Optical demultiplexing of fractal-structured beams in turbulent atmospheric environments

When information is spatially repeated in self-similar fractal beam patterns, only a portion of the diffracted beam is needed to reconstruct the kernel data. What is unique to a fractal-encoding scheme is that the image demultiplexing process can be, to a first approximation, easily performed optically. In prior work, we experimentally and numerically study fractal-encoded optical beams and their mid- and far-field propagation without added turbulence. Here, we present preliminary simulations of fractal-encoded beams with high turbulence ($C_n^2 \geq 10^{-14}$ m$^{-2/3}$) where we achieve respectable bit error rates of $10^{-3}$. These results are impressive given that: data with low fractal orders is shown, simple threshold-algorithms are used (i.e., no machine learning), and only a third of the beam, off-axis, is needed. More robust channel encoding is associated with increased fractal orders, larger collection areas, and higher kernel singular value decomposition entropy.