Analysis of beam efficiency and accuracy of Gerchberg-Saxton method in multi-beam control of free space optical communication

Free space laser communication has the characteristics of large bandwidth, high speed, high security and small size, and has become the preferred way of high-speed data transmission in space today. The realization of multi-beam control in free-space optical communication through optical phased array has obvious advantages in energy consumption and control accuracy. Gerchberg-Saxton (GS) is a commonly used modulation phase design method for optical phased arrays. This paper analyzes the relationship between the beam efficiency and accuracy and the number of iterations in the modulation phase of optical phased arrays designed by the GS algorithm. The results show that in the ideal case, the beam efficiency increases with the number of iterations of the GS algorithm, and eventually tends to be stable; the beam pointing accuracy increases with the number of iterations of the GS algorithm, and finally tends to be stable, and the speed of stable convergence is faster than the beam efficiency.