Scattering of a diagonally incident focused Gaussian beam by an infinitely long homogeneous circular cylinder

Abstract

I expand the radiation potential of an arbitrary monochromatic electromagnetic wave in the cylindrical coordinate eigenfunctions of the scalar Helmholtz equation. Since the resulting beam shape coefficients are found to be an inverse Fourier transform of the z component of the beam fields, the incident Gaussian beam is parameterized by a Fourier angular spectrum of plane waves. The beam's partial-wave coefficients are then obtained, as well as the scattered fields produced by the interaction of the beam with an infinitely long homogeneous circular cylinder. The fields are evaluated analytically in the far zone by the method of stationary phase, and the physical interpretation of the results are discussed extensively.