Trapped modes for off-centre structures in guides

The existence of trapped modes near obstacles in two-dimensional waveguides is well established when the centre-line of the guide is a line of symmetry for the geometry. In this paper we examine cases where no such line of symmetry exists. The boundary condition on the obstacle is of Neumann type and both Neumann and Dirichlet conditions on the guide walls are treated. A variety of techniques (variational methods, boundary integral equations, slender-body theory, modified residue calculus theory) are used to investigate trapped mode phenomena in a number of different frequency bands.