Anomalous diffraction and Abel transformation of astigmatic beams in photonic lattices

We identify a novel and counterintuitive regime of discrete diffraction for astigmatic light beams in 2D tight-binding photonic lattices, in which diffraction is almost inhibited along the axis with strongest localization, whereas it is enhanced along the axis with weakest localization. Furthermore, beams of these kind exhibit dichotomy wave packet splitting during propagation, and each of the two wings of the wave packet turns out to implement an Abel transformation of the initial envelope of the astigmatic beam.