Tunable Fano resonances of a graphene/waveguide hybrid structure at mid-infrared wavelength.

A planar graphene/dielectric multilayer structure is investigated, where the graphene surface plasmon polariton and the planar waveguide mode are coupled to realize Fano resonances. Few-layer graphene with high doping levels is used to excite surface plasmons at mid-infrared wavelength. Reflectance of the structure is calculated numerically by transfer-matrix method, and tunable Fano resonances with different line shapes are demonstrated by varying doping levels of graphene. Properties of the Fano resonances are discussed qualitatively by calculating electric field distribution in the structure and quantitatively by utilizing an analytical fitting equation. We also calculate Goos-Hänchen shift of the Fano resonances as an example for potential applications, and find that large Goos-Hänchen shift appears for optimized doping levels of graphene.