Photon localization barrier can be overcome

In contradistinction to a widespread belief that the spatial localization of photons is restricted by a power-law falloff of the photon energy density, Bialynicki-Birula [Phys. Rev. Lett. 80 (1998) 5247] 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.