Propagation Characteristics of Hermite–Gaussian Beam under Pointing Error in Free Space

Abstract

Hermite–Gaussian (HG) beams have significant potential to improve the capacity of free-space optical communication (FSOC). The influence of pointing error on the propagation characteristics of an HG beam cannot be ignored in the FSOC system. Although the average irradiance of the HG beam under a small pointing error from the FSOC tracking mechanism has been investigated through Taylor series approximation, here, we propose that the average irradiance of the HG beam under an arbitrary magnitude pointing error can be deduced through a statistical averaging method. We firstly found that the average irradiance profile of an HG beam finally changes into an approximately Gaussian shape with the increase in pointing error and propagation distance and a larger beam waist at the transmitter could mitigate the profile change. The correlation coefficient between deduced theoretical expression and Monte Carlo simulation reaches 0.999. Additionally, the effective spot size, location of the local extreme value, average received power and signal-to-noise ratio (SNR) loss for an HG beam under pointing error were theoretically deduced and analyzed for the first time. We found that the effective spot size of the higher-order HG beam experiences less broadening under the pointing error than that of the lower-order HG beam. The fundamental theoretical expressions of average irradiance for an HG beam under pointing error have provided effective guidance for analyzing the propagation characteristics and link performance.