Ginzburg-Landau equation bound to the metal-dielectric interface and transverse nonlinear optics with amplified plasmon polaritons

TL;DR

This paper derives a complex Ginzburg-Landau equation for amplified surface plasmon polaritons at metal-dielectric interfaces, explicitly including nonlinear boundary effects, and analyzes filamentation and localized plasmon structures.

Contribution

It introduces a novel asymptotic method that incorporates nonlinear boundary conditions to accurately model nonlinear surface waves.

Findings

Derived the Ginzburg-Landau equation for plasmon polaritons.

Analyzed filamentation and spatially localized plasmon structures.

Highlighted the importance of nonlinear boundary terms.

Abstract

Using a multiple-scale asymptotic approach, we have derived the complex cubic Ginzburg-Landau equation for amplified and nonlinearly saturated surface plasmon polaritons propagating and diffracting along a metal-dielectric interface. An important feature of our method is that it explicitly accounts for nonlinear terms in the boundary conditions, which are critical for a correct description of nonlinear surface waves. Using our model we have analyzed filamentation and discussed bright and dark spatially localized structures of plasmons.