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We develop a theoretical model to compute the local density of states in a confined plasmonic waveguide. Based on this model, we derive a simple formula with a clear physical interpretation for the lifetime modification of emitters embedded in the waveguide. The gain distribution within the active medium is then computed following the formalism developed in a recent work [Phys. Rev. B 78, 161401 (2008)], by taking rigorously into account the pump irradiance and emitters lifetime modifications in the system. We finally apply this formalism to describe gain-assisted propagation in a dielectric-loaded surface plasmon polariton waveguide.

Optical gain, spontaneous and stimulated emission of surface plasmon polaritons in confined plasmonic waveguide