Synthesis of an incident aperiodic tapered beam

This paper presents a technique for generating numerically an incident tapered beam of a prescribed polarization and a prescribed incidence angle by summing a finite number of propagating uniform plane waves, each constituent plane wave having its own magnitude, phase, incidence angle and polarization. Our three ad-hoc schemes for choosing the magnitude, the incidence angle and the polarization of a constituent plane wave are different from those by Braunisch et al. Our choice of the propagating plane waves corresponds to a sampling of the physical angular (θ, φ) space. This contrasts with the two-dimensional Fourier transform technique by Braunisch et al. and its Cartesian sampling of the (k_x, k_y) spectral plane where k_x=(k_osinθcosφ) and k_y=(k_osinθsinφ). Our technique is based on the summation of only propagating plane waves, whereas the technique by Braunisch et al. is based on the summation of both propagating and evanescent plane waves.