  We examine the spin-orbit coupling effects that appear when a wave carrying
intrinsic angular momentum interacts with a medium. The Berry phase is shown to
be a manifestation of the Coriolis effect in a non-inertial reference frame
attached to the wave. In the most general case, when both the direction of
propagation and the state of the wave are varied, the phase is given by a
simple expression that unifies the spin redirection Berry phase and the
Pancharatnam--Berry phase. The theory is supported by the experiment
demonstrating the spin-orbit coupling of electromagnetic waves via a surface
plasmon nano-structure. The measurements verify the unified geometric phase,
demonstrated by the observed polarization-dependent shift (spin-Hall effect) of
the waves.
