Injection pumped single mode surface plasmon generators: threshold, linewidth, and coherence.

We develop a theoretical model for the semiconductor generator of the sub-wavelength surface plasmons, operating on a single mode and often referred to as a spaser. We show that input-output characteristics of the single mode spaser does not exhibit nonlinearity inherent in most lasers, but the linewidth of the emission collapses, as in any laser which allows us to define the threshold. Our rigorous derivations show that as long as the mode remains substantially sub-wavelength in all three dimensions, the threshold current (power) shows virtually no dependence on the gain material and geometry of the active layer and is determined solely by the intrinsic loss of the metal in the device. For the semiconductor single mode surface plasmon generators operating in the telecommunication range the threshold current is on the order of 10-20 mA, and the threshold current density grows fast with the decrease of the device size reaching 100's of kA/cm(2) or more. This fact makes coherent sources of sub-wavelength SP's unattainable from our point of view, but there exists a room for efficient broad-band incoherent SP sources either optically or electrically pumped.