**2.1 Beam focalization and steering effect**

In the traditional research of ultrasound and microwave domain, the concept of phased array antenna is introduced as a set of radiators with the designed phase and amplitude over the synthetic aperture. In order to simplify the design procedure and extend the possibility to more complex functionalities, the concept of the phased array model could be used here to explain the physics of the metalens [3]. For example, a focusing metalens could be recognized as the phased-array antenna with the special case of the spherical phase profile.

We assume the periodic metasurface could be regarded as a plane distributed with radiator array as shown in **Figure 1** to start a general discussion. In this case, the most common case of "lens" could be understood from the focalization effect, which of metalens could be achieved by distributing the spherical phase profile over the plane surface, as shown in Eq. (1) [4]. The wavefront generated by the phased array reach the focus at the same time, as shown in **Figure 1(b)**.

$$\log(\mathbf{x}, \mathbf{y}) = 2\pi - \frac{2\pi}{\lambda\_{\mathrm{cl}}} (\sqrt{\mathbf{x}^2 + \mathbf{y}^2 + \mathbf{f}^2} - \mathbf{f}) \tag{1}$$

Starting from a general discussion, due to the periodicity of a phased array, beam narrow effect is invoked by the nature of the periodic array. The focalization effect only happens when the wavesfronts reach at the focus point simultaneously by spherical phase shift, as shown in **Figure 1(b)**. At the focus point, the maximum intensity is obtained as the result of the interference of each "meta-atom". The beam steering effect could be realized by adding the constant phase increment between two adjacent elements, as shown in **Figure 1(c)**. Furthermore, the steering *Metalens Antennas in Microwave, Terahertz and Optical Domain Applications DOI: http://dx.doi.org/10.5772/intechopen.99034*

#### **Figure 1.**

*(a) Focalization effect (b) beam narrowing effect (c) beam steering and (d) focus steering effects generated by a phased array surface. (e) the far-field radiation pattern of phased array of FDTD simulation, SAM and AFM model results and (f) the enlarged region of the maximum radiation peaks.*

angle could be tuned by controlling the phase increment [3]. **Figure 1(d)** gives another instance of the combination of focusing and steering if the spherical phase shift and constant phase increment are added on top of the phase shift. Based on the phased array models described here, full-wave solver as FDTD simulator and analytical models, such as Synthetic Aperture Method (SAM) and Array Factor Method (AFM), are investigated to give the radiation pattern at far field. **Figure 1(e)** and **(f )** shows the far-field radiation patterns of the metalens model for optical frequency at 193THz, obtained by FDTD simulator, SAM model and (AFM) model respectively, which shows that the phased array models highly agree with the full-wave simulation result. Theoretically, the focalization and steering effects can be realized at the same time, which makes more advanced features highly possible, especially for tele-communication system by replacing the bulky scanning infrastructure and project the wavefront to desired location with speed up to hundreds mega-Hertz.
