Stability of Exponential Tails in the Scattering on Wedges and Impurities

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.