Reconfigurable intelligent surfaces (RISs), which developed from metasurfaces, are two-dimensional artificial electromagnetic materials which can be assembled in the wireless channel to improve or even customize the wireless channel by changing the environment of electromagnetic (EM) wave propagation in space (Basar et al., 2019) (Wu and Zhang, 2019) (Di Renzo et al., 2020) (Dai et al., 2020) (Sur and Bera, 2021). In recent years, RISs have attracted great research interest in the wireless communication community due to their great application potential. Metasurfaces, which have strong abilities to manipulate the EM waves, have also experienced a rapid development from analog to digital and from untunable to programmable (Cui et al., 2014) (Jing et al., 2019) (Ma et al., 2019) (Jing et al., 2019) (Cui et al., 2020). Therefore, the digital and programmable metasurfaces are important platforms to realize RIS-based wireless communication.

The proposal of the convolution theorem (Cui et al., 2016a) and the addition theorem (Wu et al., 2018) make it possible for RISs to form more advanced beam patterns. However, only the phase responses of the elements are considered while their amplitude responses are ignored in these metasurface designs (Cui et al., 2014) (Cui et al., 2016b) (Chen et al., 2018) (Wu et al., 2018) (Chen et al., 2019) (Liu et al., 2020) (Zhang et al., 2020) (Zhao et al., 2020) (Chen et al., 2021) (Huang et al., 2021) (Gao et al., 2021). In Ref. (Bao et al., 2019) (Rajabalipanah et al., 2019), both the amplitude and phase responses of the element are taken into consideration at the same time, thus forming a more complex multiple beams with controllable deflection angles and power intensities.

However, most of the reported metasurfaces with independent control of amplitude and phase are not programmable (Bao et al., 2019) (Rajabalipanah et al., 2019). Liao et al. (2021) proposed a PIN-diode-based 1-bit programmable element in which one PIN-diode was used to achieve two states with a 180° phase difference, and one PIN-diode was used to achieve variable attenuation of reflection amplitude. The proposed element in Liao et al. (2021) only realized symmetrical beams with large sidelobes due to the 1-bit phase accuracy. Li et al. (2022) proposed a programmable element with independent controls of transmission amplitude and phase, but its complicated structure makes manufacturing difficult. And Dai et al. (2018) realized the independent control of the amplitude-phase by introducing time dimension into the coding sequences, which is only effective for high-order harmonics.

In this article, we propose a programmable element whose reflection amplitude and phase can be jointly controlled by its own embedded PIN-diode and varactor. Three states of reflection amplitude and four states of reflection phase can be obtained by changing the operating states of the PIN-diode and varactor. In addition, numerous metallic vias are introduced in the programmable element to maintain a stable reflection amplitude and phase responses under the illumination of transverse magnetic (TM) waves with the incident angle of 0°–60°. Finally, in order to verify the performance of the proposed RIS element, the independent control of the deflection angles and power intensities of the dual-beam scattering patterns is realized by the addition theorem of complex reflection coefficients.

The proposed programmable element is a typical double-layered metal structure and can be fabricated by Print Circuit Board (PCB) technology. Figure 1 shows the schematic of the RIS array and its close-up view of programmable elements. Figure 2 shows the three-view of the programmable element labeled with structure parameters. F4B substrate ( tan δ = 0.001 , ε r = 2.65 ) with a thickness of 3 mm is used to isolate the top and bottom metal layers. The bottom layer with a complete metal ground is used as a reflector plate. The top metal layer of the element is mainly composed of three patches with a thickness of 0.035 mm.

A PIN-diode and a varactor connect the patches over the narrow slot between the three main surface patches. The PIN-diode (SMP1321-040LF) can be modeled as a series connection of a tunable resistor R _PIN and an inductor L _PIN (0.27–0.36 nH). When the forward direct current (DC) decreases from 100 mA to 100 uA, the R _PIN increases from 0.46 to 19.7 Ω. The varactor (SMV1405-079LF) can be modeled as a series connection of a tunable capacitor C _Var, a resistor R _Var (0.63 Ω), and an inductor L _Var (0.7 nH). When the reverse DC voltage increases from 0 to 30 V, C _Var decreases from 2.6 to 0.6 pF. The DC feeding lines are designed for the PIN-diode and varactor to set desired working states. The thin metallic strip on the top layer serves as a DC ground, which crosses the element and connects the adjacent element. There are also thin metal strips going through the two larger patches. In such a design of DC feeding lines, all elements along the x-axis direction work in the same state for simplifying the DC control circuit to some extent.

Liang et al. (2021) proposed a method to decrease angular sensitivity by introducing metallic vias between adjacent elements. The dielectric discontinuity caused by the metallic vias destroys the original EM wave propagation mode and builds a more stable propagation mode. Considering the machining accuracy and approximate effect, metallic vias with a diameter (D) of 0.3 mm and a spacing (S) of 0.3 mm are drilled in the dielectric substrate. Other dimensional parameters in Figure 2 are Px = 9.5 mm, Py = 17.6 mm, L1 = 8.7 mm, L2 = 8.4 mm, L3 = 1.7 mm, L4 = 1 mm, L5 = 1.7 mm, W1 = 3.7 mm, W2 = 2.4 mm, W3 = 1.9 mm, W4 = 3 mm, W5 = 0.4 mm, W6 = 1.9 mm, and H = 3 mm.

The equivalent circuit model theory can be used to explain the operating mechanism of the proposed programmable element (Liang et al., 2021) (Vendik and Nikol, 2001). As shown in Figure 3, the element can be regarded as the load terminal when it is illuminated by a plane wave. The internal resistance of free space is η 0 = 377 Ohm. Three parallel capacitors, C ₁, C _2, and C ₃, are formed between the three main surface patches. The grounded dielectric substrate operates as a transmission line with a terminal short-circuit, and its equivalent impedance can be calculated as (Pozar, 2005) (Yu et al., 2011): Z a = j η 0 ε r tan 2 π f ε r H c (1)

in which j is the imaginary unit.   ε r and H are the relative permittivity and the thickness of the dielectric substrate, respectively. f is the frequency of the incident EM wave, and c is the velocity of light in the vacuum. A capacitor C _SIW is formed by metallic vias between adjacent elements. The PIN-diode and the varactor are in parallel connection with C ₁ and C _2, respectively. The overall input admittance Y in can be easily achieved as: Y in = 1 Z a + j ω C SIW + ( j ω C 1 + 1 R PIN + j ω L PIN ) + ( j ω C 2 + 1 R Var + j ω L Var + 1 j ω C Var ) + j ω C 3 (2)

The reflection coefficient in the far-field is given as: Γ = 1 η 0 − Y in 1 η 0 + Y in (3)

Eq. 3 indicates that the amplitude and phase of the reflection coefficient can be jointly controlled by adjusting R PIN   and C Var in the model of PIN-diode and the varactor together.

The commercial EM simulation software, CST Microwave Studio 2021, is employed to calculate the EM responses of the programmable element. To simulate an infinite array, Floquet periodic boundaries are set along the x- and y-axes, and a Floquet port along the z-axis is used as an excitation to simulate the incidence of a plane wave. The excited electric field is set along the y-axis.

Figure 4 shows the numerical full-wave simulation results of the element at the normal incidence. “A⁰A¹A²A³B⁰B¹B²B³C⁰” is defined as nine coding states, which can be roughly divided into three groups. In the first group of states, the amplitude of states “A⁰A¹A²A³” is about 0.85, and there is a 90° phase shift among adjacent states. Different PIN states are employed to obtain the same reflection amplitude between states of A⁰∼A³. In the second group, the amplitude of states “B⁰B¹B²B³” is about 0.6, also with a 90° phase shift interval. The state “C⁰” has the lowest amplitude of about 0.2. The nine coding states corresponding to R _PIN and C _Var are listed in Table 1.

Wu et al. (2018) mentioned a special situation of “indefinite coding addition” when applying the addition theorem for RIS. This situation is caused by a 180° phase difference between the corresponding digits in the two sets of coding sequences before the addition operation. (Wu et al. (2018) makes artificial interventions for this special situation by introducing more coding states for the programmable element. However, it is not very friendly to the RIS loaded with tunable devices when balancing phase shift range and EM wave loss. Thus, the low-amplitude state (“C⁰”) is designed to deal with this indefinite situation. Due to its low amplitude, the error caused by its phase can be negligible.

To visually display the EM response of the programmable element, Figure 5A shows the reflection coefficients of nine coding states on the complex plane at normal incidence at 3 GHz. The position of the reflection coefficient A ⋅ e j φ of each state is determined by its amplitude A and phase φ simultaneously. To investigate the impact of oblique incidence, Figures 5B, C show the reflection coefficient at TM incidence angles of 30 and 60°. The reflection coefficients of nine coding states exhibit stable amplitude and phase responses at different incident angles, which is very important to ensure angular reciprocity in wireless communications (Liang et al., 2021).

According to the generalized Snell’s law, anomalous reflection or refraction of EM waves will occur when there is a phase discontinuity on the material interface [30]. A phase gradient along the RIS can be set to realize beam steering. In addition, since the coding states “A⁰A¹A²A³” and “B⁰B¹B²B³” exhibit similar phase responses but different amplitude responses, they can be directly used to generate beams in the same direction but with different power intensities.

As a proof-of-principle example, an RIS array with 12 × 24 elements is considered, which has more elements in the direction of phase gradient, that is y-axis, to reduce the influence of truncated boundaries on the array simulation. The RIS array is illuminated by a normal incident uniform plane wave. For an array consisting of M × N elements, its scattering pattern in the far-field can be calculated as (Cui et al., 2014): f ( θ , φ ) = ∑ m = 1 M ∑ n = 1 N f m n ( θ , φ ) e − j ⋅ φ m n − j ⋅ k ⋅ d ⋅ sin ⁡ θ ( ( m − 1 2 ) cos ⁡ φ + ( n − 1 2 ) sin ⁡ φ ) (4) in which f m n ( θ , φ ) is the scattering pattern of the mn-th element. k is the wavenumber of the EM wave in the vacuum. d is the period of the element.

Figures 6A–C shows the scattering patterns of two set of coding sequences “A⁰A⁰A⁰A¹A¹A¹A²A²A²A³A³A³...” and “B⁰B⁰B⁰B¹B¹B¹B²B²B²B³B³B³...ˮ. The two sets of coding sequences form the same phase gradient on the RIS and thus deflect the beam in the same direction θ = − 27 ° . However, since the reflection amplitudes of the elements in the first coding sequence are larger than that in the second coding sequence, the beam intensity of the first coding sequence is larger than that of the second coding sequence. Figures 6D–F shows the simulation results of another two set of coding sequences “A³A³A²A²A¹A¹A⁰A⁰...” and “B³B³B²B²B¹B¹B⁰B⁰...ˮ, it can be observed that two beams are pointed to the same direction of θ = 47 ° with different power intensities.

According to the addition theorem of the complex reflection coefficient in Bao et al. (2019) and Rajabalipanah et al. (2019), the proposed programmable element with independent control of amplitude and phase can also be used to generate dual beams with independent control of deflection angles and power intensities. In this theorem, two sets of coding arrays S1 and S2 are considered. The complex coding sequences of S1 and S2 are set as [ A 1 ] ⋅ e j [ φ 1 ] and [ A 2 ] ⋅ e j [ φ 2 ] , in which [ A ] and [ φ ] represent the amplitude and phase distribution in the coding array, respectively. The coding array S1 and S2 can redirect the incident EM waves to two angles θ ₁ and θ ₂, with power intensities A ₁ and A ₂, respectively. According to the theorem, the composite coding sequences S can be obtained by S = [ A 3 ] ⋅ e j [ φ 3 ] = [ A 1 ] ⋅ e j [ φ 1 ] + [ A 2 ] ⋅ e j [ φ 2 ] (5)

The coding sequence S will redistribute the incident wave into two main beams pointing at angles θ ₁ and θ ₂ simultaneously, with a power intensity ratio of A ₁/A ₂. Theoretically, the proposed element can be used to form the arbitrary shape of dual or multiple beams.

To verify the ability to generate the arbitrary shape of dual beams, two groups of simulations are carried out. In the first simulation, two sets of coding sequences with different intensities pointing to −27° and 47° are arranged on the RIS array. The vector sums of the two sets of coding sequences are quantized according to the coding states in Table 1. Figures 7A–E shows the dual beams pointing at −27° and 47° simultaneously, with power intensity ratios of 0:1, 0.5:1, 1:1, 1:0.5, and 1:0, respectively. Both 3D and 2D far-field scattering patterns are displayed. Similarly, in the second group of simulations, the dual beams pointing at −21 and 37° simultaneously with different power intensity ratios are achieved, as shown in Figures 8A–E. The simulation results are well consistent with those calculated by Eq. 4.

It should be noted that in some sets of coding sequences, sidelobes appear at some unexpected angles. One of the reasons for this phenomenon is quantization errors. The amplitude and phase of the RIS array after the addition are not the precise preset coding states in Table 1 in some situations, and this approximation leads to quantization errors. In addition, truncating the boundaries also contributes to side lobes for the limited size of the RIS array.

In Bao et al. (2019) and Rajabalipanah et al. (2019), a freer intensity distribution for arbitrary multiple beams can be realized. However, due to the limitation of bit width, there will be more side lobes when realizing multiple beams by the proposed element, which is one of the problems that needs to be solved in the future.

In this article, a programmable element with independent control of amplitude and phase is designed and is applied to construct RIS arrays to generate scattered beams with controllable deflection angles and power intensities. A PIN-diode and a varactor are loaded into the programmable element simultaneously, and nine coding states with different reflection amplitudes and phases are obtained. The well-designed element exhibits good angular stability by introducing numerous metallic vias in the substrate. Numerical simulations of a single beam in the same directions but with different power intensities are performed by applying different coding states. Furthermore, under the guidance of the addition theorem of complex reflection coefficients, dual beams with independently controllable deflection angles and power intensities are investigated with theoretical calculations and full-wave simulations. All simulation results are basically consistent with the theoretical ones. This design of RIS with independent control of amplitude and phase has potential applications in next-generation wireless communications.