We show that an analog of the physics at the Planck scale can be found in the
propagation of tightly focused laser beams. Various equations that occur in
generalized quantum mechanics are formally identical to those describing the
nonlinear nonlocal propagation of nonparaxial laser beams. The analysis
includes a generalized uncertainty principle and shows that the nonlinear
focusing of a light beam with dimensions comparable to the wavelength
corresponds to the spontaneous excitation of the so-called maximally localized
states. The approach, driven by the ideas of the quantum gravity physics,
allows one to predict the existence of self-trapped subwavelength solitary
waves for both focusing and defocusing nonlinearities, and opens the way to
laboratory simulations of phenomena that have been considered to be
inaccessible
