Nonlinear response of surface plasmon polaritons: a systematic comparison with new insights

The nonlinear coefficient gamma is a key parameter for studying nonlinear pulse propagation, as it relates the power in a waveguide mode to the nonlinear phase shift per unit length. It is well understood in dielectric waveguides, but less so in lossy plasmonic waveguides. A number of methods for calculating gamma have been proposed, each producing different expressions. Here, we comprehensively compare these methods for a surface plasmon polariton propagating at a gold-air interface, obtaining new insights into the nonlinear response of lossy waveguides.