Conditions for Loss Compensation of Surface Plasmon Polaritons Propagation on a Metal/Gain Medium Boundary

One way to compensate for the surface plasmon polariton (SPP) propagation losses is to use a gain medium. However, simply ensuring high enough gain is not sufficient because it may violate the bounded character of the wave. Therefore, a detailed theoretical analysis is needed for the determination of the conditions for lossless or amplified SPP propagation. Here presented is an exact theoretical analysis of the SPP propagation in the case of an infinite metal/gain medium boundary. It is shown that the conditions for lossless/amplified SPP propagation can be conveniently examined and presented as a simply connected region in the complex plane of the gain medium dielectric function. Effective and minimum gain parameters are introduced, which facilitates the simultaneous analyses of different gain media/metals combinations. The practical application of these results is illustrated for several gain media/metal (silver, gold and aluminium) systems.