Spin-Momentum Interlocking in Classical Fields

The relationship between spin and momentum is a cornerstone of wave physics, exemplified by the recent discovery of unidirectional spin-momentum locking. Here, we propose a fundamental and generalized spin-momentum relation, termed bidirectional interlocking, that treats spin and momentum as symmetric field constituents. We demonstrate that in N-wave lattices, the spin and momentum densities emerge as the mutual curls of one another─a universal relationship extending beyond electromagnetism to acoustic and water wave systems. This interlocking framework reveals a unique mechanical phenomenon valid for scatterers of arbitrary size: a dynamically tunable, purely spin-induced lateral force and an in-plane trapping force. We show that by simply tuning the phase difference or polarization of the incident waves, one can precisely control the equilibrium position or transport direction of the manipulated particle within the lattice. Such dynamic manipulation, akin to an optical conveyor belt, provides a level of reconfigurability that conventional static optical traps lack. Finally, we confirm that this interlocking remains robust under experimentally realistic conditions, including Gaussian-beam lattices and structural perturbations. Our results establish a unified paradigm for spin-momentum physics across classical wave systems, providing a versatile foundation for advanced wave-matter interactions and manipulation.