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, and b), we establish precise control rules for petal morphology. Quantitative evaluations via the Pearson correlation coefficient (PCC) confirm that the topological structures of the beams are robustly preserved against atmospheric turbulence. Furthermore, we propose a multidimensional encoding scheme that multiplexes petal number (m), morphology (n₂), and symmetry factors (a,b) as degrees of freedom, enabling robust 8-bit grayscale image transmission via a CNN-based intelligent decoder with a BER of 0.076 under Cn2=5×10^-17m^-2/3 turbulence conditions. This work not only demonstrates a novel multidegree-of-freedom controllable optical field but also provides a new paradigm, to the best of our knowledge, for coded optical communication in complex atmospheric environments.