Abstract
Surface plasmons in graphene have mainly been affected by intrinsic optical phonons due to the vibrations of the carbon atoms and surface polar optical phonons (S-POPs) of the underlying dielectric surface. This plasmon hybridization dramatically changes the features of the plasmonic devices. However, a complete theoretical model for the graphene impedance to consider the optical phonons effects is yet remained to be developed. Here, we show how to derive a model for graphene impedance to include such impacts on graphene surface plasmons. Earlier models suffer from two limitations-i.e., the inability to show (i) the transformation of a single pure plasmonic mode into multiple hybrid plasmon-phonon excitations and (ii) the damping effect for energies beyond that of the intrinsic optical phonons due to the phonon emission. Our new model overcomes these two limitations. Then, we calculate the extinction spectra for a one-dimensional periodic array of graphene ribbons obtained through the impedance boundary condition method, addressing these obstacles. These spectra are directly related to graphene impedance, modeled using the dielectric function we developed in our earlier work. The extinction spectra show the presented model overcoming the limitations, firmly fitting the experimental data reported by others. Furthermore, we introduce our developed model for graphene to the CST Studio software to verify the accuracy of our extinction relation and impedance model. This study can be a step forward correctly predicting the behavior of graphene-based plasmonic devices.