Temporal Nonlinear Dynamics of Plasmon-Solitons, a Duffing Oscillator-Based Approach

Plasmon-Solitons are quasi-particles resulting from coupling the plasmon modes and solitary solutions. This coupling can be intrinsically resonant in order to form plasmon-solitons with a high localization and large propagation length. This paper deals with the temporal nonlinear dynamics of plasmon-solitons in a plasmonic waveguide. Duffing equation is recognized as the temporal part of the nonlinear amplitude equation governing the plasmonic waveguide. Duffing equation is analytically solved for the low nonlinearity regime. It is shown that the Duffing oscillator waveforms stand for the temporal nonlinear dynamics of plasmon-solitons. The energy exchange of Lorentz-type bright and dark modes gives rise to a Fano resonance. It is thus shown that the interaction of solitons and the formation of plasmon- solitons is inherently nonlinear. It is accordingly indicated that the nonlinear modulation of the plasmon-solitons is achievable via tuning the nonlinearity of the plasmonic waveguide. The results can be appealing for the researchers intending to design the plasmonic waveguides with the high localization as well as the large propagation length. In particular, an all-plasmonic modulation method can be contemplated.