Cyclic Evolution of Synergized Spin and Orbital Angular Momenta

Spin angular momentum (SAM) and orbital angular momentum (OAM) are fundamental physical characteristics described by polarization and spatial degrees of freedom, respectively. Polarization is a feature of vector fields while spatial phase gradient determines the OAM ubiquitous to any scalar field. Common wisdom treats these two degrees of freedom as independent principles to manipulate wave propagations. Here, their synergy is demonstrated. This is achieved by introducing two orthogonal p-orbitals as eigenbases, whose spatial modal features are exploited to generate OAM, and the associated orbital orientations provide means to simultaneously manipulate polarizations. Through periodic modulation and directional coupling, a full cyclic evolution of synchronized and synergized SAM-OAM is realized. Remarkably, this evolution acquires a nontrivial geometric phase, leading to its representation on a Möbius strip. Experimentally, an acoustic cavity array is designed, whose dipole resonances precisely mimic the p-orbitals, with pressure fields featuring the spatial characteristics and velocity fields the vectorial orientations. Based on this synergy, a spin-orbital-Hall effect is further showcased, highlighting the intricate locking of handedness, directionality, spin density, and spatial mode profile. This study unveils a fundamental connection between SAM and OAM, promising avenues for their novel applications in trapping, coding, and communications.