Exact solution of conducting half plane problems in terms of a rapidly convergent series and an application of the multiplicative calculus

Authors: ALİ UZER

Abstract: The problem of cylindrical wave incidence on a conducting half plane has been considered. A modal solution for Green's function of the problem is transformed into contour integral representations in a complex plane. Some contour deformations and changes of variables are then made for the integrals. Finally, the resultant integrals are transformed back into a series, which converges rapidly to the exact solution when the observation angles are close to the reflection/shadow boundaries (RSBs) of the conducting half plane. The multiplicative calculus is employed in deriving an expression that can be used for obtaining approximate solutions when the observation angles are away from the RSBs of the conducting half plane. The derived expressions are seen to be very simple for implementing in any computational environment.

Keywords: Diffraction, conducting half plane, half plane screen, Sommerfeld problem, steepest descent method, multiplicative calculus

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