Practicality of compensating the loss in the plasmonic waveguides using semiconductor gain medium

We consider the issue of compensating the loss in plasmonic waveguides with semiconductor gain material and show that, independent of specific geometry, full loss compensation in plasmonic waveguides with significantly sub-wavelength light confinement (less than λ/4n) requires current density well in excess of 100 kA/cm ². This high current density is attributed to the unavoidable shortening of recombination time caused by the Purcell effect inherent to sub-wavelength confinement. Consequently, an injection-pumped plasmonic laser that is truly sub-wavelength in all three dimensions (spaser) would have threshold current densities that are hard to obtain in any conceivable semiconductor device.