Stability of Exponential Tails in the Scattering on Wedges and Impurities

TL;DR

This paper analyzes a 2D quantum scattering model involving a localized particle and an impurity, revealing how exponential tail stability persists in such scattering scenarios, with implications for optical fiber impurity interactions.

Contribution

It introduces an exactly solvable 2D model for particle-impurity interaction, linking quantum scattering with classical diffraction phenomena and optical impurity interactions.

Findings

The model is exactly solvable and analogous to Sommerfeld diffraction.

Exponential tails in scattering states remain stable in the model.

Qualitative insights into optical fiber impurity interactions are provided.

Abstract

We study a simple exactly solvable 2D model describing the interaction of a localized particle with an impurity. The localization potential $V(x)=-\alpha \delta (x)$ causes the particle to be trapped in the y-axis, and the `impurity' is modeled by a straight impenetrable edge extending along the positive x-axis. We show that the problem described can be treated as the Sommerfeld diffraction from an infinite edge. We use the model to present qualitative arguments on the nature of interaction of polarized light traveling along an optical fiber with external impurities.