  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.
