  In contradistinction to a widespread belief that the spatial localization of
photons is restricted by a power-law falloff of the photon energy density,
I.Bialynicki-Birula [Phys. Rev. Lett. 80, 5247 (1998)] has proved that any
stronger -- up to an almost exponential -- falloff is allowed. We are showing
that for certain specifically designed cylindrical one-photon states the
localization is even better in lateral directions. If the photon state is built
from the so-called focus wave mode, the falloff in the waist cross-section
plane turns out to be quadratically exponential (Gaussian) and such strong
localization persists in the course of propagation.
