Optical Beams in Media with Spatial Dispersion

We theoretically predict a novel phenomenon of the diffraction-free propagation of the paraxial optical beam in the isotropic or cubic linear medium with spatial dispersion. Under the weak spatial dispersion condition, the paraxial wave equation is derived, in which there is the diffraction term with the coefficient G that depends on the compensation between the classic diffraction and spatial dispersion. Near the exciton dipole absorption line, we can have Γ = 0, then the beam propagates diffraction-freely, and its shape keeps unchangeable. Discussed are also the physical mechanism and the possible experimental candidates of crystals for the phenomenon.