Multiple bound states in scissor-shaped waveguides

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 $θ$. Such a four-terminal junction with a tunable $θ$ can realized experimentally if a right-angle structure is filled by a ferrite. It is known that for $θ=90^o$ 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 $θ$ 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 $θ$ the bound states transform into the quasi-bound states with a complex wave vector.