Faraday Rotation as a Control Parameter for Poincar´e-Sphere Polarization States

Vector beams which are described on higher-order Poincaré spheres provide a powerful framework for representing structured light fields whose polarization and spatial phase are inseparably linked. Although such states can be generated by various optical elements, a practical challenge remains in controlling their polarization change during propagation. In this work, we aim to analyze the role of the Faraday rotation angle as a tunable control parameter that couples directly to the azimuthal coordinate of the Poincaré sphere. Through theoretical modeling and visualizations, we show how linear, circular, and elliptical polarizations evolve under varying Faraday angles, highlighting similarities and differences with intrinsic Poincaré sphere rotations. Our results demonstrate that Faraday rotation can serve as an in-line, magnetically tunable actuator for polarization control, offering a compact and non-mechanical alternative to conventional polarization optics. This perspective opens new opportunities for adaptive imaging, optical communication, sensing, and integrated photonic devices where real-time polarization control of vector modes is required.