Fig. 1: Comparative analysis of radial-index, azimuthal-index, and phase-difference shift keying.
From: Partial coherence and multi-channel vortices enhance high-security free-space optical communication

The initial Gaussian width of the light beams, w0 is set at 1.5 mm, and the simulated diffraction distance in free space is 3 m. Radial-index (~LG(1, p, 0)) and azimuthal-index (~LG(l, 0, 0)) shift keying suffer from spatial channel crosstalk, whereas phase-difference shift keying (~LG(±1, 0, Δφ)), due to its minimal beam divergence, enables crosstalk-free multi-channel transmission.