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Using long-range surface plasmon polaritons light can propagate in metalnano-scale waveguides for ultracompact opto-electronic devices. Gold is animportant material for plasmonic waveguides, but although its linear opticalproperties are fairly well understood, the nonlinear response is still underinvestigation. We consider propagation of pulses in ultrathin gold stripwaveguides, modeled by the nonlinear Schr\"odinger equation. The nonlinearresponse of gold is accounted for by the two-temperature model, revealing it asa delayed nonlinearity intrinsic in gold. The consequence is that the measurednonlinearities are strongly dependent on pulse duration. This issue has so faronly been addressed phenomenologically, but we provide an accurate estimate ofthe quantitative connection as well as a phenomenological theory to understandthe enhanced nonlinear response as the gold thickness is reduced. In comparisonwith the previous works, the analytical model for the power-loss equation hasbeen improved, and can be applied now to cases with a high laser peak power. Weshow new fits to experimental data from literature and provide updated valuesfor the real and imaginary part of the nonlinear susceptibility of gold forvarious pulse durations and gold layer thicknesses. Our simulations show thatthe nonlinear loss is inhibiting efficient nonlinear interaction with low-powerlaser pulses. We therefore propose to design waveguides suitable for themid-IR, where the ponderomotive instantaneous nonlinearity can dominate overthe delayed hot-electron nonlinearity and provide a suitable plasmonicsplatform for efficient ultrafast nonlinear optics.

Ultrafast nonlinear dynamics of thin gold films due to an intrinsic delayed nonlinearity