Spin angular momentum modulation via spin-orbit interaction in fractional orbital angular momentum beams

Light exhibits both spin and orbital angular momentum (SAM and OAM). These two forms of angular momentum remain independent in paraxial fields, but become coupled in confined fields through spin-orbit interactions (SOI). The SOI mechanism allows for the manipulation of SAM to generate structured light fields featuring nontrivial topological characteristics, such as optical skyrmions. Conventional OAM beams, nonetheless, carry discrete integer topological charges (TCs), leading to discrete SAM states. This discrete property poses a persistent challenge for achieving continuous control of SAM. To tackle this fundamental issue, we explored fractional orbital angular momentum (FOAM) beams, whose TCs are extended from integers to fractions, to realize continuous and precise control of SAM. A direct mathematical relationship between the fractional effective TCs of FOAM beams and the orientation distributions of the SAM vector has been derived. This theoretical prediction has been experimentally verified using our home-built near-field mapping system, by which the distinct SAM distributions of surface cosine waves regulated by FOAM beams were mapped out. As a potential application, we also devised an inverse detection method to accurately measure the fractional effective TCs of FOAM, which achieved theoretical and experimental accuracies of 10^-5 and 10^-2, respectively. These advancements may enhance our fundamental understanding of the SOI mechanism, and hence could create novel opportunities for light field manipulation, optical communication, and other related areas.