## 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 ${M}^{2}$, 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 ${M}^{2}$, our approach gives an alternative way to describe laser beam propagation that is especially well suited to characterize Bessel-type nondiffracting beams.

© 2005 Optical Society of America

Full Article | PDF Article