Nondiffracting vortex beams with continuous orbital angular momentum order dependence

We introduce a new class of nondiffracting fractional vortex beams that connect Bessel beams of successive order in a smooth transition. The new fractional-order beams preserve the same nondiffracting feature of Bessel beams of integer order, and their orbital angular momentum per photon can take any value in a continuous range. The propagation of the more physically realizable fractional-order Bessel-Gauss beams, i.e. fractional Bessel beams apodized by a Gaussian transmittance, through general ABCD optical systems is studied in detail and is complemented by the experimental generation of several instances of fractional beams which in turn confirms our theoretical predictions.