Fano resonance generating in graphene oligomers is systematically investigated in this study. The graphene oligomer is able to form plasmonic molecule due to the strong interaction between the graphene nanodisks, which is the basic of generation of Fano resonance. The optimization of Fano resonance is discussed by varying parameters of graphene oligomers such as the size of nanodisk, the chemical potential and the electron momentum relaxation time in midinfrared frequency. All these changes have a great effect on Fano resonance. Simultaneously, the environmental index sensing effect of the Fano resonance reaches a high sensitivity.
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