The Goos-Hanchen shift analysis in optical lattices under the parity-time symmetry

This article investigates the Goos-Hanchen(GH) shift of the reflected light of an ensemble of optical lattices in a cavity. We consider a lambda-type ensemble of three-level atoms to form the optical lattice and apply three fields, two weak fields (probe and microwave) and one strong field. The microwave field transforms the medium into a gain medium, resulting in the optical lattice containing both loss and gain. The co-existence of gain and loss leads to parity-time symmetry in the system. By satisfying the parity-time symmetry condition, we can modify the magnitude of the GH shift. Our results suggest that the GH shift can be controlled in systems exhibiting parity-time symmetry.