In the case of a non-line-of-sight azimuth transmission system based on polarization-maintaining fiber, aligning the output light passing through the fiber with the photoelectric conversion receiver is necessary to increase the extremely small diameter of the outgoing light after transmission through the fiber. A beam-expanding system can be introduced to solve this problem, and the azimuth transmission can be achieved in a non-line-of-sight condition. Because the classical refractive beam spreading system is composed of lenses, the influence of lenses in polarization transmission determines the accuracy of the azimuth transmission. However, general studies of the lens focused on the influence of polarization states of incident light and lacked analyses regarding lens parameters and beam-expanding systems comprising lens groups. In the non-line-of-sight azimuth transmission system, the influence of lenses on polarization transmission is key to introducing the beam-expanding system. This system has broad application prospects in many fields, including spacecraft docking in space stations, tunneling engineering, and high-precision instrument measurement.

In this study, the analysis related to lenses is based on the Jones matrix principle and the Fresnel equation. First, the Jones vector is used to characterize the incident polarized light. Second, the incident light gets refracted after passing through the lens and the Jones vector relationship between the incident and refracted light is calculated using the Jones matrix with respect to the lens. Subsequently, the Jones matrix with respect to the lens can be characterized using the amplitude transmission ratio, which is the ratio between the angle of incidence and angle of refraction. These angles are derived based on the Fresnel equation. Finally, the geometric relationship between the light and lens is analyzed using the ray-tracing method to determine the angle of incidence and refraction. Using the Galileo beam expanding system as an example, the process of polarization transmission with respect to the lens is analyzed in detail and the equation of the deflection angle comprising lens parameters is derived. The influence of the lens parameters on polarization azimuth deflection is simulated and verified via experiments.

In this study, the influencing factors with respect to the linearly polarized light using lenses are divided into three categories: first, the polarization state of the incident light; second, the refractive effect of lens spheres; and third, the material properties of lenses. The polarization-azimuth-deflection equation comprising the lens parameters was obtained based on the study of the lens parameters and beam-expanding system comprising the lens group (Eq. 12). Simulations and experiments conducted herein show that the polarization azimuth deflection is inversely related to the radius of curvature of the lens. When the curvature radius of the lens increases, the polarization azimuth deflection decreases and tends to zero (Fig. 5 and Fig. 11). The polarization azimuth deflection is squared with the incident light radius. When the radius of incident light increases, the polarization azimuth deflection increases, and when the incident radius tends to zero, the polarization azimuth deflection tends to zero (Fig. 6 and Fig.12). The central thickness of the lens is linearly related to the polarization azimuth deflection; that is, when the center thickness of the lens increases, the polarization azimuth deflection increases (Figs. 7 and 13). Furthermore, the polarization azimuth deflection is squared with the refractive index; that is, when the refractive index increases, the polarization azimuth deflection increases (Fig. 8).

Based on Fresnel equations and Jones matrixes, this study analyzes the influence of lens parameters on polarization transmission, which is mainly reflected in the polarization azimuth deflection of polarized light. Using the Galileo beam spreading system as an example, the geometric relationship of light in the beam spreading system is analyzed via the ray-tracing method. Then, the polarization azimuth deflection equation comprising the lens parameters is derived. Subsequently, the influence of curvature radius, center thickness, the radius of incident light, and refractive index on the polarization azimuth deflection are simulated, and the principle is analyzed. The results of our study show that the curvature radius is inversely related to the polarization azimuth deflection; that is, when the curvature radius decreases, the polarization azimuth deflection increases, and when the curvature radius tends to approach ∞, the polarization azimuth deflection tends to be zero. Meanwhile, the center thickness is linearly related to the polarization azimuth deflection; that is, when the center thickness increases, the deflection angle increases. The incident light radius is squarely related to the polarization azimuth deflection; that is, when the incident light radius increases, the polarization azimuth deflection increases, and when the incident light radius tends to be zero, the polarization azimuth deflection also tends to be zero. The refractive index is squared with the deflection angle; that is, when the refractive index increases, the polarization azimuth deflection also increases, and when the refractive index tends to zero, the polarization azimuth deflection tends to be zero. This study provides a reference for the introduction of the beam-expanding system in the non-line-of-sight azimuth transmission system based on the polarization-maintaining fiber.