A quantum field theory approach is presented to show that paraxial photons of any frequency in the full electromagnetic spectrum may posses arbitrary values of the orbital angular momentum along their propagation direction. Our framework also enables to propose multi-dimensional geometric quantum gates exploiting the orbital angular momentum of photons. The action of these gates is shown to be describable in a remarkably compact form by resorting to the Wigner representation.
We investigate light beam propagation in a fast photorefractive medium placed in an alternating electric ac-field to enhance the nonlinear response. It is shown that the joint action of the optical and material nonlinearities leads to formation of a narrow singularity of the light-induced space charge at the intensity maximum and to self-trapping of the light energy near the corresponding discontinuity of the index profile. Owing to the strong saturation of the material nonlinearity, the trapped beam propagates over long distances with only a weak loss of its power.