Radiation-type space-time metasurface for arbitrary beamforming by simultaneous and independent modulation of amplitude and phase for orthogonal polarization

Lixin Jiang; Hao Yang; Yongfeng Li; Wanwan Yang; Yongqiang Pang; Jinming Jiang; Zhe Qin; Mingbao Yan; Yueyu Meng; Lin Zheng; Wenjie Wang; Jiafu Wang; Shaobo Qu

doi:10.1364/PRJ.550482

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Abstract

Programmable metasurfaces are revolutionizing the field of communication and perception by dynamically modulating properties such as amplitude and phase of electromagnetic (EM) waves. Nevertheless, it is challenging for existing programmable metasurfaces to attain fully independent dynamic modulation of amplitude and phase due to the significant correlation between these two parameters. In this paper, we propose a radiation-type metasurface that can realize radiation space-time coding of the joint amplitude-phase. Hence, independent and arbitrary modulation of amplitudes and phases can be achieved for both

x

-polarized and

y

-polarized EM waves. For demonstration, the dynamic beam scanning with ultra-low sidelobe levels (SLLs) is validated. Moreover, we propose a strategy of stochastic coding and non-uniform modulation to suppress the harmonic energy, thereby obtaining the ultra-low sideband levels (SBLs). Prototypes were fabricated and measured, and all simulations and measurements demonstrated the superiority of the proposed strategy. In addition, the proposed strategy is optimization-free and highly integrated, which has unrivaled potential in the field of compact communication systems and radar systems.

1. INTRODUCTION

Metasurfaces [1,2] are two-dimensional structures comprising subwavelength meta-atoms that have demonstrated considerable potential in the modulation of electromagnetic (EM) waves. The modulation of intrinsic EM wave properties, including amplitude, phase, and polarization [3], has enabled the realization of a series of remarkable functions, such as holography [4 –6], circular dichroism [7 –9], vortex beams [10], cloaking [11 –13], and more [14]. In particular, the programmable metasurface [15] is capable of achieving tunable amplitude [16], phase [17], and polarization [18] through the introduction of active devices, thereby facilitating the integration of a variety of EM functions [19].

Moreover, the space-time-coding metasurface (STCM) [20 –22], which employs time modulation, demonstrates enhanced capabilities in the modulation of frequency and polarization [23]. The utilization of STCM has enabled the further realization of a number of sophisticated technologies, including Doppler cloaking [24], radar jamming [25], direction of arrival estimation [26], and spatiotemporal vortex [27,28]. The aforementioned function is frequently accomplished by loading varactor diodes to obtain tunable phase states, which are then combined with space-time coding. The resulting phase is frequently dispersion. Moreover, there is a paucity of research investigating the simultaneous implementation of amplitude and phase space-time coding in metasurfaces.

In contrast to conventional reflection/transmission metasurfaces [29 –32], which rely on an external feeding source, radiation-type metasurfaces [33 –35] reduce the profile of the structure. Some of the reported works have achieved beam scanning [33] and polarization modulation [34] by integrating PIN diodes. These works exhibit advantageous characteristics, including highly precise and customized far-field beamforming [35] and enhanced aperture efficiency [33] compared with conventional T/R metasurfaces. Moreover, the elimination of the need for an external feeding source enables the utilization of radiation-type metasurfaces in compact systems. Nevertheless, the primary focus of these works is on phase modulation, although the attained number of phase states remains limited. The absence of amplitude modulation imposes significant constraints on its capacity to accomplish functions such as ultra-low SLL beam scanning and low scattering. In particular, the fully independent modulation in both amplitude and phase is imperative for energy distribution and wavefront tailoring of EM waves, but remains a challenge. Amplitude and phase modulation of $x$ -polarization and $y$ -polarization was implemented in Ref. [36], but the limited degree of freedom of modulation and the narrow operating frequency band hindered its application. Furthermore, the space-time coding of the joint amplitude-phase has seldom been reported, yet it is crucial for enhancing the modulation ability of the metasurface with respect to center frequencies and harmonics. Some works have also realized amplitude-phase space-time coding for scattering [37], but amplitude-phase space-time coding for radiation is still unexplored. This reported amplitude-phase space-time-coding tends to be single-polarized as well, limiting its application prospects. Furthermore, the suppression of harmonics generated by space-time coding has rarely been investigated.

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In this paper, we propose and experimentally verify a radiation-type amplitude-phase-coded space-time metasurface (RASM). The tunable coding states can be obtained by modulating the switching diodes and varactor diodes integrated into the meta-atom. The amplitude and phase of both $x$ -polarized and $y$ -polarized EM waves can be reconfigured to obtain five coding states by controlling only two voltages: $V_{x}$ and $V_{1}$ (or $V_{y}$ and $V_{1}$ ), as shown in Fig. 1. The stochastic coding of amplitude-phase can disperse harmonic power and thereby reduce SBL. The use of different modulation frequencies for each meta-atom effectively mitigates the spatial superposition of harmonics, thereby reducing the SBL. Amplitude-phase coding easily achieves Chebyshev weighting, realizing dynamic beam scanning with low SLL. Furthermore, the proposed strategy of integrating diodes has a minimal hardware loss, which has enhanced efficiency. Finally, a prototype consisting of $8 \times 8$ meta-atoms was fabricated. Experiments were conducted by generating square wave signals using an arbitrary wave generator (AWG). The experiment and simulation results are in good agreement, indicating the effectiveness of the proposed strategy.

The proposed framework for the RASM.

Figure 1.The proposed framework for the RASM.

2. CONCEPT AND OPERATION PRINCIPLE

A. Theory of Space-Time Coding

Here, it is considered that each meta-atom can realize $n$ stepped phases. The far-field factor for a metasurface with N isotropic meta-atoms can be represented as $F (θ, t) = e^{j 2 π f_{c} t} \sum_{q = 1}^{N} Γ_{q} (t) e^{j (q - 1) k d \sin θ},$ (1)where $k = 2 π / λ_{c}$ is the wavenumber, $λ_{c}$ is the wavelength, and $d$ denotes the distance between two meta-atoms. $Γ_{q} (t)$ is the time-modulated coefficient of the meta-atom, which is a periodic function of time, i.e., $Γ_{q} (t) = Γ_{q} (t + T_{0})$ . During a modulation period $T_{0}$ , $Γ_{q} (t)$ consists of $L$ rectangular pulse functions: $Γ_{q} (t) = \sum_{n = 1}^{L} a_{q}^{n} e^{j β_{q}^{n}} U_{q}^{n} (t) (0 < t < T_{0}),$ (2) $U_{q}^{n} (t) = {\begin{matrix} 1 & (n - 1) τ \leq t < n τ \\ 0 & Others \end{matrix},$ (3)where $a_{q}^{n}$ and $β_{q}^{n}$ are the static amplitude and phase of the $q$ -th meta-atom. $τ = T_{0} / L$ is the width of the rectangular pulse. For the sake of simplicity in presentation, all subsequent symbols will be presented without the subscript “ $q$ .” Decomposing $U_{q}^{n} (t)$ into Fourier series, $U^{n} (t) = \sum_{m = - \infty}^{+ \infty} c^{m} e^{j 2 π m f_{0} t},$ (4) $c^{m} = f_{0} \int_{0}^{T_{0}} U^{n} (t) e^{- j 2 π m f_{0} t} d t,$ (5)where $f_{0} = 1 / T_{0}$ is the switching frequency. Hence, the Fourier series coefficient $r^{m}$ of $Γ_{q} (t)$ can be obtained [21]: $r^{m} = \sum_{n = 1}^{L} a^{n} \frac{\sin (π m / L)}{π m} \exp (j β^{n} - j π m (2 n - 1) / L), m \neq 0,$ (6) $r^{0} = \sum_{n = 1}^{L} \frac{a^{n} \exp (j β^{n})}{L} .$ (7)

In this article, two states (0, 1) for $a^{n}$ and four states (0°, 90°, 180°, 270°) for $β^{n}$ are designed for each meta-atom. Switching between states is accomplished by varying the two voltages, which conduct different diodes, as shown in Fig. 1. Here, the varactor diode is shown in black, and the PIN diode is in red. The PIN diodes used to adjust 0° and 90° are loaded into the structure. In contrast, the PIN diodes used to adjust 0° and 180° are loaded on the voltage inputs and therefore do not affect the EM performance of the meta-atom. Hence, the meta-atoms can obtain arbitrary equivalent amplitudes and phases by judicious design of the time-coding sequence. According to Eq. (7), the equivalent amplitude and phase at the center frequency $f_{c}$ are independent of the order of the time-coding sequence. The length of $L$ determines the accuracy of the equivalent magnitude and phase.

B. Principle of Beam Scanning

The equivalent phase achieved at the center frequency must be between $\min (β^{n})$ and $\max (β^{n})$ according to Eq. (7). Hence, the time-coding sequence employs only two-phase codes for the target equivalent phase $β$ : $β^{n, 1} \leq β < β^{n, 2}, β^{n, 2} = π / 2 + β^{n, 1} .$ (8)

That is, when $L$ is determined, an arbitrary equivalent phase $β$ can be realized by designing the ratio of $β^{n, 1}$ and $β^{n, 2}$ in the time-coding sequence: $R_{1} = Number (β^{n, 1}), R_{2} = Number (β^{n, 2}) .$ (9)

As shown in Eq. (6), there is a strong correlation between the equivalent amplitude and phase of the center frequency $f_{c}$ and that of the harmonics. When performing beam scanning at the center frequency, achieving the target phase using a time-coding sequence is accompanied by undesired harmonics, resulting in high SBL [38]: $MAX (SBL) = \underset{m \in Z, m \neq 0}{MAX} (abs (\sum_{q = 1}^{N} r^{m} e^{j (q - 1) k d \sin θ} e^{j 2 π (f_{c} + m f_{0}) t})) .$ (10)

High SBLs have an adverse effect on the transmission of the center frequency. The SBL can then be reduced by stochastically ordering the time-coding sequences while maintaining the phase distribution ratio. Furthermore, if the same $f_{0}$ is utilized for each meta-atom, it generates identical harmonics $f_{c} + m f_{0}$ . The combination of the harmonics from the meta-atoms results in a significant increase in SBL [39]. To simplify the design and reduce the SBL, each meta-atom is kept with the same $L$ but different $τ_{q}$ . Currently, the largest SBL is considered to be the max equivalent amplitude of harmonics. As a result, a smaller SBL can be obtained: $MAX (SBL) = \underset{m \in Z, m \neq 0}{MAX} (abs (r_{q}^{m})) .$ (11)

Furthermore, even though $τ$ has different values, the harmonic power still accumulates at common multiples of $τ_{q}$ . If the common multiple of $τ_{q}$ of any two meta-atoms is much larger than $τ_{q}$ , the harmonic components will accumulate at higher frequencies, reducing the SBL. Hence, $τ_{q} = (1 + 0.09 q) μ s$ is chosen here. In addition, SBL is further degraded because phase gradients are formed at harmonics when beam scanning is performed. Moreover, the SBL is further reduced because the harmonics are deflected in a different direction when beam scanning is performed at the center frequency. This is due to the formation of a phase gradient at harmonics, which differs from that formed at the center frequency.

In addition, according to Eq. (7), the equivalent amplitude at the equivalent phase of $β$ is $a$ : $a = \frac{\sqrt{R_{1}^{2} + R_{2}^{2}}}{L} .$ (12)

When the target phase differs, its corresponding equivalent amplitude also differs, which can result in a large SLL. Here, the identical equivalent amplitude is obtained by introducing a state $a = 0$ in the time-coding sequence: $a_{MAX} = \underset{q \in N}{MIN} (a_{q}) .$ (13)

Thus, the time-coding sequence design steps can be summarized as follows.

Step 1: Go through all the target phases $β$ and find $a_{MAX}$ .

Step 2: Based on the amplitude of the target phase, the proportions of $β^{n, 1}$ , $β^{n, 2}$ , and non-radiating states in the time-coding sequence were calculated ( $R_{0}$ , $R_{1}$ , $R_{2}$ ), where $R_{0}$ represents the number of non-radiating states and $R_{0} + R_{1} + R_{2} = L$ .

Step 3: Randomize the ordering of the three codes and take different $τ_{q}$ .

Furthermore, according to Ref. [40], modulation efficiency $η$ and modulation loss $δ$ are introduced to evaluate the proposed strategy: $η = \frac{P_{T}}{P_{0}},$ (14) $δ = - 10 \lg (η),$ (15)where $P_{0}$ is the total mean power radiated by uniformly excited RASM and $P_{T}$ is useful mean power radiated by time-modulated RASM at center frequency. In fact, there are two principal aspects of RASM’s loss $δ$ : firstly, there is the loss of hardware $δ_{h}$ , which encompasses components such as PCBs and diodes; and secondly, the losses $δ_{t}$ caused by time coding, i.e., unwanted radiation outside the target frequency range.

3. RECONFIGURABLE META-ATOM DESIGN

In this article, a meta-atom with a tunable 2-bit phase state is designed by integrating varactors and switching diodes in the radiation layer and phase-shift network (PSN). The meta-atom operates in the C-band and the switching of the 2-bit phase is realized by controlling only two voltages. The meta-atom structure is shown in Fig. 2(a) and consists of a radiating layer, a varactor diode feeding layer [Fig. 2(d)], a metallic ground, a switching diode feeding layer [Fig. 2(e)], and a power division network layer [Fig. 5(a)] from top to bottom. The radiation layer is isotropic and connected to the underlying feeding layer through four metallized vias in four directions. The center hole serves as both the negative terminal of the biasing network and the feed source connected to PSN. Note that there is only one layer of 0.2 mm thick bonding plate R4450B between the second feeding layer and ground, which has minimal impact on the radiation performance. There are four varactor diodes and 2.2 nH inductors in the $x$ -direction and $y$ -direction, respectively. The negative of the varactor oriented in the $+ y$ -direction and the positive of the varactor oriented in the $- y$ -direction are connected to the middle via. Upon the application of an input voltage $V_{y}$ , each varactor diode is connected in series with a PIN diode with the same positive and negative directions, as shown in Fig. 1. The $x$ -direction varactor diode is connected to the voltage $V_{x}$ in the same way. The varactor diode used is the SMV1405-079LF, which can be simulated equivalently as a series connection of a 0.7 nH inductor, a $0.8 Ω$ resistor, and a variable capacitor $c$ (0.63–2.67 pF).

Figure 2.Schematic diagram of the meta-atom structure. (a) 3D structural diagram, $h_{1} = 3.248 mm$ , $h_{2} = 0.2 mm$ , $h_{3} = 0.5 mm$ . (b) The front view of the meta-atom. The optimized geometrical parameters are as follows: $p = 25 mm$ , $l_{1} = 10 mm$ , $l_{2} = 6 mm$ , $l_{3} = 3 mm$ , $l_{4} = 7.4 mm$ , $l_{5} = 2 mm$ , $w_{1} = 4 mm$ , $w_{2} = 5 mm$ , $w_{3} = 1.9 mm$ , $w_{4} = 3.4 mm$ , $g_{1} = 0.7 mm$ , $g_{2} = 0.1 mm$ , $g_{3} = 0.1 mm$ , $k_{1} = 0.2 mm$ , $r_{1} = 0.8 mm$ . (c) The phase shift network. The biasing layer for (d) varactors and (e) PIN diodes.

Subsequently, the physical mechanisms underlying the polarization and phase modulation were revealed through an analysis of the surface currents within the meta-atom. By varying the varactor in different directions, a loop surface current is formed that radiates through the metal sheets in various directions, as shown in Fig. 3. The meta-atom radiates $x$ -polarized EM waves when the varactor in the $x$ -direction is conducting, and $y$ -polarized EM waves when the varactor in the $y$ -direction is conducting. The surface currents in these two cases oscillate along the $x$ -direction and $y$ -direction, as shown in Figs. 3(a)–3(d). Additionally, when $V_{x} = 0$ and $V_{y} = + v_{0}$ , the diode in the $+ y$ -direction conducts, and the meta-atom radiates $y$ -polarized EM waves. Similarly, when $V_{x} = 0$ and $V_{y} = - v_{0}$ , the diode in the $- y$ -direction conducts, and the meta-atom radiates $y$ -polarized EM waves with a 180° phase difference. The surface currents in these two cases oscillate along the $+ y$ - and $- y$ -directions, respectively, as demonstrated in Figs. 3(c) and 3(d). An intrinsic phase shift of 180° can be obtained due to the inversion of the relative spatial position [41].

Figure 3.The simulated surface currents at 6.4 GHz. (a) $V_{x} = 0$ and $V_{y} = - v_{0}$ . (b) $V_{x} = 0$ and $V_{y} = v_{0}$ . (c) $V_{x} = - v_{0}$ and $V_{y} = 0$ . (d) $V_{x} = v_{0}$ and $V_{y} = 0$ . (e) $V_{1} = - v_{1}$ . (f) $V_{1} = + v_{1}$ .

To achieve more phase shifts, an additional PSN is designed at the bottom of the structure, as shown in Fig. 2(c). The PSN connects the power division network and the feeding hole through two cross-finger structures to isolate AC and DC signals, respectively. Here, two microstrip lines of different lengths are designed to generate a 90° phase difference. Two sets of diodes are soldered to the power division end and the feeding hole. The inductor with a value of 30 nH in blue color is used to isolate the feed network from the PSN. When $V_{1} = - v_{1}$ , the phase delay is 0°, and the phase delay is 90° when $V_{1} = + v_{1}$ . The simulated surface current shown in Figs. 3(e) and 3(f) effectively demonstrates this design. However, when a specific microstrip line is activated, a strong surface current is also induced on the other microstrip line. Nevertheless, due to the diode obstruction, the surface current can only oscillate and cannot propagate to the feeding hole. Additionally, the meta-atom does not radiate when all bias voltages are 0 V. Hence, the meta-atom can switch between two polarizations and possess four phases by control voltages $V_{x}$ , $V_{y}$ , and $V_{1}$ , as shown in Table 1.Table 1.

Operation Status of the Meta-Atom

$V_{x}$	$V_{y}$	$V_{1}$	Coding States
0	0	0	0
0	$- v_{0}$	$- v_{1}$	$y - 0 °$
0	$- v_{0}$	$+ v_{1}$	$y - 90 °$
0	$+ v_{0}$	$- v_{1}$	$y - 180 °$
0	$+ v_{0}$	$+ v_{1}$	$y - 270 °$
$+ v_{0}$	0	$- v_{1}$	$x - 0 °$
$+ v_{0}$	0	$+ v_{1}$	$x - 90 °$
$- v_{0}$	0	$- v_{1}$	$x - 180 °$
$- v_{0}$	0	$+ v_{1}$	$x - 270 °$

Rigorous modeling and simulation are performed in CST Microwave Studio to verify the performance of the meta-atom. The varactor and switching diode are modeled as equivalent circuits. The simulation performance for the four states when radiating $y$ -polarized EM waves is given in Fig. 4. Here, the initial ‘0’ in state ‘01’ denotes the state of $V_{y}$ , while the second ‘1’ denotes the state of $V_{1}$ . The value ‘0’ represents a negative voltage, and ‘1’ represents a positive voltage. The increase in return loss for states 00 and 10 is due to stronger surface currents being excited on the other microstrip line when $V_{1} = - v_{1}$ . However, simulations indicate that the realized gain is identical for all four states, and the phase difference between neighboring states is strictly 90°, which agrees perfectly with the theoretical analysis. The 3 dB bandwidth of the proposed metasurface is 6.275–6.7 GHz, which is also the operating band. Additionally, the radiation patterns of the four states depicted in Fig. 4(c) are identical. The phases exhibit a constant phase difference of 90° within the angular range of $- 90 °$ to $+ 90 °$ . It should be noted that the meta-atom performances are identical for $x$ -polarization and $y$ -polarization since the proposed meta-atom is entirely symmetric with regard to the $x$ -axis and $y$ -axis. The simulated performance of the meta-atom for $x$ -polarization is given in Appendix A. Subsequently, $y$ -polarization is employed as a demonstration to validate the proposed strategy.

Figure 4.The simulated performance of the meta-atom. (a) The simulated $S_{11}$ in four states. (b) The realized gain and phase varying with frequency. The simulated radiation pattern in four states: (c) realized gain and (d) phase. The measured (e) $S_{11}$ and (f) realized gain and phase varying with frequency for $y$ -polarization when all meta-atoms maintain the same state.

Finally, a prototype comprising $8 \times 8$ meta-atoms was fabricated. Each meta-atom was fed by a power division network of equal amplitude and phase, as shown in Figs. 5(a) and 5(b). The simulated S-parameters are shown in Figs. 5(c) and 5(d). The value of $S_{11}$ is less than $- 15 dB$ , while the values of $S_{21}$ and $S_{31}$ are identical, equaling approximately $- 3.4 dB$ . Hence, the loss from the power division network is about 0.4 dB. Additionally, each meta-atom was followed by an independent PSN for time modulation. Furthermore, we measured the realized gain of the RASM when all meta-atoms share the same state, as shown in Figs. 4(e) and 4(f). The RASM possesses good gain across a broad frequency range, with a phase difference of 90° in the normal direction, as demonstrated by the phase difference of the meta-atom. It is observed that in the vicinity of the side frequencies (6.1 GHz and 6.8 GHz), the $S_{11}$ value is considerably less than $- 10 dB$ , yet the realized gain is not particularly elevated. This phenomenon may be attributed to the coupling between the meta-atoms, the power division network, and the feeding network, which results in a significant reduction in the $S_{11}$ . However, the radiation pattern is poorly oriented, resulting in a relatively low gain in the normal direction. Furthermore, the measured gain exhibits a decrease at specific frequency points (6.55 GHz), which may be attributable to the varying degree of coupling between the power division network and the feeder at different frequencies. It is also possible that the gain in the normal direction is reduced due to poor directionality of the radiation.

Figure 5.(a) The bottom power division network and PSN. (b) The detailed structure of the power division network, and $d_{1} = 1.9 mm$ , $d_{2} = 0.75 mm$ , $d_{3} = 1.6 mm$ , $d_{4} = 1.734 mm$ , $d_{5} = 1.06 mm$ , $q_{1} = 2.94 mm$ , $q_{2} = 4 mm$ , $q_{3} = 12.3 mm$ . (c) $S_{11}$ and (d) $S_{21}$ and $S_{31}$ of the power division network.

4. REALIZATION OF BEAM SCANNING

The following section exhibits how to achieve beam scanning. Using the theory presented in Section 2, it is possible to design the desired phase distribution for any scan angle. Specifically, the required control voltage signals can then be obtained based on Table 1 to achieve beam scanning.

A. Time-Coding-Enabled Beam Scanning

The relationship between the ideal phase gradient and the angle of the beam scanning is $β_{x} = - (q - 1) k d \sin (θ) \cos (φ), β_{y} = - (q - 1) k d \sin (θ) \sin (φ),$ (16)where $β_{x}$ ( $β_{y}$ ) represents the phase difference in the $x$ - ( $y$ -)-direction. As a demonstration, a one-dimensional beam scanning is performed, where $φ = 0 °$ . The target angle $θ$ is set to 10°, 20°, 30°, 40°, 50°, and 60°; $f_{c} = 6.4 GHz$ was chosen for demonstration in the following discussion. The target phase distribution at different scanning angles is initially calculated based on Eq. (16), as illustrated in Fig. 6(a). Here, $θ = 10 °$ was first chosen as an illustration, and the equivalent amplitudes of different meta-atoms were calculated for different values of $L$ , as shown in Fig. 6(c). As $L$ increases, the difference in magnitude between the meta-atoms decreases, and the equivalent amplitudes of each meta-atom are almost equal when $L$ is greater than 500. In addition, Fig. 6(d) demonstrates that the disparity between the equivalent and desired phases diminishes as $L$ increases, with negligible alteration when $L$ exceeds 1000. Increasing $L$ enhances the stability of the equivalent amplitude and improves the accuracy of the equivalent phase. However, the benefits of increasing $L$ beyond 1000 are not obvious. Figure 7 shows the calculated values of MAX(SBL) for different $L$ . Obviously, an increase in $L$ also reduces MAX(SBL). This is because the harmonic energy is more uniformly distributed with an increase in $L$ . However, an excessively large $L$ can create significant design and control challenges, as well as increase control errors. Therefore, $L = 50$ and $L = 1000$ were used for comparison in later designs to achieve stable amplitude, precise phase, and lower SBL.

Figure 6.(a) The ideal phase distribution corresponding to the scanning angle. (b) The ideal amplitude distribution for different SLLs. (c) The amplitude difference between the actual generated amplitude and the target amplitude for different $L$ . (d) The phase difference between the actual generated phase and the target phase for different $L$ .

Figure 7.MAX(SBL) that varies with $L$ .

The time-coding sequences required for each meta-atom at each scanning angle are determined using the time-coding sequence design steps outlined in Section 2. Figure 8(a) gives the time-coding sequence for scanning angles 10°. Based on the designed time-coding sequence, the radiation pattern of the center frequency is calculated, as shown in Fig. 8(b). The gain at the main lobe decreases as $θ$ increases. This is mainly caused by the increase of the SLL with the increase of $θ$ . In particular, a larger SLL appears at its mirror position after $θ > 50 °$ . For beam scans up to 50°, however, the SLL is $- 13.5 dB$ , consistent with theoretical values. To achieve a scanning beam with SLL less than $- 30 dB$ , Chebyshev amplitude weighting was employed, as shown in Fig. 6(b). The target scan angles are 10°, 20°, 30°, and 40°. Figure 8(d) displays the radiation pattern, which exhibits a large SLL for angles greater than 40°. This is mainly due to the limited number of meta-atoms. In addition, some of the sidelobes exceed $- 30 dB$ , which is mainly due to the fact that the equivalent amplitude does not strictly satisfy the Chebyshev distribution. Nevertheless, each designed time-coding sequence achieves the desired beam scan, indicating the effectiveness of the proposed strategy. It is noteworthy that the coding for $SLL = - 30 dB$ introduces an excess of “none” states, which results in a reduction of the radiated gain. The maximum gain of the code of $SLL = - 13.5 dB$ is approximately 0.8 dB greater than the maximum gain of $SLL = - 30 dB$ .

Figure 8.The time-coding sequences for $θ = 10 °$ with (a) $SLL = - 13 dB$ and (c) $SLL = - 30 dB$ . The simulated radiation patterns with (b) $SLL = - 13 dB$ and (d) $SLL = - 30 dB$ .

B. Time Modulation Efficiency and SBL

Without loss of generality, the MAX(SBL) is discussed when $θ = 10 °$ . When sequential distribution is used, i.e., there are no multiple jumps between coding states in one period. Thus, the sequential distribution results in the accumulation of a significant amount of low-order harmonic power. When using a stochastic distribution, the harmonic power is distributed more evenly, achieving $MAX (SBL) = - 28 dB$ , and when using a sequential distribution, achieving $MAX (SBL) = - 17 dB$ , as shown in Fig. 9(a). To illustrate the benefits of employing distinct modulation speeds for each meta-atom, the power spectra generated using identical modulation speeds and varying modulation speeds $τ_{q} = (1 + 0.09 q) μ s$ are presented in Fig. 9(b). It is evident that SBL can be more effectively mitigated by employing varying modulation speeds. The use of varying modulation speeds enables the harmonic energy to distribute more evenly across the frequency spectrum. Although different $τ_{q}$ are used to distribute the harmonic powers as uniformly as possible, harmonics of different orders from different meta-atoms may still be synthesized in space. Thus, it should be noted that Eq. (11) represents an ideal scenario. To compare the SBL when achieving a low SLL, we calculated the power spectrum for $SLL = - 30 dB$ . The higher $SBL = - 25 dB$ is obtained when $SLL = - 30 dB$ . Nevertheless, the SBL remains at a relatively low level in this instance. A longer $L$ was used to achieve a lower SBL, as shown in Fig. 9(d). When $L = 1000$ , $SBL = - 38 dB$ . And SBL can be further reduced as $L$ increases.

Figure 9.(a) Power spectrum corresponding to stochastic and sequential distributions of time-coding sequences. (b) The power spectrum for modulation periods $τ_{q} = [1 + 0.09 (q - 1)] μ s$ and $τ_{q} = 1 μ s$ . (c) The power spectrum for $SLL = - 13.5 dB$ and $SLL = - 30 dB$ . (d) Power spectrum for $L = 50$ and $L = 1000$ .

The time modulation efficiency $η_{t}$ and time modulation loss $δ_{t}$ of the proposed strategy are further evaluated. Given that the equivalent amplitude is determined for a fixed SLL, the equivalent phase and scanning angle exert minimal influence on the value of $η_{t}$ . Additionally, $L$ and $τ$ only determine the frequency of the harmonics and have minimal impact on $η_{t}$ . Therefore, the factor that has the greatest impact on $η_{t}$ should be the equivalent amplitude. As the value of SLL decreases, the number of “none” states is increased, which results in a reduction in efficiency $η_{t}$ . The detailed discussion about the loss and efficiency will be in the subsequent section.

5. EXPERIMENTAL VALIDATIONS

This section presents measurement results that demonstrate the effectiveness of using reconfigurable meta-atoms to achieve amplitude-phase-coded TMA. A prototype with $8 \times 8$ meta-atoms was fabricated. Figures 10(a) and 10(b) show the front and back views.

Figure 10.The (a) front and (b) back of the prototype. (c) The measurement setup.

A. Measurement Setups

Measurements are conducted in the microwave chamber. Measurements were performed using the following parameters:

•center frequency $f_{c} = 6.2$ , 6.4, and 6.6 GHz,
• $θ = 10 °$ , 20°, 30°, and 40°,
• $τ_{q} = (1 + 0.09 q) μ s$ ( $q = 1, 2, \dots, 8$ ),
• $L = 1000$ ,
• $SLL = - 13.5 dB$ .

The time-coding sequences for 10°, 20°, 30°, and 40° beam scanning are obtained according to the proposed method outlined in Section 2. The control voltage signals of the time-coding sequences can be easily generated using an AWG without the need for complex external control systems. Two key measuring devices are employed in the measurements, including the Agilent vector network analyzer (VNA) E8363B and spectrum analyzer (SA) N9000B. The VNA is used to excite the prototype and to measure the radiation patterns. The VNA is always configured to a single frequency point $f_{c}$ excitation. The SA is used to measure and analyze the received signal; the center frequency of the SA is set to $f_{c}$ and the bandwidth is 3 MHz. The prototype is placed on the center table, as depicted in Fig. 10(c).

Given that the prototype operates within the center frequency, it is unnecessary to measure radiation patterns of harmonic. Consequently, the VNA is the sole equipment for measuring the radiation patterns at center frequency. When measuring the radiation patterns, the prototype and receiving meta-atoms are connected to a VNA. The excitation was set to 6.2 GHz, 6.4 GHz, and 6.6 GHz. The receiving meta-atom moves along a slide to receive radiation EM waves at intervals of 1°, as shown in Fig. 10(c).

When measuring the power spectrum, the scanning angle $θ$ was set at 10° in order to validate the SBL suppression. The frequency span was set to 8 MHz. The number of points was set to the lowest possible value supported by the SA. The angle between the receiving meta-atom and the prototype normal has been set to 10°, and the receiving meta-atom is connected to an SA. The prototype was connected to a VNA, with excitation frequencies set to 6.2 GHz, 6.4 GHz, and 6.6 GHz. The radiation EM waves from the prototype were analyzed by SA.

B. Measurement Results

The radiation patterns for the measurement are shown in Figs. 11(a)–11(c). All scanning angles are in agreement with the theoretical calculations. As the scan angle increases, the gain decreases in accordance with the simulation results. Furthermore, at a scan angle of 10°, the gain of 6.2 GHz is 0.58 dB smaller than that of 6.4 GHz, and the gain of 6.6 GHz is 1.15 dB smaller than that of 6.4 GHz. The slight deviations in the angles and gains may be due to sample fabrication errors and differences in the dielectric constants of the fabricated substrates. The measurement results of beam scanning demonstrate the effectiveness of both the designed reconfigurable meta-atom and the proposed time-coding modulation method.

Figure 11.Measured beams scanning at (a) 6.2 GHz, (b) 6.4 GHz, and (c) 6.6 GHz for $SLL = - 13.5 dB$ . Measured time-modulated power spectrum of the prototype with $SLL = - 13.5 dB$ , $θ = 10 °$ , and $L = 1000$ at (d) 6.2 GHz, (e) 6.4 GHz, and (f) 6.6 GHz.

Figures 11(d)–11(f) depict the power spectrum of the measurement, which is in accordance with the calculated result. The SBLs at 6.2 GHz, 6.4 GHz, and 6.6 GHz are $- 32 dB$ , $- 33 dB$ , and $- 35 dB$ , respectively. The measured results are 5 dB worse than the simulated results. This discrepancy may be attributed to the fact that the modulating voltage waveform is not a strict step waveform with the addition of diodes. In conclusion, the results of the measurement demonstrate that the designed reconfigurable RASM and the proposed time-coding modulation method are capable of effectively suppressing SBL. The low SBL ensures the broadband operation of the TMA.

The proposed strategy of integrating varactor and switching diodes enables the TMA to achieve the four states 0, $\exp (j 0)$ , $\exp (j π / 2)$ , $\exp (j π)$ , and $\exp (j 3 π / 2)$ without requiring a large number of external phase shifters and attenuators. The power divider and phase-shifted structure proposed are designed to be integrated on a PCB board in a highly integrated manner. The measured gain when the RASM is uniformly excited (i.e., all meta-atoms remain in the same state) has been given in Fig. 4(f). Given that the gain is not consistent across the four states, we have selected the mean gain of 15.8 dB at 6.4 GHz as an illustration. The measured gain at 6.4 GHz with a scanning angle of 10° and $SLL = - 13.5 dB$ is 12.7 dBi. Therefore, according to Eqs. (14) and (15), loss and efficiency are 3.1 dB and 48.9%, respectively. It should be noted that the calculation results do not account for the influence of hardware, as the measured gain of 15.8 dB generated by uniform excitation still incorporates hardware losses. Hence, $δ_{t} = 3.1 dB$ and $η_{t} = 48.9 %$ . Furthermore, the hardware loss $δ_{h}$ is difficult to measure experimentally since the proposed strategy is highly integrated. However, these losses can be evaluated through simulation and device datasheets. Here, the principal hardware losses are attributable to the switching diodes and power division networks on the PCB board [42], which amounts to approximately $δ_{h} = 0.89 dB$ (0.4 dB from the power division networks and 0.49 dB from the switching diodes [43]). Hence, the total efficiency is 39.9%. In addition, we evaluate the aperture efficiency of the arrays. The measured aperture efficiencies $η_{a}$ for beam scanning angles of 10°, 20°, 30°, and 40° are 8%, 7.6%, 6.6%, and 6.5%, respectively. The main reason for the reduced aperture efficiency is the loss resulting from the time modulation, which can be compensated for by increasing the input power.

Table 2 provides a comprehensive comparison of some of the published work with ours. It is evident that the proposed space-time-coding method combining stochastic coding and non-uniform modulation can achieve lower SBLs and also lower SLLs. Simultaneously, higher radiation efficiency is achieved by using only diodes.Table 2.

Performance Comparison

Ref.	$f_{c}$	$f_{0}$	SBL (dB)	SLL (dB)	$δ_{t}$ (dB)	$δ_{h}$ (dB)	$η_{t}$ (%)	$η$ (%)
[44]	1.16 GHz	21.9 kHz	−19	−40	1	5	79.4	25
[38]	17 GHz	500 kHz	−30	−36.5	3	4.8	50	16.6
[45]	2.45 GHz	10 kHz	−24.1	−30	1	4	80	31.6
[46]	3.25 GHz	100 kHz	−28	−30	1	3	78	39.8
[47]	2.6 GHz	100 kHz	−14	−21	2.5	3	75	37.5
[48]	9 GHz	500 kHz	−31.4	−13.5	2.88	3.4	51.5	23.6
Proposed	6.4 GHz	$\approx 1 MHz$	−38	−30	3.1	0.89	48.9	39.9

6. CONCLUSION

In this paper, we proposed an RASM with low hardware loss and low hardware complexity. The strategy proposed for employing varactor and switching diodes is not only highly integrated but also hardware-simple and low-cost. Beam scanning with low SLL is effectively achieved through the use of stochastic time-coding sequences and non-uniform modulation frequencies. The proposed strategy effectively suppresses SBL without the aid of an optimization algorithm. Prototypes were fabricated and measured. The measurement results are in good agreement with the theoretical calculations, both proving the feasibility of the proposed strategy. The strategy proposed can be readily extended to metasurfaces operating at high frequencies. Furthermore, the straightforward control and unnecessary need for design optimization make this approach highly promising for a communication and radar system of real-time, cost-effective, and compact beam scanning applications.

APPENDIX A: SIMULATION AND MEASUREMENT RESULTS FOR x-POLARIZATION

x

Figure 12.The simulated (a) S₁₁ and (b) realized gain and phase varying with frequency for $x$ -polarization. (c) Measured beam scanning at 6.4 GHz for $x$ -polarization with $SLL = - 13.5 dB$ . (d) Measured time-modulated power spectrum of the prototype for $x$ -polarization with $SLL = - 13.5 dB$ and $θ = 10 °$ .

APPENDIX B: INFLUENCE OF AMPLITUDE MODULATION

SLL = - 13 dB

Figure 13.The equivalent amplitude varying with the number of “none” states.

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