Conversion of Spin-Orbit-Coupled Optical Vortices via Complex Coupling

Optical vortices provide an additional freedom because of the orbital angular momentum (OAM), enabling significant advances in high-dimensional information encoding, quantum communication, and super-resolution imaging. However, the controlled conversion between spin-orbit-coupled (SOC) optical vortices of different orders remains challenging. Here, we propose a novel four-step Floquet driving protocol governed by complex coupling to realize conversion between distinct angular momentum characteristics in strongly confined waveguide arrays. Optical vortices naturally give rise to complex-valued coupling coefficients owing to their intrinsic spatial-phase structure and spin-orbit interaction. Building on this mechanism, we implement a Floquet driving protocol in the waveguide array, which supports corner and edge states determined by the coupling parameters. Exploiting the corner states, we demonstrate dynamic conversion of total-angular-momentum order from $j$ to $-j$ across successive two or three driving periods. This work opens a pathway toward dynamic modulation of structured light and advances the integration of OAM-based functionalities in photonic platforms.