Birefringence lens effects of an atom ensemble enhanced by an electromagnetically induced transparency

We study the optical control for birefringence of a polarized light by an atomic ensemble with a tripod configuration, which is mediated by the electromagnetically induced transparency with a spatially inhomogeneous laser. The atomic ensemble splits the linearly polarized light ray into two orthogonally polarized components, whose polarizations depend on quantum superposition of the initial states of the atomic ensemble. Accompanied with this splitting, the atomic ensemble behaves as a birefringent lens, which allows one polarized light ray passing through straightly while focuses the other light of vertical polarization with finite aberration of focus.