Generalized flux trajectories: New insights into partially coherent Airy beams

Abstract: The propagation of Airy beams in free space is characterized by being non dispersive, which warrants the shape invariance of their intensity distribution, and self-accelerating along the transverse direction. These distinctive traits are still present in partially coherent Airy beams as long as the reach of their back tail (and hence their energy content) is not importantly reduced. To investigate the effects associated with the decrease of the beam coherence and its power content (by smoothly reducing the reach of their back tails), here we introduce a novel and insightful methodology based on a generalization of the concept of flux trajectory for paraxial partially coherent beams. This methodologies emphasizes the role of phase relations, thus helping to clarify why and how the beam smears out spatially along its propagation. This formalism, though, is general enough to tackle other types of structured light beams with whatever degree of partial coherence, from full coherence to total incoherence.