Enhancing transmission and coupling efficiency in Cassegrain optical systems with four-petal Gaussian beams

This study investigates the propagation characteristics of four-petal Gaussian beams through Cassegrain optical systems. With the properties of this new type of beam, the problem of masking loss in the Cassegrain optical system can be well solved. Analytical expressions of the optical field for beams after propagating the optical system are derived, considering atmospheric turbulence effects and random jitter on coupling efficiency. Simulation tests explore various factors affecting transmission efficiency. Acceptable axial mounting error tolerance and significant efficiency drops beyond specific communication distances under different turbulence conditions ($C_{n}^{2}$). Achieving over 80${\% }$ coupling efficiency is feasible with specific lens parameters (f = 0.4 - 0.5 mm, receiving position after 4 km) using standardized lenses. This work offers a theoretical model for four-petal Gaussian beams, aiding optical communication design and application, with practical engineering implications.