Electrically tunable graded photonic crystal lens based on graphene plasmons.

Controlling the nonlinear relationship between surface plasmon polariton (SPP) mode index and chemical potential of graphene can be used in the field of active transformation optics. Here, we propose an electrically tunable 2D Graded Photonic Crystal (GPC) lens based on graphene SPP platform. Our platform comprises a graphene monolayer integrated into a back-gated structure with nano-patterned gate insulators. When the chemical potential of the graphene surface is designed to operate in the nonlinear region, the designed GPC lens can be continuously transformed between a Maxwell's fish-eye lens and a Luneburg lens by tuning the gate voltage. The range of the lens background chemical potential for allowing this transformation is systematically studied. To compensate for the significant errors inherent in the conventional effective medium theory (EMT) during the homogenization of photonic crystals (PCs), we propose a generalized effective medium theory (GEMT). The validity and accuracy of this approach are verified through comparisons with true values (based on rigorous eigenvalue solutions) and EMT values. Due to its advantages of on-site controls and easy fabrication characteristics, the proposed graphene GPC provides a new way for practical on-chip light manipulation.