Vortex splitting is one of the main causes of instability in orbital angular momentum (OAM) modes transmission. Recent advances in OAM modes free-space propagation have demonstrated that abruptly autofocusing Airy vortex beams (AAVBs) can potentially mitigate the vortex splitting effect. However, different modes of vortex embedding will affect the intensity gradients of the background beams, leading to changes in the propagation characteristics of vortex beams. This study presents the unification of two common methods of coupling autofocusing Airy beams with vortices by introducing a parameter (m), which also controls the intensity gradients and focusing properties of the AAVBs. We demonstrate that vortex splitting can be effectively reduced by selecting an appropriate value of the parameter (m) according to different turbulence conditions. In this manner, the performance of OAM-based free-space optical systems can be improved.

The average bit error rate (BER) performance of a free-space optical (FOS) system based on the multi-hop parallel decode-and-forward cooperative communication method with an M-ary phase shift keying subcarrier intensity modulation is studied systematically. With the max–min criterion as the best path selection scheme, the probability density function and the cumulative distribution function of the gamma–gamma distribution random variable signal-to-noise ratio are derived. The analytical BER expression is then obtained in terms of the Gauss–Laguerre quadrature rule. Monte Carlo simulation is also provided to confirm the validity of the presented average BER model.