Non-diffractive Hankel beams

Diffraction is an all-present phenomenon associated to the spreading of the transverse profile of a traveling wave. During the years, several works have shown the possibility to define invariant or non-diffractive solutions of the Helmholtz equation to limit the diffraction spreading in a certain region of space known as non-diffractive zone. Among these invariant solutions, Bessel beams have received a lot of attention since their introduction and experimentally validation by Durnin (J. Durnin, J. J. Miceli, Jr., and J. H. Eberly, Phys. Rev. Lett. 58, 1499, 1987). In particular, Bessel beams are generated by the combination of two cylindrical waves or Hankel functions, one traveling outward and the other inward over a radiating aperture (M. Ettorre and A. Grbic, IEEE Trans. Antennas Propag., vol. 60, no. 8, pp. 3605-3605, Aug. 2012). Therefore, a Bessel radiation is achieved on a small frequency band by means of a resonant radiating aperture. The properties of ideal Bessel beams are well established in literature. However, few works have been focusing on their composing cylindrical waves and relative non-diffractive behavior (J. C. Gutiérrez-Vega, M. D. Iturbe-Castillo, and S. Chávez-Cerda, Opt. Lett. 25, 1493, 2000).