Modeling surface plasmon-polariton gain in planar metallic structures.

Amplification of the single-interface and long-range surface plasmon-polariton modes is studied in planar metallic structures incorporating gain media formed by Rhodamine 6G dye molecules in solution. We employ a theoretical model that accounts for the nonuniformity of the gain medium close to the metal surface due to position-dependent dipole lifetime and pump irradiance. The results of this model are used as a baseline for a comparative study against two simplified models: one neglects the position-dependent dipole lifetime while the other assumes a uniform gain medium. The discrepancies between the models are explained in terms of the mode overlap with the gain distribution near the metal. For the cases under analysis, the simplified models estimate the required pump irradiance with deviation factors that vary from 1.45 at the lossless conditions to 8 for gains near saturation. The relevance of describing properly the amount o gain interacting with the SPP mode and the role played by the dipole quantum efficiency are discussed.