Comparative analysis of geometric transformation-based sorting systems for fractional vector beams with polarization mutation angle indeterminacy

The Polarization Topological Charge (PTC) is a crucial parameter of a Cylindrical Vector Beam (CVB). Defined as the repetition number of polarization state changes along the azimuth axis, its sign indicates the polarization’s rotation direction. This paper delves into the effects of polarization mutation within Fractional Vector Beams (FVB) with angular uncertainty on PTC sorting systems. We compare three optical geometric coordinate transformation methods: Log-Polar (LP), Beam-Copying (BC), and Spiral Transformation (ST), focusing on their robustness and suitability. Our findings show that the azimuth angle of polarization mutation markedly influences the PTC sorting system’s output, leading to measurable uncertainties. Importantly, these uncertainties are not intrinsic to the FVB, but rather stem from the sorting system itself. Our study concludes that the BC method is optimal for PTC spectra analysis, whereas the ST method with carefully selected parameters is preferable for average PTC analysis.