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.

Tecently, Panuski and Mungan presented the results of their study of light diffraction from a variable-width single slit by observing and measuring the diffraction pattern on an observation screen placed at a fixed distance. In this way, the authors were able to demonstrate to students the important near-field effects for single-slit diffraction, which most often have been neglected in introductory courses. In this paper, we show that there exists very good agreement between observed data and theoretical calculations by plotting intensity from single slits using a method with Fresnel-Kirchhoff integrals (Fig. 1). In addition to these comparisons, and with the evaluation of the Fresnel numbers, we argue that Panuski and Mungan demonstrated not only the near-field Fresnel, but also the far-field Fraunhofer regimes as well as the transition between the two. Furthermore, with a greater increase in the slit width, the transition to the geometric regime can be demonstrated (Fig. 2).