  Spin-momentum locking is an intrinsic property of surface electromagnetic
fields and its study has led to the discovery of photonic spin lattices and
diverse applications. Previously, dispersion was ignored in the spin-momentum
locking, giving rise to abnormal phenomena contradictory to the physical
realities. Here, we formulate four dispersive spin-momentum equations for
surface waves, revealing universally that the transverse spin vector is locked
with the momentum. The locking property obeys the right-hand rule in the
dielectric but the left-hand rule in the dispersive metal/magnetic materials.
In addition to the dispersion, the structural features can affect the
spin-momentum locking significantly. Remarkably, an extraordinary longitudinal
spin originating from the coupling polarization ellipticity is uncovered even
for the purely polarized state. We further demonstrate the spin-momentum
locking properties with diverse photonic topological lattices by engineering
the rotating symmetry. The findings open up opportunities for designing robust
nanodevices with practical importance in chiral quantum optics.
