Mode energy of graphene plasmons and its role in determining the local field magnitudes

We theoretically study the mode energy of graphene plasmons and its fundamental role in determining the local field magnitudes. While neglecting the magnetic field energy of the mode, we derive a concise expression for the total mode energy, which is independent on the details of the mode field distributions and valid for both propagating and localized modes. We find that the mean square of the local electric fields of a graphene plasmonic mode scales linearly with the light absorption rate of the mode and the electron relaxation time of graphene. The possible strategies for improving the local field magnitudes of graphene plasmons are also discussed. Our theoretical analysis presented here may benefit the design of various graphene-based optical and optoelectronic devices for light-harvesting or energy conversion.