Accelerating beams are a class of laser beam that consist of a strongly localized high intensity lobe that follows a curved trajectory. Since their discovery in 2007 (Siviloglou et al), they have been applied to particle sorting and nonlinear optics.
We have developed an approach based on identifying accelerating beams as a specific case of caustics to generate arbitrary accelerating beams, even in the nonparaxial regime.
A very novel application of ultraintense nonparaxial femtosecond accelerating beams to laser processing has been recently reported in our group: the unique structure of accelerating beams allow for straightforward edge profiling, as can be seen on the SEM picture on the left. See Mathis et al, Appl. Phys. Lett. 101,071110 (2012) (link)