Heat-induced soliton self-frequency redshift in the ultrafast nonlinear dynamics of active plasmonic waveguides

We investigate the ultrafast nonlinear dynamics of light propagating in an active plasmonic waveguide composed of a thin film of gold sandwiched by two silicon layers immersed in externally pumped Al2O3:Er3+. We model optical propagation in such system through a generalized Ginzburg-Landau equation, finding that heating affects the temporal dynamics of dissipative solitons by inducing a self-frequency redshift accompanied by deceleration in the time domain. We further evaluate the dependence of the self-induced redshift by developing a semianalytical variational approach, providing analytical predictions that are in excellent agreement with direct numerical simulations of the generalized Ginzburg-Landau equation. Our results provide a general understanding of ultrafast nonlinear dynamics in gold-based active plasmonic waveguides, as in particular the spectral shaping properties of propagating optical pulses.