Nonlinearity of surface-plasmon polaritons in sub-wavelength metal nanowires

We investigate the nonlinear propagation of surface plasmon polaritons guided on gold nanowires surrounded by silica glass. Based on the Lorentz reciprocity theorem, we derive a formula for the complex nonlinear susceptibility, and study its dependence on waveguide parameters and wavelength for the fundamental mode. Depending on these parameters both positive and negative signs of the real and imaginary parts of the nonlinear coefficient are predicted. This implies that nanowires exhibit the property of saturable absorption or optical limiting as well as positive and negative nonlinear phase shifts. The physical origin of this phenomenon is discussed.