Lymarenko R. The properties of singular component of diffraction field and its application for apertured electromagnetic field modeling.

The dissertation is devoted to developing new methods of analytical and experimental investigation the diffraction phenomena. A new treatment of the well-known Sommerfeld solution of the problem of plane-wave diffraction from a perfectly conducting half-plane is reported. The investigation of the singular wave component as informative part of diffraction field is an important new trend. It was shown that a system of dislocation in singular component composes the skeleton and represents the diffraction field topology. The analysis of topology of the diffraction field in case of plane wave diffraction on a slit and elliptical aperture was performed. The transformation of optical vortices trajectory under smooth deformation of aperture from circular to elliptical was studied. The vortices generation by plane wave diffraction on a wireframe elliptical aperture was considered. New compact solution for a field, which formed by linearly polarized plane wave diffraction on a perfectly conducting slit and a str ip, was obtained. For thoroughness the structure of additional evanescent wave for exact satisfying the boundary condition was considered. On the basis of this new representation the problem of diffraction arbitrary beam on the perfectly conducted half plane was solved. Due to this approach the symmetry features of diffraction process of arbitrary beams on half-plane, in particular symmetry in a far field are found out at a various degree of blocking of a beam by the screen. It was proposed a new method of apertured field modeling, based on the integral EDW-representation of diffraction field without paraxial approximation. Due to peculiarity of kernel this representation is very useful for providing numerical modeling the laser beam diffraction on complex amplitude-phase mask.