Articles | Volume 13
https://doi.org/10.5194/ars-13-57-2015
https://doi.org/10.5194/ars-13-57-2015
03 Nov 2015
 | 03 Nov 2015

Spherical-multipole analysis of an arbitrarily directed complex-source beam diffracted by an acoustically soft or hard circular cone

A. Reinhardt, H. Bruens, L. Klinkenbusch, M. Katsav, and E. Heyman

Abstract. An analytical approach to analyze the diffraction of an arbitrarily directed complex-source beam (CSB) by an acoustically soft or hard semi-infinite circular cone is presented. The beam is generated by assigning a complex-valued location to a point source; its waist and direction are defined by the real and imaginary parts of the source coordinate, respectively. The corresponding scalar boundary-value problem is solved by a spherical-multipole analysis. The solution requires the calculation of associated Legendre functions of the first kind for complex-valued arguments which turns out to be a non-trivial task. Beside a numerical analysis of the corresponding algorithms we present numerical results for the total near- and scattered far-fields.

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Short summary
An arbitrarily directed complex-source beam (CSB) is diffracted by an acoustically soft or hard semi-infinite circular cone. The method can be used to probe any desired part of the cone inclduing its tip. The scattered field is isolated by subtracting the incident from the diffracted field and can be used to derive diffraction coefficients for improving asymptotic methods such as the GTD or the UTD.