Transparent Graphene-Based RIS for 6G Communications in the THz Spectrum

In the quest for sixth-generation wireless communication technology (6G), Terahertz waves represent a key technology due to their distinct advantages over microwaves and infrared radiation. Reconfigurable intelligent surfaces (RIS) emerge as a critical technology within this context. This paper presents a numerical investigation and the optimized design of a transparent graphene-based RIS operating in the THz spectrum. The aim of the paper is twofold: the former is to demonstrate the reconfigurability of the proposed RIS by exploiting two methods, referred to as “digital” and “analogical”. The latter is to demonstrate the effects of the losses and of the mutual coupling among unit cells on the power flow pattern. This aspect is crucial in the design of the RIS and cannot be overlooked, differently from other papers reported in the literature which analyze the RIS as an “ideal” structure evaluating only an analytical estimation of the array factor and neglecting the interaction among the unit cells. Our results hold significant promise for improving the development of a new class of smart devices crucial for 6G wireless communication systems.

SECTION I. Introduction

Research on sixth-generation wireless communication technology (6G) is actively progressing, aiming to significantly advance communications. 6G has the potential to achieve significantly higher data rates of 1 Gbps and lower latency of $100~\mu$ s compared to 5G and 4G, enabling applications requiring massive device connectivity and real-time responsiveness [1], [2].

One of the key technologies for 6G is the utilization of TeraHertz (THz) frequencies, covering a vast spectrum from 0.1 THz to 10 THz (corresponding to wavelengths of 3 mm to $30~\mu$ m) [3], [4]. THz boasts several advantageous features: they are non-ionizing; thus, they pose no health risks like X-rays. Additionally, their short pulse duration, on the order of picoseconds, which is ideal for real-time applications, facilitates ultra-high-speed communications. Compared to microwaves, they offer superior material penetration capabilities, enabling application in imaging and sensing through plastics, textiles, and walls. However, THz frequencies suffer from significant atmospheric absorption, hindering long-distance signal transmission and reception. In this context, researchers are tackling this challenge by pioneering new beamforming approaches and designing novel hardware components, such as antennas and metasurfaces [5].

Reconfigurable intelligent surfaces (RIS) have emerged as key players in the THz spectrum, offering several distinct advantages [6], [7]. Firstly, they enable frequency reuse by manipulating and controlling THz waves (which helps maximize the channel capacity) [8], [9]. Secondly, RIS facilitates the development of miniaturized and lightweight THz devices, suitable for Internet of Things (IoT) applications. Finally, RISs can be installed on buildings and infrastructures with the aim to redirect the incident waves in a desired direction, enabling non-line-of-sight (NLOS) transmissions [6]. Consequently, a reconfigurable propagation environment with improved coverage can be achieved. Indeed, the deployment of RISs makes the communication between base stations (BSs) and users possible even in situations in which the line-of-sight (LOS) path is obstructed by obstacles. Moreover, the negligible reflection losses which characterize such devices can be exploited to increase the link distance that, at Terahertz frequencies, is restricted by the wave interaction with the common materials making up buildings and walls [7]. RISs-aided THz communication find applications in several 6G use cases which require advanced beamforming and beam steering capabilities. Going into details, RISs can be used to avoid information leakage on behalf of eavesdroppers, enhancing the network physical layer security. Moreover, the high speed of THz communications can be exploited by mobile edge computing (MEC) architectures only if a stable offloading channel, not hindered by obstacles, is ensured by means of RISs [7], [10]. The THz band has also emerged as a candidate technology for providing high data rates in inter-satellite links (ISLs) between LEO satellites [11]. Even if atmospheric absorption does not influence such links, the power limits of LEO satellites impose the adoption of solutions able to meet the need for energy-efficient systems. In this context, RISs-aided THz ISLs can enable an energy-efficient, high-speed ubiquitous connectivity, without the need for active elements such as multiple-input multiple-output (MIMO) and relay-based systems [12]. Except for their use in outdoor scenarios, RIS-assisted THz links could foster the development of smart logistics inside warehouses, where optimized communications capabilities are necessary to coordinate the interactions among IoT devices [3]. Finally, this technology could be employed in indoor high-speed networks as well as for localization purposes [12], [13].

Metasurfaces can be realized by exploiting different materials: metals like gold or copper [14], [15] since their high conductivity, dielectrics like silicon or polymers, which guarantee low losses, or a combination of them to enhance reflection/absorption capabilities or polarization control [16], [17], [18].

Among other materials, 2D graphene stands out as a promising material for the development of RIS owing to its unique properties [19]. This single-atom-thick layer of carbon possesses a very high carrier mobility. The true strength of graphene lies in its remarkable tunability: by simply adjusting a single parameter via electrostatic or chemical doping, the Fermi level, graphene conductivity can be tailored, leading to dynamic control over the intensity and the phase of the reflected and transmitted wave [20], [21]. Several studies have demonstrated the effectiveness of graphene-based RIS as both reflectors and absorbers. Hosseininejad et al., [22], detail the design of 1-bit and 2-bit digital metasurfaces tuned by adjusting the graphene chemical potential. However, the 1-bit design offers only a single reflective state due to the limited combination of $\mu {_{\text {c}}}$ values.

It is worth pointing out that the fabrication of such structures poses significant challenges, as the complex shape of the graphene patch hinders the application of tuning voltage from the sides of the unit cell. References [23] and [24] investigate the use of multilayer structures. While reflecting metasurfaces present good beam steering capabilities, their implementation faces two key challenges. Firstly, the unit cell stack comprising several materials increases the design and fabrication complexity. Secondly, ensuring stability and compatibility between graphene and other materials represents a challenge to be overcome. As an additional example, the work presented in [25], demonstrates a 1nm-thick graphene-based metasurface working as both reflector and absorber. The structure presents some drawbacks compared to its two-dimensional counterpart. The structure suffers from high scattering and absorption losses, hindering the overall performance. Additionally, the presence of interconnections between graphene layers decreases its optical conductivity, limiting its effectiveness compared to monolayer graphene.

Moreover, there are some examples of graphene coding metasurfaces for THz communication in which the tunability of graphene has been performed by changing the Fermi level [26], [27]; in both these cases, the operational frequency range is very narrow (less than 1 THz). Finally, it is worth stressing that, in the majority of works in literature, metasurfaces have been analyzed as an “ideal” structure without considering the mutual coupling among the unit cells. This aspect is crucial in the design of a RIS and cannot be overlooked as described in detail in [28]. The study of the mutual coupling in RIS-assisted communications has been deepened by some research groups by exploiting circuit-based communication models. In [29] and [30] the authors exploit an end-to-end model for RIS-assisted wireless systems based on the mutual impedances between all the existing radiating elements. This model accounts for the mutual coupling among closely spaced scattering elements of the RIS, as well as the circuits of the electronic components that are used to make the RIS reconfigurable. In [31], the same authors introduce analytical and numerical frameworks for optimizing the tunable impedances of the RIS to maximize the end-to-end received power. They demonstrated the algorithm convergence as a function of both the number of the scattering elements and their inter-distance. Their analysis revealed that accounting for mutual coupling during the optimization stage can significantly increase the end-to-end received power, as evidenced by the numerical results. Another communication model incorporating mutual coupling was applied to a Large Intelligent Surface (LIS) in [32]. The authors demonstrated the potential of super-directivity for LISs and that the system can theoretically achieve unbounded directivity by densely populating the LIS with closely spaced antenna elements. Furthermore, a recent study [33] examined the effect of mutual coupling on holographic reconfigurable intelligent surfaces (RISs). Using a misspecified Cramér-Rao bound analysis within an electromagnetics-compliant communication model, they performed a quantitative evaluation of the impact of mutual coupling on RIS-assisted channel estimation. These circuit-based communication models perform the evaluation of the mutual impedance matrices among the unit cells and channel matrices for the estimation of the received power and Signal to Noise Ratio (SNR).

In this paper, by exploiting a fullwave approach, the effect of the losses and of the mutual coupling on the radiation pattern of the normalized power has been observed in a finite graphene-based metasurface composed of 24x24 unit cells. In particular, we will show that the accounting of the mutual coupling has a non-negligeable impact on the beam splitting function. To emphasize this crucial aspect, we compared the fullwave results with analytical estimations derived from the array factor (AF) theory which treats each unit RIS cell as an ideal radiating element whose radiation pattern is unaffected by neighbouring elements. The paper is organized as follows: Section II reports the design and the numerical analysis of the RIS. The analysis has been performed in a wide frequency range from 1 THz to 5 THz. Then, in Section III an in-depth study evaluates RIS performance as a reflecting surface. By optimizing the geometrical parameters and the chemical potential of the graphene patch, it is possible to identify multiple pairs of reflecting states differing for a 180° phase shift: each state of a pair incarnates 1-bit of a digital coding scheme defined as “state 0” and “state 1”, enabling digital programmability. In contrast to the digital approach, a second approach, hereafter referred to as ‘analogical,’ has been developed. The latter allows to perform beam steering by varying the geometry of the graphene layer. Finally, in Section IV the paper focuses on the investigation of a larger metasurface composed of 24x24 unit cells in terms of power radiation pattern by implementing different coding.

SECTION II. Design of the Metasurface

Figure 1 (a,b) depicts the proposed design, which consists of 3 layers: a dielectric substrate sandwiched between a ground plane and a graphene-based layer patterned with rectangular patches. This stack of materials enables the design of a transparent and flat device that can be reconfigured by tuning the chemical potential of graphene elements.

FIGURE 1.

Sketch of the structure: a) unit cell and b) entire metasurface.

The unit cell is composed of a sapphire dielectric layer with a thickness h ${=} \,\, 9.5~\mu$ m, designed for a central frequency of 2.5 THz within the range of interest (1-6 THz). This thickness corresponds to $\lambda$ /$4\cdot$ n, where $\lambda \,\, {=} \,\, 120~\mu$ m is the wavelength at 2.5 THz and n ${=} \,\, 3.09$ is the refractive index of sapphire at the same frequency. The analysis considers the full dispersion curve of sapphire within the spectral range of interest [34]. Additionally, sapphire is modeled as a lossy material whose real part of the relative permittivity and loss tangent are specified in Table 1. This material is assumed to be transparent in the visible regime [35]. Unit cells are spaced by a subwavelength period p ${=} \,\, 30~\mu$ m, equivalent to $\lambda /4$ at the design frequency. The proposed structure utilizes a 5-nm-thick gold layer acting as a mirror to achieve the perfect reflection of incident waves.

TABLE 1 Real Part $\epsilon _{r}$ and $tan\delta$ of the Relative Permittivity of Sapphire

Finally, a patterned graphene monolayer (T$\sim \,\, {=} \,\, 97.7$ % in the visible spectrum [36]) is introduced on the top layer. In this frequency range, the 2D graphene conductivity $\sigma$ is modeled as a surface impedance, Z =1/$\sigma$ [37], based on the Kubo formula [38].

This model incorporates two distinct sigma contributions intraband $(\sigma _{intra})$ and interband $(\sigma _{inter})$ , as expressed in the following formulas: $$\begin{align*} \sigma =& \sigma _{intra}+\sigma _{inter} \tag {1}\\ \sigma _{intra}=& - \frac {ie^{2}k_{B}T}{\pi h^{2}\left ({{\omega - i2\Gamma }}\right)}x\left \{{{\left ({{ \frac {\mu _{c}}{k_{B}T} }}\right) }}\right. \\& {}+2ln\left.{{\left [{{\exp \left ({{ - \frac {\mu _{c}}{k_{B}T} }}\right) + 1}}\right ]}}\right \} \tag {2}\\ \sigma _{inter}=& - \frac {i{e}^{2}}{4\pi h ln\left ({{ \frac {2\left |{{ \mu _{c} }}\right | - h\left ({{\omega - i2\Gamma }}\right)}{2\left |{{ \mu _{c} }}\right | + h\left ({{\omega - i2\Gamma }}\right)} }}\right)} \tag {3}\end{align*}$$ where $\mu {_{\text {c}}}$ is the chemical potential, T is the temperature set at 300 K, and $\Gamma$ is equal to 0.11 meV. Within the considered frequency range, the imaginary component of the surface impedance significantly dominates over the real part, as discussed in [37].

In the proposed structure, the graphene top layer is organized into strips of adjacent rectangular rings, providing electrical continuity along the y-axis. Along the x-axis, the strips are discontinuous and separated by a gap g ${=} \,\, 2.5~\mu$ m. With this approach, each vertical line effectively acts as a single bit, enabling straightforward implementation of arbitrary coding functionalities on the metasurface. Each graphene ring that makes up the strip has an outer dimension of L$\times$ W and an inner rectangular aperture of size w${_{\text {p}}} \,\, {\times }$ w_p which will be varied. The analysis of the unit cell leverages the well-established commercial software CST Studio in the frequency domain, exploiting a fullwave method which takes into accounts all linear effects. The unit cell is excited by a TE-polarized incident plane wave. Similar results have been obtained also for TM-polarized waves which will not be discussed in this work.

SECTION III. Reconfigurability: Digital and Analogical Approach

As a first step, an in-depth investigation evaluated the behavior of the metasurface as a reflector. Simulations have been performed by sweeping across a range of chemical potentials for graphene between 0.05 and 0.55 eV and aperture widths w_p between 5 and $20~\mu$ m. The extracted data, in terms of amplitude and phase of the scattering parameter S₁₁, was fed into a custom database encompassing all possible pairs (without considering permutations) of $\mu {_{\text {c}}}$ for each value of w_p. Each pair within the database identifies a binary state, denoted as “0” and “1”. Within this database, we searched for specific configurations meeting the criteria defined in (4) and (5): $$\begin{align*}& {|S}_{11}\left ({{\mu _{c1}}}\right) - S_{11}\left ({{\mu _{c2}}}\right)| = 0 \tag {4}\\& \Delta \Phi = 180{^{\circ }} \tag {5}\end{align*}$$

These criteria necessitate a zero difference in amplitude and a phase difference of $180^{\circ } \,\, {+} \,\, 2$ m$\pi$ (where m is an integer) between the two retrieved S₁₁ values (corresponding to specific $\mu {_{\text {c}}}$ combinations) for each w_p value. The retrieved configurations are reported in Table 2 which identifies seven configurations that satisfy the desired criteria. The first two configurations have w_p equal to $5~\mu$ m and $10~\mu$ m, respectively. Notably, both configurations achieve 180° phase shifts at the same frequency of 4.6 THz. The first configuration exhibits amplitude $(|S_{1}1|)$ values of −0.72 dB (state “0”, $\mu {_{\text {c}}} {=}0.05$ eV) and −0.65 dB (state “1”, $\mu {_{\text {c}}} {=}0.55$ eV), while the second exhibits −0.61 dB (state “0”, $\mu {_{\text {c}}} {=}0.10$ eV) and −0.49 dB (state “1”, $\mu {_{\text {c}}} {=}0.55$ eV).

TABLE 2 Pairs of ‘Digital’ States Identified as a Function of wp, Working Frequency f, Chemical Potentials ( $\mu _{c}1$ and $\mu _{c}2$ ), Corresponding Amplitudes of the Scattering Parameters ( $S_{11} \text {(}\mu _{c1}$ ) and $S_{11}$ ( $\mu _{c2}$ )) and Their Difference ( $\Delta S_{1}1$ )

The remaining six configurations involve different chemical potential combinations for a $20~\mu$ m aperture width. In these cases, the 180° phase shifts are achieved across a wider frequency range, between 4 and 4.7 THz.

To complement the previously discussed “digital” method, an “analogical” approach has been developed. This approach enables the achievement of virtually any desired steering angles by tailoring the graphene aperture size. To demonstrate this approach, we start from the $5{^{\text {th}}}$ configuration identified in Table 2 using the digital approach (since in this case the minimum difference between S₁₁ in the two states has been obtained). This configuration is retrieved at a frequency of 4.41 THz and with a chemical potential of the graphene equal to 0.45 eV. Figure 2 shows the phase response against w_p for different chemical potentials. Remarkably, all configurations exhibit a magnitude of the scattering parameter S₁₁ close to 0 dB, as shown in Figure 2. As can be seen from the figure, when w_p varies from 5 to $20~\mu$ m, the phase undergoes an ample shift from –556° to –1368°. Varying the geometrical parameter w_p in the range between 5 and $20~\mu$ m, an arbitrary steering angle can be then achieved by exploiting the classical phased array antennas paradigm. It is important to underline that this approach may face challenges when considering fabrication tolerances. Nonetheless, it demonstrates the versatility of the proposed metasurface that can be harnessed for beam steering and enhancing line of sight in communication channel systems.

FIGURE 2.

Analogical approach: amplitude and phase of scattering parameter $S_{11}$ for increasing values of w_p, when f=4.41 THz and $\mu {_{\text {c}}} {=}0.45$ eV.

SECTION IV. Finite Metasurface: The Effects of Mutual Coupling

This section aims to investigate the behavior of a finite metasurface by exploiting an approach that incorporates both the losses and the mutual coupling existing between unit cells, a crucial aspect that cannot be overlooked [28] and that is often neglected in previous published papers [25], [39], [40], [41]. Among all the solutions obtained, the one at 4.41 THz (the $5{^{\text {th}}}$ configuration reported in Table 2) was considered because the minimum difference between the $S_{11}$ of the two states, equal to 0.05 dB, has been obtained with this specific configuration. At this frequency, the chosen period equal to $30~\mu$ m is shorter than half the wavelength. This requirement is sufficient to satisfy the Petersen-Middleton theorem, which ensures that the metasurface is able to “reconstruct” an arbitrary far-field [28]. We consider a metasurface composed of 24x24 unit cells having a period of $30~\mu$ m. Two distinct chemical potential values are used: 0.10 eV for state 0 and 0.45 eV for state 1. The working frequency is set to 4.41 THz and a TE-polarized plane wave serves as the excitation source.

We explore different coding schemes represented by a subvector C(n,m) as defined in [41]. Here, n=m assumes the value corresponding to the dividers of 24, (i.e., 1, 2, 3, 4, 6, 12) and represents the consecutive number of “0” and “1” states in the period in one row. Each row is then repeated vertically 23 times.

Our analysis focuses on the reflected power radiation pattern, which represents the time-averaged Poynting vector per unit solid angle. To account for the total incident power, this value is normalized by the reflected power from a perfect electric conductor foil matching the metasurface area equal to $7.7\times 10{^{-}8 }$ W/ m². The normalized radiation patterns for different codings are shown in polar form in Figure 3(a). The codings have been assigned to the entire metasurface (Figure 3(b)) as sketched in Figure 3(c), where green and white cells represent the state “0” and “1”, respectively.

FIGURE 3.

a) Radiation pattern (normalized power) of the 24x24 metasurface for different codings, sketch of b) the entire 24x24 metasurface and of c) some of the assigned codings. Green and white cells indicate the metasurface columns of unit cells set as states “0” and “1”, respectively.

As it is possible to observe for all the cases, the radiation pattern is composed of two twin lobes, whose aperture changes according to the considered coding. The only exception is represented by C(1, 1) characterized by a single lobe at around 0° with a magnitude of 0.07. More in detail, in the case of C(12, 12), the highest value of magnitude is reported for $\Phi \,\, {=} \,\, 3.4{^{\circ }}$ . For C(6, 6), C(4, 4), and C(3, 3), by referring only to the positive angles, the magnitude starts to decrease with lobes placed at $\Phi \,\, {=} \,\, 9.8{^{\circ }}$ , $\Phi \,\, {=} \,\, 21.4{^{\circ }}$ and $\Phi \,\, {=} \,\, 15.8{^{\circ }}$ , respectively. Finally, for C(2, 2) the lobes are placed at $\Phi {=} 33.4{^{\circ }}$ and are characterized by a low magnitude. Moreover, for negative angles, a twin beam can be observed for each coding. However, these beams exhibit a noticeable asymmetry, which mirrors the asymmetry present in the coding scheme itself.

To gain a deeper understanding of the metasurface potentialities and limitations, we compared previous results with analytical estimations derived from the array factor (AF). We calculated the power radiation pattern of an equivalent antenna array consisting of 24x24 elements, with the same periodicity as the metasurface. The array factor of the entire metasurface can be evaluated as the product of the array factors along the x- and y-directions: $$\begin{align*} \text {AF}=& \text {AF}_{x} \cdot \text {AF}_{y} \tag {6}\\ \text {AF}_{x}=& \sum _{m = 0}^{N - 1}\exp \{j\left \lbrack {{ kmd\sin \left ({{\vartheta }}\right)\cos \left ({{\varphi }}\right) + \boldsymbol {\xi }_{\mathbf {x}} }}\right \rbrack \} \tag {7}\\ \text {AF}_{y}=& \sum _{n = 0}^{N - 1}\exp \left \{{{ j\left \lbrack {{ knd\sin \left ({{\vartheta }}\right)\sin \left ({{\varphi }}\right) + \boldsymbol {\xi }_{\mathbf {y}} }}\right \rbrack }}\right \} \tag {8}\end{align*}$$ where, N is the number of unit cells in both x and y directions (a square metasurface is assumed), d is the period of the unit cells, $\theta$ and $\phi$ are the elevation and azimuth coordinates, k $=2\pi$ /$\lambda$ is the wavenumber (where $\lambda$ is the operating wavelength). $\xi {_{\text {x}}}$ a and $\xi {_{\text {y}}}$ are N-elements arrays accounting for the phase shifts introduced by two adjacent unit cells along x- and y-directions, respectively. $\xi {_{\text {y}}} {=}0$ , since graphene strips are electrically continuous along the y-direction. Thus, $\xi {_{\text {x}}}$ will ultimately account for the encoding [41].

This array reflects the coding applied to the metasurface through assigned weights, while neglects the interaction between individual elements. As before, we normalized the power values against a reference maximum obtained with a constant ‘0’-coding. The results are represented in Figure 5 for the same codings as the previous Figure 4.

FIGURE 4.

Analytically calculated radiation pattern (normalized power) of the 24x24 metasurface for different codings.

FIGURE 5.

Normalized power flow pattern for a) asymmetric and b) symmetric codings.

It is possible to observe that for all the configurations the beam is composed of two twin lobes having magnitude comparable with the previous analysis. The angle of the aperture of these lobes decreases from C(12, 12) to C(1, 1). As before, by referring only to the positive angles, the highest value of magnitude was obtained for case C(12, 12) with lobes placed at $\Phi \,\, {=} \,\, 4{^{\circ }}$ . Moreover, for C(6, 6), C(4, 4), C(3, 3), and C(2.2) the lobes were at $\Phi \,\, {=} \,\, 10{^{\circ }}$ , $\Phi \,\, {=} \,\, 16{^{\circ }}$ and $\Phi \,\, {=} \,\, 22{^{\circ }}$ , respectively. Finally, for C(1,1) the beam presents two lobes characterized by very low magnitude and by angle of aperture at $\Phi = 90{^{\circ }}$ . This analytical method highlights symmetric lobes despite the asymmetry of the coding. This behavior differs from that shown in Figure 4, since the simulations of the entire metasurface accounts for losses and mutual coupling.

A comparison between the two metasurfaces is shown in Table 3, where we reported the magnitude and the angle of aperture of the left and right lobe (M_LL, M_RL, $\Phi {_{\text {LL}}}$ , $\Phi {_{\text {RL}}}$ ) for the different codings.

TABLE 3 Comparison Between Characteristics of Power Pattern for Both Simulated (SIM) and Analytical (ANA) Structure in Terms of: Magnitude of Left (MLL) and Right (MRL) Lobe and Angle of Aperture of the Left ( $\Phi {_{\text {LL}}}$ ) and Right ( $\Phi {_{\text {RL}}}$ ) Lobe

To investigate the influence of coding asymmetry on metasurface behavior while considering mutual coupling and losses, we conducted an additional analysis. More in detail, we started with a 24x24 metasurface encoded with C(3, 3) (= “000 111 000 111 000 111 000 111”). The corresponding normalized radiation pattern was retrieved. Subsequentially, we analyze progressively smaller metasurfaces (down to 3x3 unit cells). For each size reduction, the tailing vector of three elements (“000” or “111”) was subtracted from the original coding sequence. The analyzed coding schemes lead to either symmetric or asymmetric radiation patterns, mirroring the corresponding symmetry or asymmetry of the coding pattern with respect to the metasurface center of symmetry. These results, presented in terms of normalized power flow patterns, are reported in Figure 5.

Notably, for asymmetric coding pattern the resulting radiation pattern exhibit asymmetrical lobes, as depicted in Figure 5a. Conversely, symmetrical lobes of Figure 5b follow the symmetry of the coding. It is worth noting that the slight asymmetry observed in the 21x21 case is due to the non-uniform mesh used in the simulations. Our analysis shows that, by taking into account losses and mutual coupling between unit cells in finite metasurfaces, significant deviations from the results obtained using the approach which solely analyzes the array factor, are observed. This finding underscores the critical need for such simulations in the future fabrication and characterization of the proposed device.

SECTION V. Conclusion

In this contribution, we proposed a graphene-based 1-bit coding RIS working in the frequency range between 1 THz and 6 THz. Its design has been approached through two methods: “digital” and “analogical” programming. The “digital” approach involved finding pairs of states, defined by their chemical potential, that meet the following two criteria: (i) the amplitude of S₁₁ remains constant, while (2) the phase of S₁₁ shifts by $180{^{\circ }} \,\, {+} \,\, 2$ m$\pi$ , being m an integer. The “analogical” approach enables virtually arbitrary steering angles by modifying the geometry of graphene’s aperture of few microns. We simulated a finite RIS with 24x24 unit cells and compared the power radiation pattern with that provided by calculating the array factor of an ideal case (without losses and mutual coupling between the unit cells). This analysis allowed us to highlight (i) the asymmetries present in the beamforming that follow the asymmetry of the coding and (ii) the amplitude reduction due to the losses present in the real structure. Such effects are often overlooked in analyses based solely on the array factor, which are therefore less realistic. Graphene-based metasurfaces can enhance wireless communications and their spatial and temporal modulation capabilities pave the way for advanced signal processing, enabling adaptive technologies.

ACKNOWLEDGMENT

The authors would like to express their heartfelt gratitude to Dr. Marco Grande from the Department of Electrical and Information Engineering, Polytechnic University of Bari. His guidance and expertise were invaluable in shaping the direction of this research.

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