Abruptly autofocusing and autodefocusing optical beams with arbitrary caustics

We propose a simple yet efficient method for generating abruptly autofocusing optical beams with arbitrary caustics. In addition, we introduce a family of abruptly autodefocusing beams whose maximum intensity suddenly decreases by orders of magnitude right after the target. The method relies on appropriately modulating the phase of a circularly symmetric optical wavefront, such as that of a Gaussian, and subsequently on Fourier-transforming it by means of a lens. If two such beams are superimposed in a Bessel-like standing wave pattern, then a complete mirror-symmetric, with respect to the focal plane, caustic surface of revolution is formed that can be used as an optical bottle. We also show how the same method can be used to produce accelerating 1D or 2D optical beams with arbitrary convex caustics.