# 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 ro-
tating 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 calcu-
lus 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.

## History

## School

- Science

## Department

- Mathematical Sciences