Combination of Fourier transform Jones matrix and beam coherence polarization matrix: Application to a double polarizer rectangular aperture

Abstract

In this work, we extend the Fourier transform Jones (FTJ) matrix approach to handle input scalar fields with spatially variant transverse profiles. Additionally, we integrate the FTJ matrix with the beam coherence-polarization (BCP) matrix, suitable for describing partially coherent and partially polarized light. This approach is particularly effective when the polarization diffractive optical element is illuminated with a quasi-monochromatic paraxial scalar field with transverse spatial coherence, but with any degree of polarization and transverse profile. We apply the method to a meaningful example: a rectangular aperture with orthogonal polarizers on each half, illuminated with uniform randomly polarized light. We provide experimental validation using a randomly polarized He-Ne laser and a specially fabricated double polarizer mask. Furthermore, by placing a polarizer behind the polarization diffractive optical element, we generate a scalar beam with spatial incoherence across two distinct zones, suggesting the potential use of randomly polarized lasers with binary patterned polarizers to encode arbitrary binary coherence functions.

Keywords

• Polarization
• Diffraction
• Fourier Transform
• Coherence