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In this paper, we propose a structure for graphene spaser (Surface Plasmon Amplification by Stimulated Emission of Radiation) 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.

In the present work, we propose using doped Silicon Quantum Dot (SiQD) as a source of coherent surface plasmons (SPASER). The possibility of spasing in single SiQD is investigated theoretically utilizing full quantum mechanical treatment. We show that spasing can take place in doped SiQDs whenever Quality factor of a plasmon mode exceeds some minimum value. The minimum value depends on size and doping concentration of SiQDs. It can be used to design an optimum structure as SPASER in silicon technologies. The condition on Quality factor is translated to a condition for radius and it is shown that for a given Localized Surface Plasmon (LSP) mode, the radius should be less than some critical value. This value only depends on mode index. The required relations for design purposes are derived and, as an example of feasibility of the approach, a SPASER is designed for mid infrared. Moreover, we propose a more applicable device by arranging an array of doped SiQDs on top of a graphene layer. Coupling the Surface Plasmon Polariton (SPP) modes of graphene with LSP modes of SiQDs causes outcoupling of an intense ultra narrow beam of coherent SPPs to be used in real probable applications.

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