Features of the gouy phase of nondiffracting beams

Abstract

It is shown how the linear Gouy phase of an ideal nondiffracting beam of ±(k-kz)z form, with kz being the projection of the wavevector of modulus k of the plane wave spectrum onto the propagation axis z, is built from a rigorous treatment based on the successive approximations to the Helmholtz equation. The so much different families of nondiffracting beams with a continuum spectrum, as Bessel beams, Mathieu beams and Parabolic ones, as well as nondiffracting beams with a discrete spectrum, as kaleidoscopic beams, have an identical Gouy phase, which fully governs the beam propagation dynamics. Hence, a real beam whose Gouy phase is close to that linear Gouy phase in a given range, will have nondiffracting-like properties on such a range. These results are applied to determine the effective regime in which a physically realizable beam can be treated as a nondiffracting one. As an fruitful example, the Gouy phase analysis is applied to fully establish the regime in which a Helmholtz-Gauss beam propagates with nondiffracting-like properties.