  Optical rogue waves are demonstrated in the far-field scattered radiation
from photonic arrays designed according to the aperiodic distributions of prime
elements in complex quadratic fields. Specifically, by studying light
diffraction from Eisenstein and Gaussian prime arrays we establish a connection
between the formation of optical rogue waves and multifractality in the visible
single-scattering regime. We link strong multifractality with the heavy-tail
probability distributions that describe the fluctuations of scattered radiation
from the fabricated arrays. Our findings pave the way to control high-intensity
rogue waves using deterministic arrays of dielectric nanostructures for
enhanced sensing and lithographic applications.
