Bound state for dielectric waveguide with high contrast inset in the core

Abstract

We consider cylindrical dielectric waveguide with a core having a high contrast inset. It is assumed, that for certain conditions, for a waveguide with an insertion in the core there is a bound state appears below the bottom of the continuous spectrum. In this paper we pose the problem of proving the existence of such state and obtain an upper estimate of the distance from the eigenvalue to the threshold.