Hermite-Bessel beams and the geometrical representation of nondiffracting beams with orbital angular momentum.

We investigate theoretically and experimentally the decomposition of high-order Bessel beams in terms of a new family of nondiffracting beams, referred as Hermite-Bessel beams, which are solutions of the Helmholtz equation in Cartesian coordinates. Based on this decomposition we develop a geometrical representation of first-order Bessel beams, equivalent to the Poincaré sphere for the polarization states of light and implement an unitary transformation within our geometrical representation using linear optical elements.