One-dimensional description of cylindrically symmetric laser beams: application to bessel-type nondiffracting beams.
(2005) Journal of the Optical Society of America. A, Optics, image science, and vision — Vol. 22, n° 7, p. 1274-1287 (2005)
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- Abstract
- We introduce a new representation of coherent laser beams that are usually described in circular cylindrical coordinates. This representation is based on the decomposition of a laser beam of a given azimuthal order into beams exhibiting Cartesian symmetry. These beams, which we call constituent waves, diffract along only one of their transverse dimensions and propagate noncollinearly with the propagation axis. A cylindrically symmetric laser beam is then considered a coherent superposition of constituent waves and is represented by an integral over an angular variable. Such a representation allows for the introduction of the propagation factor M2, defined in terms of one-dimensional root-mean-square (rms) quantities, in the treatment of two-dimensional beams. The representation naturally leads to the definition of a new rms parameter that we call the quality factor Q. It is shown that the quality factor defines in quantitative terms the nondiffracting character of a laser beam. The representation is first applied to characterize Laguerre-Gauss beams in terms of these one-dimensional rms parameters. This analysis reveals an asymptotic link between Laguerre-Gauss beams and one-dimensional Hermite-Gauss beams in the limit of high azimuthal orders. The representation is also applied to Bessel-Gauss beams and demonstrates the geometrical and one-dimensional characters of the Bessel-Gauss beams that propagate in a nondiffracting regime. By using two separate rms parameters, Q and M2, our approach gives an alternative way to describe laser beam propagation that is especially well suited to characterize Bessel-type nondiffracting beams.
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Rousseau, G., Gay, D., & Piché, M. (2005). One-dimensional description of cylindrically symmetric laser beams: application to bessel-type nondiffracting beams. Journal of the Optical Society of America. A, Optics, image science, and vision, 22(7), 1274-1287. https://doi.org/10.1364/JOSAA.22.001274 (Original work published 2005)