Abstract
Abstract. A new multipole solution in plane-polar coordinates for the scattering of an arbitrary TE- or TM-polarized incident field by an infinitely extended slit in a plane screen is derived. To this end a classical three-domain problem with a complete multipole expansion in each of the domains is formulated. The unknown multipole amplitudes are found from the continuity conditions of the tangential electric and magnetic field components. Finally an infinite system of linear equations is derived which can be approximated by a numerically tractable finite one leading to a solution with an arbitrary accuracy. The results are numerically successfully compared to those ones obtained by classically solving the strip problem using Mathieu functions and by a subsequent application of the rigorous form of the Babinet principle. Numerical results include the comparison of the scattered fields obtained for an incident uniform complex-source beam and for an incident plane wave.
Highlights
Because of its general theoretical and practical interest the scattering and diffraction of acoustic and electromagnetic waves by a slit has been very often discussed in the literature
The results are numerically successfully compared to those ones obtained by classically solving the strip problem using Mathieu functions and by a subsequent application of the rigorous form of the Babinet principle
Numerical results include the comparison of the scattered fields obtained for an incident uniform complex-source beam and for an incident plane wave
Summary
Because of its general theoretical and practical interest the scattering and diffraction of acoustic and electromagnetic waves by a slit has been very often discussed in the literature. Morse and Rubinstein (1938) used this method and computed first numerical results for the scattering of TM- and TE-polarized plane waves by a strip/slit. The numerical evaluation includes a successful validation of the method by comparing the results with those obtained by the aforementioned solution of the strip problem and application of the Babinet principle. We compare the scattered fields for an incident plane wave to those obtained for an incident uniform complex-source beam with different parameters. The goal of this investigation is to find out if and for which parameters a uniform CSB can replace an incident plane wave. Ticularly in the context of scattering from special sections as part of infinitely extended structures like the scattering by the tip of a circular or elliptic cone
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