▎ 摘　　要

In this letter, we have studied the optical lateral shifts of transmitted and reflected lights in a defect structure doped by a single layer of graphene nanostructure. For adapting the optical features of the lateral shifts, we have first studied the refractive index properties of the defect layer. We have studied the conditions for achieving the negative and positive refractive index of the graphene monolayer system. After that, we have discussed the optical lateral shifts of the reflected and transmitted light beams when the refractive index of the graphene nanostructure become positive or negative, respectively. We have found that the enhanced lateral shifts for reflected and transmitted lights may be possible for a positive refractive index. For the negative refractive index, we have realized that simultaneous negative or positive lateral shifts are possible for the reflected and transmitted light beams. In our proposed scheme, the lateral shifts at the fixed incident angle are possible only by tuning the optical parameters without needing to change the cavity structure.