Scattering and diffraction of an arbitrarily directed complex-source beam by a semi-infinite circular cone

The problem of an arbitrarily directed Gaussian beam (GB) illuminating an acoustically soft or hard semi-infinite circular cone is solved by using a complex source beam (CSB) whose 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 assigning a complex-valued source coordinate into the conventional spherical-multipole expression of the Green´s function, thus converting it to the response to the incident CSB. The solution requires the calculation of the associated Legendre functions of the 1st kind for a complex-valued argument. Beside a numerical analysis of these calculations, we also present numerical results for the total near- and far-fields.