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.