Shaping the far-zone intensity, degree of polarization, angle of polarization, and ellipticity angle using vector Schell-model sources

Abstract

This paper presents a method to control both the shape and polarization of a beam in the far field using a vector Schell-model source. Given a desired far-zone beam shape and polarization, and applying Fourier and statistical optics theory, we derive the requisite second-order moments of said source, discuss what aspects of the far-zone beam can be controlled, and develop a step-by-step procedure for synthesizing the required random vector field instances. We validate this approach with Monte-Carlo wave-optics simulations. The results are found to be in very good agreement with the desired far-zone beam characteristics. The beam-shaping technique developed in this paper will find use in optical trapping, optical communications, directed energy, remote sensing, and medical applications. Keywords: Beam shaping, Coherence, Polarization, Random sources, Schell-model sources, Statistical optics