## Electromagnetic Diffraction and Propagation Problems |

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### Contents

New methods in diffraction theory Fock 1948 | 3 |

The distribution of currents induced by a plane wave on the surface of a con | 10 |

Theory of diffraction by a paraboloid of revolution Fock 1957 | 23 |

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### Common terms and phrases

absolute value Airy functions amplitude analytic continuation analytic function angle of incidence anomalous propagation approximate asymptotic expressions atmospheric waveguide attenuation factor Bessel functions body boundary conditions calculated Chapter characteristic equation coefficient common logarithms complex complex plane considered constant contour contour integral convex body coordinates corresponding cosine series covariant and contravariant covariant derivative critical wavelength cubic equation current density curvature curve curvilinear coordinates denote derivatives dielectric constant differential equation differential geometry diffraction dimensionless quantities dipole displacement vector distance earth earth's surface electric field electromagnetic electromagnetic field electromagnetic waves equal exact solution exponential function expressed in terms extremum field components finite Fourier series Fresnel diffraction Fresnel formulae Fresnel integral Fresnel reflection function W geometrical meaning geometrical optics Green's function Hankel function height Hertz function holomorphic function horizon Huygens principle illuminated region incident wave infinity integral integral equation integrand introduce inversion layer ionosphere Laplace operator Legendre polynomials Leontovich local field M-curve magnetic magnetic field magnetic permeability magnetic potentials Maxwell equations meromorphic function metric tensor negative obtain parabolic parabolic coordinates parabolic cylinder functions parabolic equation paraboloid paraboloid of revolution parameter penumbra region perfect conductor phase plane wave problem quadratic form quantity quantum mechanics radiation condition radio waves radiowave propagation radius radius of curvature ray optics real axis recurrence relations reflected wave reflection formula refractive index regions of convergence relation residue roots satisfies Section shadow singularity solution spherical coordinates spherical earth stationary phase tangential components tion transcendental function tropospheric unit vector upper half-plane V. A. FOCK valid values variable vector wave equation wave vector waveguide wavelength Wronskian zero