Nonlinear surface plasmons

TL;DR

This paper derives an asymptotic nonlinear equation for surface plasmons on a planar interface, analyzing their properties, solutions, and potential for spatial focusing, with implications for nonlinear plasmonic phenomena.

Contribution

It introduces a new nonlocal, cubically nonlinear evolution equation for surface plasmons and proves existence results and Hamiltonian structure, advancing understanding of nonlinear plasmon dynamics.

Findings

Nonlinear effects can cause strong spatial focusing of plasmons.

Short-time existence of smooth solutions is established.

Numerical solutions suggest smoothness persists during focusing.

Abstract

We derive an asymptotic equation for quasi-static, nonlinear surface plasmons propagating on a planar interface between isotropic media. The plasmons are nondispersive with a constant linearized frequency that is independent of their wavenumber. The spatial profile of a weakly nonlinear plasmon satisfies a nonlocal, cubically nonlinear evolution equation that couples its left-moving and right-moving Fourier components. We prove short-time existence of smooth solutions of the asymptotic equation and describe its Hamiltonian structure. We also prove global existence of weak solutions of a unidirectional reduction of the asymptotic equation. Numerical solutions show that nonlinear effects can lead to the strong spatial focusing of plasmons. Solutions of the unidirectional equation appear to remain smooth when they focus, but it is unclear whether or not focusing can lead to singularity formation in solutions of the bidirectional equation.