# Multi-Beam Focusing and Deflecting Characteristics of Liquid Crystal Optical Phased Array
## 3 Results  
In this paper, we developed a transmissive liquid crystal optical phased array device. The LCOPA device has 240 ITO electrodes, each of which are controlled independently. Schematic and actual images of the programmable beam control experimental setup are shown in Figures 4 and 5, respectively. The laser emits a red light beam with a wavelength of 650 nm. The laser passes through an aperture, making the spot size of the incident light conform to the effective aperture of the LCOPA device. As the laser beam passes through a linear polarizer, the polarized orientation is consistent with the rubbing direction of the liquid crystal molecules inside the LCOPA device. We can observe the diffraction intensity distribution through the receiver screen from a certain distance away. For the convenience of the LCOPA device, we developed a fully embedded human-computer interaction system, which only needs a touch screen. Some working interfaces are designed according to different requirements, including laser scanning, focusing, and multi-beam fan-out with focusing, as shown in Figure 6a-c, respectively. Due to the simple connection with driving circuits, human-computer interaction manipulation is very easy and convenient. Figure 4: Schematic diagram of the experimental setup for programmable beam control. We can input some parameters, such as wavelength, angles, and focus length, on the touch screen by capacitive pen or finger. The data are sent to the microcontroller through the serial port once the touch screen has received the setting signal. After receiving the parameter data, the microcontroller uses an interrupt program to update the liquid crystal driving voltage data. Based on the look-up table (LUT) of the voltage-phase characteristic curve of the liquid crystal material, the relationship between the phase distribution and driving voltage data can be set up and translated. And according to the relationship between phase distribution and optical intensity distribution that is desired in the far field, the LCOPA device can achieve corresponding functions, including laser scanning, multi-beam fan-out, and focusing. In order to verify the validity of the fully embedded human-computer interaction system, we firstly demonstrate the laser scanning function. Laser scanning includes many deflecting angles at a certain interval. Assuming the desired beam deflection angle is \(\theta\) = 4 mrad, the phase distribution (mod 2\(\pi\)) in the near field can be designed by the grating equation, which is shown in Figure 7a. The experimental result of light intensity distribution in the far field is shown in Figure 7b. Assume that the transversal offset distance of the far-field diffracted spot is \(X\) and the distance between the LCOPA device and the viewing screen is \(L\), where \(L\) equals 2 m in experiments. According to Equation (3), we can obtain \(X\) = 8 mm. The actual measured offset distance of far-field spots is also approximately 8 mm, which is consistent with the theoretical value. We can also achieve beam deflection with other angles. \[X=\sin\theta*L \tag{3}\]  
Figure 5: Experimental setup of programmable beam control. Figure 6: Working interfaces of the touch screen: (**a**) functional interface of laser scanning; (**b**) functional interface of focusing; and (**c**) functional interface of multi-beam fan-out with focusing. Secondly, we demonstrate the laser focusing function of the LCOPA device. Since the phase of lens focusing \(\varphi_{L}(i)\) can be expressed by Equation (1), a serial of decent voltages on each electrode of the LCOPA device are loaded, according to the electro-optical curve of the liquid crystal cell. In the working interface of focusing, we can input the focus length parameter on the touch screen. As shown in Figure 8, when the receiver screen is 0.6 m away from the LCOPA device, the focal length of the light spot varies, with 0.6 m, 1 m, and 1.4 m. We can observe the shape change of the light spot from thinner to wider.