Asymmetric trapped modes in a tube waveguide with a bulge

Asymmetric trapped modes in a waveguide of a cylindrical hollow tube with a local bulge are studied. The problem is converted to solving a nonaxisymmetric boundary value problem associated with the three-dimensional Helmholtz equation subject to Dirichlet boundary condition. The domain decomposition method and matching technique are invoked for an infinitely long tube with a bulge and a semi-infinitely long tube with an end bulge. Asymmetric trapped modes along with the frequencies are determined and can be decomposed into a linear combination of those with the n-fold periodic symmetry. For each n-fold periodic trapped mode, whether azimuthal trapped modes exist depends on the radius and width of the bulge. The influence of the bulge’s size on the frequencies and intensity location of localized vibration is analyzed. The obtained results can be extended to analyze bound states in quantum wires.