Bound states in coupled guides. I. Two dimensions

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Abstract
Bound states that can occur in coupled quantum wires are investigated. We consider a two-dimensional configuration in which two parallel waveguides (of different widths) are coupled laterally through a finite length window and construct modes which exist local to the window connecting the two guides. We study both modes above and below the first cutoff for energy propagation down the coupled guide. The main tool used in the analysis is the so-called residue calculus technique, in which complex variable theory is used to solve a system of equations which is derived from a mode-matching approach. For bound states below the first cutoff a single existence condition is derived, but for modes above this cutoff (but below the second cutoff), two conditions must be satisfied simultaneously. A number of results have been presented which show how the bound-state energies vary with the other parameters in the problem.

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