The diffraction theory of Kirchhoff is applied to the semi-infinite aperture of a black half-screen. The derivative of the spherical Green's function is taken into account without any approximation. The uniformly evaluated scattering integral is compared with the physical optics solution. It is shown that the non-omitted term causes the existence of fictitious diffracted waves.

We derive integral representations suitable for studying the focusing of electromagnetic waves through a symmetrically hyperbolic focusing lens into uniaxial crystal in the presence of cylindrical and coma aberrations using Maslov’s method. The uniaxial crystal used is the negative crystal LiNbO3. Numerical computations are made to obtain the results for focused fields inside negative uniaxial ...

Vacuum energy and other spectral functions of Laplace-type differential operators have been studied approximately by classical-path constructions and more fundamentally by boundary integral equations. As the first step in a program of elucidating the connections between these approaches and improving the resulting calculations, I show here how the known solutions for Kirchhoff quantum graphs em...

The Huygens-Fresnel diffraction integral has been formulated for incident spherical waves with use of the Kirchhoff obliquity factor and the wave front as the surface of integration instead of the aperture plane. Accurate numerical integration calculations were used to investigate very-near-field (a few aperture diameters or less) diffraction for the well-established case of a circular aperture...

A method is proposed for the calculation of the short-range wake field potentials of an ultra-relativistic bunch passing near some irregularities in a beam pipe. The method is based on the space-time domain integration of Maxwell’s equations using Kirchhoff’s formulation. We demonstrate this method on two cases where we obtain the wake potentials for the energy loss of a bunch traversing an iri...

A method for evaluation of scattering from rough surfaces which is similar to the Kirchhoff approximation is considered. However, it is based on a local parabolic approximation of the surface irregularities rather than a tangent plane approximation and two iterations of the surface field integral equation. The method, first proposed by Belobrov and Fuks [Izv. VUZ Radiofiz. 29, 1083-1089 (1986);...

In this sequel to a rather recent paper on the classical problem of Helmholtz–Kirchhoff flows by Vic. V. Sychev, TsAGI Science Journal 41(5), 531–533 (2010), the representation of the flow far from the body and its specific implications discussed in that study are revisited. Here the concise derivation of these findings resorts to well-known Levi-Cività’s method and, alternatively, only fundame...

For any simple connected undirected graph, it is well known that the Kirchhoff and multiplicative degree-Kirchhoff indices can be computed using the Laplacian matrix. We show that the same is true for the additive degree-Kirchhoff index and give a compact Matlab program that computes all three Kirchhoffian indices with the Laplacian matrix as the only input.

We show explicitly that the well-known Gouy phase shift of any focused beam originates from transverse spatial confinement, which, through the uncertainty principle, introduces a spread in the transverse momenta and hence a shift in the expectation value of the axial propagation constant. A general expression is given for the Gouy phase shift in terms of expectation values of the squares of the...