2002/03/15 by A. J. Turski, B. Atamaniuk, Turski, A. J. +3
Physics and Astronomy · #FOS: Physical sciences #Optics (physics.optics) #physics.optics
paper · pdf · doi:10.48550/arxiv.physics/0203047
14 pages, 3 figures, zipped file, submitted to Journal of Technical Physics (Warsaw, Poland)
arxiv created 2002/03/15 · arxiv updated 2009/12/01
Fundamental rules and definitions of Fractional Differintegrals are outlined. Factorizing 1-D and 2-D Helmholtz equations four fractional eigenfunctions are determined. The functions exhibit incident and reflected plane waves as well as diffracted incident and reflected waves of the half-plane edge. They allow to construct the Sommerfeld half-plane diffraction solutions. Parabolic-Wave Equation (PWE, Leontovich-Fock) for paraxial propagation is factorized and differetial fractional solutions of Fresnel-integral type are derived. We arrived at two solutions, which are the mothers of known and new solutions.