Bound states in coupled guides . II . Three dimensions

We compute bound-state energies in two three-dimensional coupled waveguides, each obtained from the two-dimensional configuration considered in part I by rotating the geometry about a different axis. The first geometry consists of two concentric circular cylindrical waveguides coupled by a finite length gap along the axis of the inner cylinder and the second is a pair of planar layers coupled laterally by a circular hole. We have also extended the theory for this latter case to include the possibility of multiple circular windows. Both problems are formulated using a mode-matching technique, and in the cylindrical guide case the same residue calculus theory as used in I is employed to find the bound-state energies. For the coupled planar layers we proceed differently, computing the zeros of a matrix derived from the matching analysis directly. Department of Mathematical Sciences, Loughborough University, LE11 3TU, UK ([email protected]). 1