Khoroshun G. Phase singularities analysis in a diffraction light field

The conditions of the wavefront dislocations and amplitude extrema formation in a wave field produced by diffraction on opaque obstructions and by two-beam interference are analyzed. The predicted model of the formation of wavefront dislocations, their evolution and topology in the paraxial approximation is developed. The stationary problem of a perturbed beam evolution in space XYZ was reduced to dynamical problem of the field component diffusion at the plane XY in formal ІtimeІ t ( ). The dislocations in form of "dipoles" of optical vortices appear in perpendicular direction to the strong inhomogeneity area of a light stream G(x, y, t) in two possible mechanisms. On this basis the regeneration of singular beam and the efficient synthesis of singular beam from Gaussian beam by the phase wedge technique are analyzed. The problem of plane wave diffraction by a circular aperture is solved rigorously using Hankel transform and Kirchhoff boundary conditions. No phase singularities are found on the axis andthe shift of the amplitude extrema was detected with respect to Zommefield solution in paraxial approximation. The phase velocity modulation to c/2 at the distances corresponding to even Fresnel numbers is revealed. Similar analysis for Fresnel diffraction field behind a non-transparent disk has shown that the phase velocity at the shadow area can noticeably exceed c. The appearance of the phase delay was revealed theoretically by wavefront shape calculation and was measured experimentally by the method of interference of the diffracted beam with tilted plane wave.