Multidimensional controllable sunflower beams: turbulence-resistant encoding in free-space optical communication

Atmospheric turbulence-induced orbital angular momentum (OAM) mode distortion remains a fundamental limitation in free-space optical (FSO) communication. We develop a sunflower-structured optical field featuring multidimensional controllability and turbulence resilience through superformula-phase modulated circular Airy beams. By systematically exploring the six-parameter space (m, n₁, n₂, n₃, a, b), we establish precise control rules for petal morphology. Quantitative analysis demonstrates 46% lower OAM mode diffusion coefficients (σ) in beams with high phase-modulation gradients (n₂ = n₃ = 4) under strong turbulence (Cn2 = 1 × 10^(-15)m^(−2/3)), attributed to enhanced energy localization. Furthermore, we propose an encoding communication scheme utilizing petal number (m) as the degree of freedom to transmit 8-bit grayscale images.This work not only demonstrates a novel multidegree-of-freedom controllable optical field but also provides a new paradigm for coded optical communication in complex atmospheric environments.