Measurement of the complex nonlinear optical response of a surface plasmon-polariton

We observe experimentally the self-phase modulation of a surface plasmon-polariton (SPP) propagating along a gold film bounded by air in a Kretschmann-Raether configuration. Through analyzing the power dependence of the reflectance curve as a function of the incidence angle, we characterize the complex-valued nonlinear propagation coefficient of the SPP. Moreover, we present a procedure that can further extract the complex value of the third-order nonlinear susceptibility of gold from our experimental data. Our work provides direct insights into nonlinear control of SPPs utilizing the nonlinearity of metals, and serves as a practical method to measure the complex-valued third-order nonlinear susceptibility of metallic materials.