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

## TL;DR

This paper explores how heating affects ultrafast soliton dynamics in active plasmonic waveguides, revealing a heat-induced redshift and deceleration of solitons, with analytical models matching numerical simulations.

## Contribution

It introduces a semi-analytical approach to understand heat-induced soliton redshift and dynamics in active plasmonic waveguides, combining modeling and numerical validation.

## Key findings

- Heating causes soliton self-frequency redshift.
- Analytical predictions match numerical simulations.
- Spectral shaping of optical pulses is achievable.

## Abstract

We investigate the ultrafast nonlinear dynamics of light emitted in an active plasmonic waveguide composed of a thin film of gold sandwiched by two silicon layers immersed in externally pumped Al$_2$O$_3$:Er$^{3+}$. We model optical propagation in such a dissipative system through a generalized cubic Ginzburg-Landau equation accounting for the amplification of the active medium and the effect of absorption and thermo-modulational nonlinearity of gold. We find that heating heavily affects the propagation of temporal dissipative solitons in such a plasmonic waveguide by producing a soliton self-frequency redshift accompanied by soliton deceleration in the time domain. By adopting a semi-analytical variational approach, we evaluate the dependence of the self-induced redshift by deriving a set of coupled differential equations for the pulse parameters. These equations provide physical insight into the complex nonlinear dynamics through simple approximate analytic expressions for temporal and frequency shifts. Such analytical predictions are found in excellent agreement with direct numerical simulations of the generalized cubic 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.