Progress In Electromagnetics Research
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By P. Vaveliuk, O. M. Matos, and G. A. Torchia

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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.

P. Vaveliuk, O. M. Matos, and G. A. Torchia, "Features of the Gouy Phase of Nondiffracting Beams," Progress In Electromagnetics Research, Vol. 140, 599-611, 2013.

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