  Polaritons are the collective excitations of many atoms dressed by resonant
photons, which can be used to explain the slow light propagation with the
mechanism of electromagnetically induced transparency. As quasi-particles,
these collective excitations possess the typical feature of the matter
particles, which can be reflected and deflected by the inhomogeneous medium in
its spatial motion with some velocity. In this paper we develop a quantum
theory to systematically describe the spatial motion of polaritons in
inhomogeneous magnetic and optical fields. This theoretical approach treats
these quasi-particles through an effective Schr\"{o}dinger equation with
anisotropic depression that the longitudinal motion is like a
ultra-relativistic motion of a "slow light velocity" while the transverse
motion is of non-relativity with certain effective mass. We find that, after
passing through the EIT medium, the light ray bends due to the
spatial-dependent profile of external field. This phenomenon explicitly
demonstrates the exotic corpuscular property of polaritons with anisotropic
nature.
