Quantization and soliton-like solutions for the $\Phi\Psi$-model in a optic fiber

TL;DR

This paper models electromagnetic fields in an optical fiber with a dielectric sample, providing analytical solutions, quantization, and identifying soliton-like solutions in the nonlinear dielectric medium.

Contribution

It introduces a mesoscopic model for dielectric media in optical fibers, offering analytical descriptions, quantization methods, and soliton solutions not previously detailed.

Findings

Analytical scattering basis for the system

Quantization of the electromagnetic field

Existence of soliton-like solutions in the dielectric

Abstract

In the framework of a mesoscopical model for dielectric media we provide an analytical description for the electromagnetic field confined in a cylindrical cavity containing a finite dielectric sample. This system is apted to simulate the electromagnetic field in a optic fiber, in which two different regions, a vacuum region and a dielectric one, appear. A complete description for the scattering basis is introduced, together with field quantization and the two-point function. Furthermore, we also determine soliton-like solutions in the dielectric, propagating in the sample of nonlinear dielectric medium.