Efficient and low-crosstalk propagation of perfect vortex beams in free space and atmospheric turbulence

This study derives an exact analytical solution for the diffraction field of perfect vortex (PV) beams modulated by a Cassegrain system, rigorously characterizing their propagation dynamics in both free space and non-Kolmogorov turbulence with a focus on beam propagation efficiency and orbital angular momentum (OAM) mode crosstalk. Results demonstrate that under turbulence-free conditions, PV beam propagation evolves through sequential non-diffracting and self-focusing stages preceding multi-ring distribution formation. Cassegrain system modulation extends the propagation distance of both stages through beam expansion and collimation. During extended transmission distances, this modulation enhances beam propagation efficiency in free space while simultaneously increasing OAM mode detection probability under atmospheric turbulence. Co-optimization of the system magnification factor and receiver aperture radius enables concurrent achievement of high beam propagation efficiency and low OAM crosstalk at extended ranges. The proposed beam control method effectively extends diffraction-free and self-focusing propagation regimes, thereby enhancing beam propagation efficiency in turbulence-free channel and improving OAM mode detection probability in turbulent atmospheres. This approach provides what is believed to be a novel beam modulation scheme for enhancing mode division multiplexing (MDM) system performance.