**1. Introduction**

In the last decade, due to the increasing number of wireless and mobile devices being used, charging these devices has become a crucial problem, which is now capturing massive attention. The traditional charging method with cords is not preferable for futuristic systems and devices (e.g., Internet of Things, wireless sensor networks (WSN)). Wireless power transfer (WPT), allowing us to charge a device without any wire, is emerging as a promising technology for resolving the battery charging problem.

Since the first demonstration of WPT by Tesla in early 1900, engineers and researchers have recently come up with various techniques to transfer power wirelessly [1–3]. Among them, electrical methods, consisting of inductive coupling, magnetic resonant coupling, and electromagnetic (EM) radiation, are pervasive. While the first two methods are able to provide high transmission efficiency within a short range, EM radiation is capable of providing long-range WPT but with low efficiency [2]. Achieving both long range and high efficiency is still the main challenge in WPT which requires optimal solutions. For the case of EM radiation, beam forming and focusing is a potential solution for both long distance and high efficiency, which is enabled using phased-array antennas (PAA).

Recently, a novel concept of coding and digital metasurface has emerged as a promising and alternative technique that can perform beam focusing, multibeam, or scattering [4,5]. A metasurface consists of hundreds to thousands of unit cells which have different reflection responses to incident EM waves. In contrast to PAA, which depends on power-hungry and active components, coding metasurface enables beam synthesis by just turning ON or OFF the PIN diode integrated with each unit cell in the metasurface. By doing that, we can actually control the reflected signal outgoing from the metasurface.

The term coding metasurface was first coined by Cui and colleagues in 2014 [4]. Since then, several works and progress have been made in this area [5–7]. Different designs of 1-bit unit cell and metasurface have been proposed in [8–13]. Yang and colleagues proposed a simple rectangular element but working effectively in metasurface. The authors first designed and fabricated 10 × 10 array to demonstrate the working ability of the unit cell and metasurface [8,9]. Afterwards, this work was extended to 1600 element metasurface [10–12]. In these papers, the authors theoretically and experimentally demonstrated that the 1-bit metasurface is capable of digital beam focusing, multibeam focusing, scattering, and broadside beam synthesis. A 1-bit digital reconfigurable reflective metasurface with 20 × 20 cells is presented for beam-scanning in [13]. In that work, the authors used a varactor diode instead of a PIN diode for achieving wider bandwidth. Some works have also focused on designing 2-bit metasurface [14,15]. For instance, a dynamic beam manipulation based on 2-bit digitally controlled coding metasurface was proposed in [14] by Huang and colleagues. To enable a 2-bit operation, the authors used two PIN diodes in each meta-atom to produce four phase responses of 0, *π*/2, *π*, and 3*π*/2, which correspond to four basic digital elements "00", "01", "10", and "11". Experiments and measurements were conducted, which demonstrate one-beam deflection, two- and four-beam splitting, and beam diffusion by real-time control of the bias voltage. Another work is a transmission-type 2-bit programmable metasurface for single-sensor and single-frequency microwave imaging in [15]. The authors designed the unit-cell with two layers, in which each layer contains a switchable diode for providing 2-bit control ability. Recently, there has been an increasing number of research works which focus on using metasurface in wireless power transfer [16–22]. Nevertheless, these works are just able to do fixed focusing and are definitely inapplicable for mobile devices.

For an adaptive beam focusing, the channel between each unit cell of the metasurface and the receiver should be estimated. The authors in [23–25] theoretically analyzed and proposed the method for estimating the channel in intelligent surface or programmable metasurface. The method enables channel estimation by setting a single unit cell in "ON" state and the others in "OFF" state in a training time. However, this method might be impractical, especially when it comes to huge number of unit cells in the metasurface, as the reflected signal from one unit cell is too feeble compared to the rest.

In this paper, we propose a novel 1-bit coding metasurface that can dynamically perform beam focusing to the desired direction for WPT applications. Indeed, the proposed metasurface consists of 16 × 16 unit cells which are designed to operate at 5.8 GHz with two states (ON/OFF states) corresponding to a 0◦ or 180◦ phase shift of the reflected signal. To obtain the unit cell for a real metasurface, we applied the fractal structure in designing the unit cell. Therefore, the unit cell has ca ompact size with dimensions of 11 × <sup>11</sup> × 1.52 mm3. In order to electrically steer the beam, appropriate ON/OFF states of the unit cells in the metasurface should be set by a control board. The beam-focusing ability of the proposed coding metasurface has been validated by the experiment. The experimental results showed that the metasurface can steer and focus the beam within the range of (60◦, 0◦) in the elevation angle. For practical scenarios, an optimal phase control scheme is proposed and applied to adaptively track the mobile devices. The experimental results showed that the optimal phase control scheme performs better than the random phase control and beam synthesis schemes.

## **2. Coding Metasurface Theory**

In contrast to the existing metasurfaces that change the design structure of each unit cell to acquire the desired reflective phase shift, the coding and digital metasurface manipulates and reflects the impinged EM wave via different states of identical unit cells with the help of PIN diodes. For the theoretical analysis, we considered a coding metasurface with *M* × *N* 1-bit unit cells as shown in Figure 1. Specifically, as incident with an EM wave, the unit cell can operate in two states with the same reflected magnitude but 180◦ phase change. There are possibly two types of illuminating sources (plane wave and a point source) to be considered.

**Figure 1.** The coding metasurface model.

With x- or y-polarized EM wave incidence, the scattering field from the coding metasurface can be theoretically expressed as [12]

$$E(\theta,\varphi) = \sum\_{m=0}^{M-1} \sum\_{n=0}^{N-1} A\_{nm} e^{j\mathbf{a}\_{mn}} \cdot \Gamma\_{mn} e^{j\phi\_{mn}} \cdot f\_{mn}(\theta,\varphi) \cdot e^{j\mathbf{k}\_0(md\_x\sin\theta\cos\varphi + nd\_g\sin\theta\cos\varphi)},\tag{1}$$

where *Amn*, *αmn* are the relative illuminating amplitude and phase with respect to each unit cell in the metasurface (*Amn* = 1, *αmn* = 0◦ if the source is plane wave), Γ*mn*, *φmn* are the reflection amplitude and phase of *mn*th unit cell, *fmn*(*θ*, *ϕ*) is the scattering pattern of the unit cell, and *dx* and *dy* indicate the unit cell spacing in x and y directions.

According to Equation (1), the scattering EM wave from the metasurface can be controlled and formed by adjusting the reflection amplitude (Γ*mn*) and phase (*φmn*) of each unit cell. Therefore, we can say that the metasurface may possibly be encoded via these two parameters. Assuming that the reflection magnitude is identical, the reflection phase matrix with respect to the coding metasurface can be described by:

$$
\Phi = \begin{bmatrix}
\Phi\_{11} & \Phi\_{12} & \dots & \Phi\_{1n} \\
\Phi\_{21} & \Phi\_{22} & \dots & \Phi\_{2n} \\
\vdots & \vdots & \ddots & \vdots \\
\Phi\_{m1} & \Phi\_{m2} & \dots & \Phi\_{mn}
\end{bmatrix}\_{M \times N} \tag{2}
$$

One should obtain the appropriate Φ matrix for a specific beam pattern synthesis. To focus the beam to the desired direction, the phase compensation of each unit cell can be calculated by [21]:

$$
\phi\_{\rm min} = k(|\mathbf{f} - \mathbf{r}\_{\rm min}| + |\mathbf{d} - \mathbf{r}\_{\rm min}|),
\tag{3}
$$

where *k* is the wavenumber, **f** is the location of the EM source, **d** is the location of the focusing point, and **r***mn* is the position of the *mn*th unit cell.
