Lossless tapers, Gaussian beams, free-space modes: Standing waves versus through-flowing waves

It was noticed in the past that, to avoid physical inconsistencies, in Marcatili's lossless tapers through-flowing waves must be drastically different from standing waves. First, we reconfirm this by means of numerical results based on an extended BPM algorithm. Next, we show that this apparently surprising behavior is a straightforward fallout of Maxwell's equations. Very similar remarks apply to Gaussian beams in a homogeneous medium. As a consequence, Gaussian beams are shown to carry reactive powers, and their active power distributions depart slightly from their standard pictures. Similar conclusions hold for free-space modes expressed in terms of Bessel functions.