced as where is the weight factor to establish a feedback mechanism for dynamically regulating the energy ratio among these pixels of the reconstructed image, and the initial value of is set as . represents the strength of the th pixel on the target image. According to Eq. (5), the phase shift of each dipole can be retrieved, and then it will be quantified into
Typically, following the 1-bit quantization, the metasurface’s capability to manipulate the EM field tends to diminish, giving rise to the emergence of high-order spatial harmonics. However, the guided-wave-excited metasurface exhibits efficient suppression of these high-order spatial harmonics, as illustrated in Fig. 12 in Appendix B.
B. Dynamic Focusing Lens
Figure 9.(a) Calculated, (b) simulated, and (c) measured results of dynamic focusing and six-point-flower pattern focused at different planes at 26.5 GHz. (d) Measured results of the single-point focus with from 25 to 28 GHz.
To further evaluate the holographic imaging capabilities of the RGWEM, more complex holographic images, such as the heart symbol and the letters “S,” “E,” “U,” are calculated, simulated, and measured at , as shown in Fig. 10. Benefitting from the electronic control architecture of this metasurface, a switching speed of 2 ns can be achieved by the PIN diode, facilitating fast-dynamic holography display among different images. Despite some distortions, the simulated and measured results exhibit remarkable visual fidelity and are satisfactorily congruous with the calculated outcomes.
Figure 10.Calculated, simulated, and measured results of holographic images of (a1)–(a3) symbol heart, (b1)–(b3) letter S, (c1)–(c3) letter E, and (d1)–(d3) letter U.
For quantitative evaluation of generated holographic images, correlation coefficients (Co) between the reconstructed results and theoretical patterns, as well as imaging efficiencies (defined as the fraction of radiated energy contributing to the holographic image, such as the energy enclosed in the dotted-line range in Fig. 10), are computed and analyzed. The calculated Co values between reconstructed results and theoretical patterns are shown in Fig. 11(c) with 0.75/0.51 (simulation/experiment) for the heart symbol, 0.7/0.49 for “S,” 0.78/0.69 for “E,” and 0.71/0.7 for “U,” The quantitative evaluation results of the different number of focus are also shown in Figs. 11(a) and 11(b). Overall, as the number of focuses increases or the complexity of the imaging pattern rises (with “S” having the highest complexity and “E” having the lowest), the correlation coefficient between the reconstructed image and the theoretical pattern decreases. This is because metasurfaces require greater degrees of control freedom for optimal solutions when dealing with more complex patterns, which can be attained through the utilization of smaller and more numerous metasurface elements. Combining the G–S algorithm with other intelligent algorithms, such as the genetic algorithm, particle swarm optimization algorithm, and neural networks, is also a highly promising method for further performance enhancement. Differently, the imaging efficiency of focuses and holographic imaging, obtained by simulation and experiment, is not significantly affected by the complexity of the target patterns. Among them, experimental imaging efficiencies are less than the simulated values but remain above 60%, revealing the high energy utilization of the proposed RGWEM.
Figure 11.Simulated and measured Co values and imaging efficiencies of (a), (b) different focus numbers and (c), (d) different holographic images. Calculated (orange dash line), simulated (green dash line), and measured (red dash line) results of holographic images scanning at (e) and (f) .
Information multiplexing of metasurface holograms is required for high-speed and large-capacity information transmission. An effective solution to extend the number of multiplexing channels is 3D holography, which can form different images on various cutting planes along the propagation path but is also rarely considered at present [49,50]. We have endeavored to expand the manipulation freedom of the proposed RGWEM and have experimentally verified its 3D multiplexing holography proficiency. In the modified G–S algorithm iteration process used to obtain the coding sequence of multi-plane imaging, the number of pixels becomes the sum of pixels on all imaging planes, while the number of metasurface elements remains unchanged. Taking the simultaneous generation of holographic image “L” at and one-point focusing at as an example, the measured results are displayed in Figs. 11(e)(iii) and 11(f)(iii). The calculated Co values between reconstructed results and theoretical patterns for both simulation and experiment are 0.81/0.80 at and 0.81/0.88 at , while imaging efficiencies for both simulation and experiment are 0.65/0.55 at and 0.54/0.51 at , fully demonstrating the potential of the proposed metasurface for multi-channel information encoding and the reconstruction of 3D imaging.
5. DISCUSSION AND CONCLUSION
In this paper, we have presented and demonstrated a reprogrammable guided-wave-excited metasurface embedded with PIN diodes for electronically dynamic integrated manipulation of near-field and far-field radiation EM waves. The metasurface leverages the binary-amplitude holographic theory and the modified G–S algorithm based on the dipole radiation model, enabling accurate prediction and reconstruction of both far-field and near-field EM waves. In the far-field control mode, the metasurface exhibited a scanning range of over in azimuth and at least in elevation. In the near-field control mode, it demonstrated precise control of EM waves, enabling the dynamic focusing lens, holographic imaging, and 3D imaging multiplexing functions. The measured holographic images achieved imaging efficiencies of over 60%, and the measured Co values between reconstructed results and theoretical patterns exceeded 49%. Furthermore, the proposed RGWEM can operate within the impedance bandwidth range of 25–28 GHz, covering a frequency scanning range of over 15° and a focus lateral bias range of 22 mm. This metasurface architecture can be upgraded to a multi-bit configuration by employing variable capacitors, enabling it to exhibit powerful performance and potential applications in areas such as detection and tracking, near-/far-field wireless communication, wireless power transmission, data storage and security, and 3D virtual reality technology.
APPENDIX A: SAMPLE FABRICATION
The RGWEM prototype with an overall dimension of is fabricated by an industry-standard printed circuit board (PCB) process. An FR4 routing board is welded on the back of the metasurface using flip-chip bonding. Next, 240 PIN diodes are embedded on the target position of each element (marked with green oil during processing) by reflow soldering. As shown in Fig. 4, eight through-wall SMP connectors are attached at the beginning of eight SIW channels for RF excitation, and eight 50 Ω terminators are connected at the end of these SIW channels to minimize reflections.
APPENDIX B: THEORETICAL ANALYSIS OF THE HIGH-ORDER SPATIAL HARMONICS SUPPRESSION MECHANISM
For the guided-wave-excited (GWE) metasurface, the radiating electric field intensity at any observation point by each dipole source can be expressed as where is the binary code of the th dipole, is the distance from the source point to the observation point, is the position vector of the dipole source, is the position vector of the observation point as shown in Fig. 12, and is the scattering pattern of a dipole.
Figure 12.Schematic diagram of radiation from the hologram plane to the imaging plane.
Figure 13.The binary hologram mask of one focus and the corresponding calculated radiating patterns. (a), (c) The binary hologram mask and the calculated radiating pattern of the GWE metasurface. (b), (d) The binary hologram mask and the calculated radiating pattern of the FSW metasurface.
APPENDIX C: ISOLATION DESIGN BETWEEN RF AND DC SIGNALS
A fan-shaped capacitor was carefully designed and added to the bias line to achieve good isolation between RF and DC signals. Figure 14(a) shows the transmission isolation, which is also the transmission coefficient through the bias line (BL), compared with the bare microstrip line (ML). It is observed that the more than 10 dB transmission isolation of the BL with the fan-shaped capacitor is obtained from 23 to 30 GHz. The electric field distribution in Fig. 14(b) well verifies that electromagnetic fields are intercepted at the fan-shaped capacitor.
Figure 14.(a) Transmission isolation and (b) electric field distribution of the BL compared with the ML.
APPENDIX D: BINARY AMPLITUDE MASKS CALCULATED BY THE MODIFIED G–S ALGORITHM
By using the modified G–S algorithm based on the radiation pattern of a dipole for about 300 iterations, a relatively ideal reconstruction image can be obtained. Figure 15 shows the 1-bit coding sequences on the metasurface aperture corresponding to different target focusing modes and holographic images.
Figure 15.1-bit encode sequences calculated by the modified G–S algorithm based on the radiation pattern of a dipole. One-point focus at (a) , (b) 58 mm, (c) 92 mm. (d) Two-point focus, (e) four-point focus, (f) six-point-flower pattern, (h) symbol music, (i) symbol heart, (j) letter S, (k) letter E, and (l) letter U at . (g) 3D multiplexing holography.
Shuang Peng, Fei Yang, Han Zhang, Zhan Yi Fu, Chen Xi Liu, Hai Ying Lu, Ya Ting Xie, Qian Yu, Rui Huang, Xiao Jian Fu, Jun Wei Wu, "Dynamic near-field and far-field radiation manipulation using a reprogrammable guided-wave-excited metasurface," Photonics Res. 12, 2056 (2024)