The nonlinear propagation constant of a surface plasmon

A surface plasmon that is excited on the interface separating a metal and a nonlinear semiconductor has a propagation constant that depends on the power carried by the plasmon. We present an analytic expression for the change in the propagation constant of the plasmon, KΔβ, as a function of the dielectric constants of the two media, the nonlinear refractive index of the semiconductor, n2,E, and the power carried by the plasmon. We define a figure of merit, P0, which is the power required for shifting the phase of the plasmon by π/2 along a distance S, (S = 1/2α, where α is the plasmon decay constant), and find the wavelength dependence of KΔβ and P0.