J. D. Ring, J. Lindberg, A. Mourka, M. Mazilu, K. Dholakia, and M. R. Dennis
Optics Express 20(17), 18955-18966 (2012)
We present a new solution of the paraxial equation based on the Pearcey function, which is related to the Airy function and describes diffraction about a cusp caustic. The Pearcey beam displays properties similar not only to Airy beams but also Gaussian and Bessel beams. These properties include an inherent auto-focusing effect, as well as form-invariance on propagation and self-healing. We describe the theory of propagating Pearcey beams and present experimental verification of their auto-focusing and self-healing behaviour.