Marcatili's Lossless Tapers and Bends: an Apparent Paradox and its Solution

Numerical results based on an extended BPM algorithm indicate that, in Marcatili's lossless tapers and bends, through-flowing waves are drastically different from standing waves. The source of this surprising behavior is inherent in Maxwell's equations. Indeed, if the magnetic field is correctly derived from the electric one, and the Poynting vector is calculated, then the analytical results are reconciled with the numerical ones. Similar considerations are shown to apply to Gaussian beams in free space.