Plasmon-soliton waves in planar slot waveguides: I. Modeling

TL;DR

This paper develops two models to analyze stationary nonlinear plasmonic waves in one-dimensional slot waveguides with a Kerr nonlinear dielectric core, providing analytical and numerical tools for understanding their behavior.

Contribution

It introduces a simplified analytical model and a comprehensive numerical model for studying nonlinear plasmon-soliton waves in slot waveguides.

Findings

Analytical solutions for field profiles using Jacobi elliptic functions.

Closed-form nonlinear dispersion relation derived.

Numerical solutions constrained by analytical conditions.

Abstract

We present two complementary models to study stationary nonlinear solutions in one-dimensional plasmonic slot waveguides made of a finite-thickness nonlinear dielectric core surrounded by metal regions. The considered nonlinearity is of focusing Kerr type. In the first model, it is assumed that the nonlinear term depends only on the transverse component of the electric field and that the nonlinear refractive index change is small compared to the linear part of the refractive index. This first model allows us to describe analytically the field profiles in the whole waveguide using Jacobi elliptic special functions. It also provides a closed analytical formula for the nonlinear dispersion relation. In the second model, the full dependency of the Kerr nonlinearity on the electric field components is taken into account and no assumption is required on the amplitude of the nonlinear term. The disadvantage of this approach is that the field profiles must be computed numerically. Nevertheless analytical constraints are obtained to reduce the parameter space where the solutions of the nonlinear dispersion relations are sought.