Caustic light in nonlinear photonic media

Light rays naturally focus to bright intensity lines, which are called caustics. They occur as sunlight forms ramified networks at the bottom of swimming pools or lines of bright intensity behind drinking glasses. Generating artificial caustic light became an active branch in the timely field of structured light with open questions how to control these complex intensity distributions and their propagation. This talk will address fundamental aspects on the evolution of higher-dimensional caustics in 3D laser light, of which the Airy beam is only the first light structure in a row of many. Further, we present novel techniques to shape desired caustics into propagation-invariant, so-called non-diffracting beams, with potential applications in long-focal (light-sheet) microscopy. Also, we connect oceanographic rogue waves with an optical analogue system of caustic networks in nonlinear photorefractive media to simulate the effect of weakly scattering media on the amplification or hindrance of extreme waves.