Bound states of two-dimensional nonuniform waveguides

Wave amplitude gain within wedge waveguides through scattering by simple obstacles

Wave confinement, e.g., in waveguides, gives rise to a huge number of distinct phenomena. Among them, amplitude gain is a recurrent and relevant effect in undulatory processes. Using a general purpose protocol to solve wave equations, the boundary wall method, we demonstrate that for relatively simple geometries, namely, a few leaky or opaque obstacles inside a θ wedge waveguide (described by the Helmholtz equation), one can obtain a considerable wave amplification in certain spatially localized regions of the system. The approach relies on an expression for the wedge waveguide exact Green's function in the case of θ=π/M (M=1,2,...), derived through the method of images allied to group theory concepts. The formula is particularly amenable to numerical calculations, greatly facilitating simulations. As an interesting by-product of the present framework, we are able to obtain the eigenstates of certain closed shapes (billiards) placed within the waveguide, as demonstrated for triangular structures. Finally, we briefly discuss possible concrete realizations for our setups in the context of matter and electromagnetic (for some particular modes and conditions) waves.

Trapped modes in an infinite or semi-infinite tube with a local enlargement

Trapped modes in a hard cylindrical tube with a local axisymmetric enlargement or bulge and filled with a uniform acoustic medium is studied. The governing Helmholtz equation in the cylindrical coordinate system is employed to deal with this problem through the domain decomposition method and matching technique. The trapped modes and the corresponding frequencies less than the threshold frequency or cut-off frequency are derived. It is found that in addition to the fundamental mode, the second- and higher-order trapped modes exist and depend on the geometry parameters of the local bulge. The effects of the bulge radius and width on the frequencies are discussed. The local bulge leads to a decrease of the frequencies and the corresponding vibration mode is localized near the bulge. A multimodal analysis is made and frequency band gap of generalized trapped modes is also studied. A frequency band gap depends on the radius of a bulge and is independent of its width. The obtained results can be extended to analyze bound states in quantum wires.