spaser based on graphene tube

In this paper, we propose a structure for graphene spaser and develop an electrostatic model for quantizing plasmonic modes. using this model, one can analyze any spaser consisting of graphene in the electrostatic regime. the proposed structure is investigated analytically and the spasing condition is derived. we show that spasing can occur in some frequencies where the quality factor of plasmonic modes is higher than some special minimum value. finally, an algorithmic design procedure is proposed, by which one can design the structure for a given frequency. as an example, a spaser with plasmon energy of 0.1 ev is designed.