  We derived the analytical forms of refractive index and Snell law for
dipolar-exchange spin waves of reflection and refraction at a magnetically
heterogeneous interface in a geometrically confined planer structure composed
of different magnetic thin films from a microscopic scattering approach. A
novel behavior, the optical total reflection, was demonstrated for spin waves
with a specific interface between Yttrium iron garnet (Y3Fe5O12) and Permalloy
(Ni80Fe20), by analytical and micromagnetic numerical calculations.
