The nonlinear coefficient is a key parameter for studying nonlinear pulse propagation, as it relates the powerin 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 have been proposed, eachproducing different expressions. Here, we comprehensively compare these methods for a surface plasmon polaritonpropagating at a gold-air interface, obtaining new insights into the nonlinear response of lossy waveguides.
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