Bound states in coupled guides. II. Three dimensions

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Abstract
We compute bound-state energies in two three-dimensional coupled waveguides, each obtained from the two-dimensional configuration considered in paper I [J. Math. Phys. 45, 1359–1379 (2004)] 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 paper 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.

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