*2.1. Phase Quantization*

The above computed phase is the ideal phase shift of each unit cell. However, only a limited phase shift can actually be provided with the coding unit cell. Hence, it is inevitable that we have to consider the phase quantization for the coding metasurface [13]. One can realize from Equation (3) that the phase compensation might be not within the range between 0 and 2*π*. Then, it should be shifted to be in the range of [0, 2*π*] before being quantized. Considering 1-bit coding unit cell, the shifted and quantized phase can be given as:

$$
\phi\_{mn}^{-} = \phi\_{mn} - 2\pi \left[\frac{\phi\_{mn}}{2\pi}\right],
\tag{4}
$$

$$
\boldsymbol{\phi}\_{mn}^{\circ} = \begin{cases}
\boldsymbol{\pi} & \text{if } \boldsymbol{\pi}/2 \le \boldsymbol{\phi}\_{mn}^{\circ} \le 3\boldsymbol{\pi}/2 \\
\boldsymbol{0} & \text{elsewhere} \end{cases}
\tag{5}
$$

After quantization, the reflection phase of the unit cell has just two states: 0◦ or 180◦, corresponding to the coding "1" and coding "0", respectively. To demonstrate the focusing ability of the coding metasurface, we computed the ideal phase and quantized phase distribution of the 16 × 16 coding metasurface using the above phase compensation method and the corresponding beam pattern as presented in Figure 2. The metasurface is assumed to be placed in XOY plane and is excited by a point source. Although the relative power generated by the ideal phase distribution (245) is much higher compared to one of the quantized phase distribution (around 170), both cases are capable of performing good beam steering. It is clear that beam synthesis can be acquired by 1-bit coding metasurface.

**Figure 2.** Reflection phase distribution and 3D pattern of the coding metasurface with an electromagnetic (EM) source located at (0 cm, 0 cm, 10 cm) and beam focusing at (0◦, 30◦): (**a**) ideal reflection phase distribution; (**b**) quantized phase distribution; (**c**) the beam pattern w.r.t ideal phase distribution; (**d**) the beam pattern w.r.t quantized phase distribution.
