Fractional Derivative Analysis of Helmholtz and Paraxial-Wave Equations

Details Fractional Derivative Analysis of Helmholtz and Paraxial-Wave Equations Fractional Derivative Analysis of Helmholtz and Paraxial-Wave Equations

2002-03-15

arxiv.org/abs/physics/0203047v1

Physics

Optics

14 pages, 3 figures, zipped file, submitted to Journal of Technical Physics (Warsaw, Poland)

Scientific paper

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.

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