Multiple bound states in scissor-shaped waveguides

TL;DR

This paper investigates how the number and energies of bound states in a scissor-shaped waveguide depend on the crossing angle, revealing the emergence of multiple states and their transformation into quasi-bound states as the angle varies.

Contribution

It provides a detailed analysis of bound states in a tunable, open waveguide geometry, highlighting the dependence on the crossing angle and the transition to quasi-bound states.

Findings

Number of eigenvalues increases with asymmetry.

Bound-state energies increase as the angle approaches 90°.

Strongly bent states form pairs with small energy differences.

Abstract

We study bound states of the two-dimensional Helmholtz equations with Dirichlet boundary conditions in an open geometry given by two straight leads of the same width which cross at an angle $\theta$. Such a four-terminal junction with a tunable $\theta$ can realized experimentally if a right-angle structure is filled by a ferrite. It is known that for $\theta=90^o$ there is one proper bound state and one eigenvalue embedded in the continuum. We show that the number of eigenvalues becomes larger with increasing asymmetry and the bound-state energies are increasing as functions of $\theta$ in the interval $(0,90^o)$. Moreover, states which are sufficiently strongly bent exist in pairs with a small energy difference and opposite parities. Finally, we discuss how with increasing $\theta$ the bound states transform into the quasi-bound states with a complex wave vector.