Bound States in Weakly Deformed Waveguides: Numerical Versus Analytical Results

Abstract

We have studied the emergence of bound states in weakly deformed and/or heterogeneous waveguides, comparing the analytical predictions obtained using a recently developed perturbative method, with precise numerical results, for different configurations (a homogeneous asymmetric waveguide, a heterogenous asymmetric waveguide and a homogeneous broken-strip). In all the examples considered in this paper we have found excellent agreement between analytical and numerical results, thus providing a numerical verification of the analytical approach.

Weakly Bound States in Heterogeneous Waveguides: A Calculation to Fourth Order

“…The fourth order formula obtained in the present paper have been recently applied in Ref. [11] to obtain the behaviour of the lowest eigenvalue of a "broken strip", in the case of infinitesimal bendings, reproducing the numerical results in the literature [12].…”