Fourier-space generation of abruptly autofocusing beams and optical bottle beams

We demonstrate analytically and experimentally that a circular abruptly autofocusing (AAF) Airy beam can be generated by Fourier-transforming an appropriately apodized Bessel beam whose radial oscillations are chirped by a cubic phase term. Depending on the relation between the chirp rate and the focal distance of the Fourier-transforming lens, it is possible to generate AAF beams with one or two foci, the latter case leading to the formation of an elegant paraboloid optical bottle.