Fibonacci and fully degenerate conical diffraction cascades: Exploring the Poincaré sphere by path interference

Tailoring light beams in terms of intensity, phase, and polarization distribution has recently garnered significant attention. This work considers vector beams obtained by the natural conical diffraction phenomenon, occurring when a focused light beam travels along one of the optic axes of a biaxial crystal. If a cascade of several aligned biaxial crystals is used, in its sharpest plane this phenomenon usually gives rise to a concentric ring pattern with spatially varying linear polarization, thus covering the equator of the Poincaré sphere. Here, we propose smart arrangements of conical diffraction cascades based on Fibonacci and degenerate sequences leading to vectorial beams addressing multiple areas of the Poincaré sphere. The present approach is based on the concept of path interference and enables a clear spatial separation between regions exhibiting distinct polarization states (linear, elliptical, circular).