  Usual Gaussian beams are particular scalar solutions to the paraxial
Helmholtz equation, which neglect the vector nature of light. In order to
overcome this inconvenience, Simon et al. (J. Opt. Soc. Am. A 1986, 3, 536-540)
found a paraxial solution to Maxwell's equation in vacuum, which includes
polarization in a natural way, though still preserving the spatial Gaussianity
of the beams. In this regard, it seems that these solutions, known as
Gauss-Maxwell beams, are particularly appropriate and a natural tool in optical
problems dealing with Gaussian beams acted or manipulated by polarizers. In
this work, inspired in the Bohmian picture of quantum mechanics, a
hydrodynamic-type extension of such a formulation is provided and discussed,
complementing the notion of electromagnetic field with that of
(electromagnetic) flow or streamline. In this regard, the method proposed has
the advantage that the rays obtained from it render a bona fide description of
the spatial distribution of electromagnetic energy, since they are in
compliance with the local space changes undergone by the time-averaged Poynting
vector. This feature confers the approach a potential interest in the analysis
and description of single-photon experiments, because of the direct connection
between these rays and the average flow exhibited by swarms of identical
photons (regardless of the particular motion, if any, that these entities might
have), at least in the case of Gaussian input beams. In order to illustrate the
approach, here it is applied to two common scenarios, namely the diffraction
undergone by a single Gauss-Maxwell beam and the interference produced by a
coherent superposition of two of such beams.
