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Abstract
In this paper, we integrate continuous transmission amplitude modulation and phase coding into a metasurface, and dynamic transmitted electromagnetic field manipulation is realized in microwave regime. The active metasurface is obtained by placing a PIN diodes loaded amplitude modulation metasurface on a binary phase coding metasurface whose coding matrix is optimized by genetic algorithm. Changing the bias voltage applied on the diodes, the transmission amplitude of the phase coding units covered by amplitude modulation units can be tuned continuously while other coding units are not affected, leading to the fact that the transmitted field pattern of the metasurface varies from strongly directional transmission to diffusion-like radiation. By this means, two degrees of freedom of dynamic amplitude modulation and predesigned phase coding are achieved to control the electromagnetic waves. Additionally, a bias network is designed to ensure the polarization-stability of the metasurface. The proposed concept is predicted by analytical model, and verified by numerical simulations and experiment. This design with low profile and diverse functionalities can yield potential applications ranging from radio frequency energy harvesting to wireless communication systems.
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1. Introduction
Metasurfaces are planar two-dimensional electromagnetic (EM) scatterers composed of periodically or non-periodically arranged subwavelength unit cells [1–3]. Metasurface research achieved drastically growth momentum during the last decade and emerged as the most promising field in EM manipulations. Owing to powerful ability in controlling the polarization [4], amplitude [5], and phase of EM waves [6], various functional metasurfaces were designed to explore their potential applications in polarizer [7], antenna [8], holographic imaging [9], flat lens [10], absorbers [11], and so on. With the rapid development of adaptive and multifunctional systems in practical applications, the demands for active metasurfaces with multi-function and tunability are increasing dramatically. Therefore, many active metasurfaces were proposed to implement the reconfigurable functions [12,13]. The tunability can be realized by inducing active elements [14], phase changing materials [15] and mechanical deformation [16] in the design. Particularly, graphene offers more freedoms in phase and amplitude modulations in terahertz and microwave regimes [17,18]. Based on tunable Fermi level of graphene, the sandwich structure of graphen- electrolyte- graphene was widely used to provide considerable amplitude and phase modulations in microwave frequencies [19,20].
In 2014, the emergence of the concept of coding metasurface made it possible to reshape the way of manipulating EM waves [21]. The metasurfaces composed of binary phase elements arranged in different coding sequences exhibited diverse scattering characteristics. Furthermore, the encoding was extended to multi-bits to gain more flexible EM manipulations. More powerful functions such as anomalous beam reflection, anomalous refraction, and wave front tailoring have been achieved [22–24]. More importantly, incorporated with active elements such as PIN diode, varactor diode, and phases changing materials, coding metasurface could manipulate EM waves flexibly in real time. Shabanpour et al proposed a liquid crystal based 3-bit coding metasurface to achieve real-time multi-functional near-infrared wave manipulation [25]. A digital metasurface loaded with PIN diodes, which could realize full-space EM manipulations was designed by Wu et al [26]. Li et al proposed a programmable coding metasurface reflector for reconfigurable multibeam antenna application [27]. Amplitude encoding added degree of freedom for coding metasurface to manipulate EM waves recently [5,28,29]. Existing coding metasurface schemes can be divided into two categories according to the number of degrees of freedom for EM manipulation. Most of the previous work focused on dynamical single control of phase or amplitude, and a few of them refer to non-dynamic dual-tunability of phase and amplitude [28]. In fact, complete EM manipulation demands arbitrary phase and amplitude control simultaneously [30,31], but may greatly increase the complexity of the system. Some attempts have been made to achieve this goal [32–34]. However, the indirect control increases the level of sophistication due to complex time domain algorithm [32], and relatively small tunable range of the graphene resistance and the small size subject to immature manufacturing technology limit its application [34]. To date, continuous radiation waves manipulation based on metasurface through directly introducing dynamical transmission amplitude control into phase coding has not been experimentally validated yet.
In this study, we combine dynamical transmission amplitude modulation with phase coding to gain more flexible EM manipulations in microwave frequencies, and a transmission-type coding metasurface enabling continuously shaping the radiated field pattern is proposed. This metasurface comprises a 1-bit phase coding metasurfae covered by an amplitude modulation metasurface loaded with PIN diodes. Two types of phase coding elements with opposite phase responses are arranged in pseudorandom sequence optimized by the genetic algorithm on the phase coding metasurface. Tuning the forward resistances of the diodes by the applied bias voltage, continuous transmission amplitude modulations of specific coding units are achieved while the phase responses are relatively stable. By this means, the preset phase coding and dynamical amplitude modulation allow to manipulate the transmitted waves on two degrees of freedom. A prototype is fabricated and measured. The theoretical predictions, numerical simulations and experiment results demonstrate that the metasurface can perform continuously steerable transmitted pattern from diffusion-like radiation to strongly directional radiation.
2. Working principle
The working principle of the proposed metasurface is illustrated in Fig. 1. Two kinds of phase coding elements (“0” and “1”) with opposite phase responses are arranged in a pseudorandom coding matrix. The transmission amplitudes of the “0” elements can be controlled independently by the amplitude modulation units on them without affecting their phase responses. Hence, the superimposed radiation fields of all the elements on the metasurface can be steered dynamically. Changing the bias voltages applied on the diodes from 1.3 V to 0 V, the transmitted far field pattern varies from diffusion-like radiation to strongly directional radiation continuously under normal illumination, as depicted in Figs. 1(a)–1(d). This design with intriguing tunability may have potential applications in many fields. Figures 1(e) and 1(f) show an application scenario.
Fig. 1. The working principle of the proposed metasurface. (a)-(d) The radiation patterns under different bias voltages applied on the metasurface. The schematic sketches of radio frequency energy harvesting for the (e) known receiving device case and (f) the unknown receiving device case or many equally distributed receiving devices case.
Radio frequency energy harvesting is a way of power supply and has diverse low-power applications. We assume that an antenna is placed behind the proposed metasurface to supply energy for the receiving device. If the position of the device is known, the gain of the antenna should be increased to maximize the acquired power. In this case, we need to switch the bias voltage applied on the metasurface to 0 V to obtain a pencil-like transmitted beam. If the location of the receiving device is unknown or there are multiple equally distributed receiving devices, multidirectional radiation is preferable. The voltage should be set to 1.3 V to produce a diffusion-like radiation. The working state of the transmitting antenna can be tuned dynamically according to the number of receiving devices or their locations to optimize the acquired power. In addition, this design loaded antenna system with tunable gain may have potential applications in wireless communication systems.
3. Design and numerical results
The unit cell of the proposed metasurface is presented in Fig. 2. The bottom structure is the phase coding unit comprised of three layers of metallic octagon slots with the same size and two layers of F4B substrate with a relative permittivity of 2.65 and a loss tangent of 0.001. The metallic patterns loaded with four PIN diodes BAR64-02EL from Infineon, a F4B substrate and a feed line with loaded inductors make up the top amplitude modulation unit. The cross dipole is connected to the feed line by a via hole 0.2 mm in diameter. A 0.5-mm-thick air gap (${{\rm{h}}_{\rm{r}}}$) between the top and bottom units is considered due to the actual volume of the inductors. We adopt the three-layer cascaded metallic structure with the same period (${\rm{p}} = 12{\rm{\;mm}}$) for achieving enough phase shift and high transmittance when only changing the dimension of the octagon slot ${{\rm{l}}_{\rm{o}}}$. After carefully optimized, ${{\rm{l}}_{\rm{o}}} = 7.8{\rm{\;mm}}$ is chosen for the “0” phase coding unit and ${{\rm{l}}_{\rm{o}}} = 10.7{\rm{\;mm}}$ for the “1” unit. The other parameters of the unit cell are given by:${{\rm{l}}_{\rm{a}}} = 9.6{\rm{\;mm}}$, ${{\rm{w}}_{\rm{a}}} = 2.8{\rm{\;mm}}$, ${{\rm{w}}_{\rm{g}}} = 0.4{\rm{\;mm}}$, ${{\rm{w}}_{\rm{f}}} = 0.2{\rm{\;mm}}$, ${{\rm{h}}_{\rm{a}}} = 1.5{\rm{\;mm}}$, ${{\rm{h}}_{\rm{p}}} = 1.5{\rm{\;mm}}$, ${{\rm{w}}_{\rm{o}}} = 1.2{\rm{\;mm}}$.
Fig. 2. (a) The geometry of the unit cell. (b) The front side and (c) rear side of the amplitude modulation unit. (d) 2D profile of the phase coding unit.
To investigate the transmission properties of the element, numerical simulations based on CST 2020 Microwave Studio are carried out. In the simulations, unit cell boundary condition is set along the x- and y- directions, and normally incident uniform plane wave is used as the excitation source. The equivalent circuit (EC) models of the PIN diode are illustrated in Fig. 2(a) [35]. The capacitance, inductance and resistance are 0.14 pF, 0.4 nH, and 1.5 ohm, respectively. More details about the values of the components can be obtained from the official data sheet. Figure 3 depicts the transmission amplitude and phase of the binary elements. Notably, the amplitude of only one kind of phase coding unit need to be tuned in this design, hence the amplitude modulation unit is only placed on the “0” element, and a F4B substrate of the same dimension as the amplitude modulation unit covers the “1” element to ensure that the overall thickness is consistent. The transmittances of the two elements are higher than 0.8 within the frequency range of 10.38 GHz to 10.82 GHz when the PIN diodes are switched ON, and the amplitude decreases when the forward resistances of the PIN diodes increase with the decreasing forward bias voltage applied on the diodes. When the PIN diodes are switched OFF, the transmission amplitude of the “0” element can be suppressed to lower than 0.1, indicating that the transmission is blocked well. Table 1 shows the transmission amplitude of the “0” element under different bias states (corresponding to different diode forward resistance) of the PIN diodes for x- and y- polarizations at 10.45 GHz. The relationship between the voltage and resistance is obtained from the official datasheet. It can be observed that the transmittance of the element increases with the bias voltage applied on the diodes. The phase difference between the “1” and “0” elements is maintained between ${160^\circ }$ and ${200^\circ }$ from 10.2 GHz to 11 GHz (exactly ${180^\circ }$ at 10.5 GHz) when changing the working states of diodes. In this phase difference interval, the characteristic of opposite phase can be considered stable [21]. Appropriately used inductors can work as AC choke to suppress the resonance on the feeding lines without affecting the transmission characteristics of original resonant structure at desired frequencies [36]. In this design, the Inductors MLG1005S4N7STD25 (4.7 nH) and MLG1005S9N1HTD25 (9.1 nH) from TDK are loaded on the feeding lines behind “0” and “1” units respectively to suppress the undesired resonance. The dashed lines in Fig. 3 illustrate the simulated transmission responses of the unit cell for the polarization along the feeding line. It can be seen that the transmission amplitude and phase of the unit cell impinged by x- and y- polarized EM waves maintain good consistency at about 10.5 GHz, meaning that this design has good polarization stability.
Fig. 3. (a) The amplitude and (b) phase responses of the “1” element and “0” element under different states of PIN diodes. The dashed and solid lines represent the simulated results for x- and y- polarizations.
Table 1. Transmittance of “0” element under different bias states at 10.45 GHz
For a coding metasurface comprised of ${\rm{M}} \times {\rm{N}}$ elements of the same dimension illuminated by plane waves normally, the radiation pattern can be described by the following equation [21],
To achieve the best tunability of the metasurface, genetic algorithm (GA) is exploited to optimized the coding matrix. Here we consider a metasurface composed of 8×8 elements after making a compromise between the requirement of experiment and the time for optimization procedure. In the process of optimization, an initial coding matrix of which “0” elements account for 10% and “1” elements account for 90% is set firstly, and all the constituent elements are arranged randomly. Subsequently, the matrix is upgraded by the operations of selection, crossover and mutation, and the positions and values of arbitrary elements are changed. The fitness function employed to calculate the fitness value of the matrix is expressed as,
The complete geometry of the metasurface comprises a top amplitude modulation metasurface and a bottom phase coding metasurface, as illustrated in Fig. 5(a). We use Matlab software to calculate the transmitted field patterns of the metasurface based on Eq. (1), and then numerical simulations are performed by CST. Figures 5(b)–5(e) exhibit the calculated far field patterns at 10.45 GHz. The simulated 3D patterns excited by y- polarized plane waves normally and their 2D counterparts at 10.45 GHz are depicted in Figs. 5(f)–5(i), 5(n) and 5(o). Both the calculated and simulated results show that the radiation patterns can be continuously controlled through changing the forward resistances of PIN diodes. When the PIN diodes are switched ON, all the elements in the pseudorandom arrangement work and a diffusion-like radiation pattern is invoked due to destructive interference among the lattices. The EM energy is randomly dispersed in multiple directions. Subsequently, increasing the resistances of the diodes can weaken the transmission responses of the “0” lattices, a main beam rises in the normal direction of the metasurface gradually. Finally, switching OFF the PIN diodes blocks the transmission of the “0” lattices, and the radiation fields of all the “1” lattices are superimposed to form a pencil-like beam. The EM energy focuses in the normal direction of the metasurface. We can see the main lobe level increases with increasing the PIN diodes resistances gradually from the 2D radiation patterns intuitively. The simulated responses under x-polarized EM incidences are exhibited in Figs. 5(j)–5(m). The results for x- and y- polarizations show excellent agreement with each other, which demonstrates good polarization stability of this design and is of great importance for practical applications.
Fig. 4. (a) The evolution process of the optimization with GA. (b) The obtained optimal phase coding arrangement.
Fig. 5. (a) The complete geometry of the proposed metasurface. (b)-(e) The calculated radiation patterns based on the analytical model under different working states of PIN diodes at 10.45 GHz. The simulated 3D radiation patterns of the proposed metasurface impinged by (f)-(i) y- and (j)-(m) x-polarized plane waves normally with different PIN diodes loading cases at 10.45 GHz. (n) and (o) The corresponding 2D simulation results (the cut angle is ${\rm{\varphi }} = {90^\circ }$).
4. Fabrication and experiment verification
In order to validate the analytical and numerical investigations, a sample comprising $8 \times 8$ digital lattices was fabricated. Firstly, the metallic patterns of the amplitude modulation metasurface and the phase coding metasurface were etched on the F4B laminates covered by copper with a thickness of 35 ${\rm{\mu m}}$ using standard Printed Circuit Board (PCB) technology. The overall size of the fabricated amplitude modulating metasurface was $242 \times 242{\rm{\;m}}{{\rm{m}}^2}$, while the overall size of the phase coding metasurface was $232 \times 232{\rm{\;m}}{{\rm{m}}^2}$. Note that the areas occupied by the resonant structures of the two metasurfaces were $192 \times 192{\rm{\;m}}{{\rm{m}}^2}$. The copper covered redundant areas of the two metasurfaces provided convenience for connecting the bias lines and fixing the sample. At the second stage, the PIN diodes and the inductors were soldered on the amplitude modulating metasurface using surface-mount technology. Finally, the two metasurfaces were bound together with nylon screws. The photographs of the fabricated sample are exhibited in Fig. 6.
Fig. 6. (a) The front side and (b) rear side of the fabricated amplitude modulating metasurface. (c) The fabricated phase coding metasurface and (d) the complete structure after assembled.
The measurement was conducted in a microwave anechoic chamber, as shown in Fig. 7(a). The sample, transmitting horn antenna, and a DC source were fixed on a rotary platform which could be controlled to rotate from $- {90^\circ }$ to ${90^\circ }$ by computer to implement omnidirectional far-field measurements. The receiving horn antenna was placed about 6 m away from the transmitting antenna and two antennas were connected by a vector network analyzer. The sample connected the DC source to acquire desired bias voltages. It should be noted that the supplied voltages were a little higher than the corresponding voltages given in the official data sheet, because some voltages may be distributed by the elements in the designed bias network.
Fig. 7. (a) The experiment setup. (b)-(d) The measured and simulated radiation patterns under different bias states of PIN diodes.
The measured 2D radiation patterns of the sample at 10.45 GHz is presented in Figs. 7(b)–7(d). When the voltage is set to 0 V, a main lobe can be observed, and its amplitude gradually decreases with the increasing bias voltage. The fabrication tolerance, the overall stability of PIN diodes, and the experiment environment can lead to the differences between the simulations and experiments. Nevertheless, the measured results are in excellent accordance with the simulated responses, and the feasibility of this design is validated.
5. Conclusion
In summary, a strategy based on phase coding modulation and continuous amplitude modulation to fully control the transmitted wave pattern is proposed. With electrically controlling the forward resistances of the PIN diodes on the amplitude modulation metasurface which is placed on the phase coding metasurface, the amplitude responses of specific phase coding elements can be tuned dynamically while the phase responses maintain unchanged, and dynamic radiation pattern steering is achieved. We analyze the concept by the theoretical model, then validate it by numerical simulations and experiments. It is demonstrated that the radiation pattern of the metasurface can be varied from pencil-like transmission to diffusion-like transmission. This work provides a novel and feasible scheme to manipulate the transmitted waves in microwave regime, and is meaningful for manifold applications, such as radio frequency energy harvesting and wireless communication.
Funding
Shenzhen Technology Development Program (JCYJ20180508152233431); National Key Research and Development Program of China (2020YFA0709800); National Natural Science Foundation of China (61971340).
Disclosures
The authors declare that there are no conflicts of interest related to this article.
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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