# Bound states in coupled guides. I. Two dimensions.

preprint

posted on 2005-08-01, 11:20 authored by Christopher LintonChristopher Linton, Keith RatcliffeBound states that can occur in coupled quantum wires are investigated. We
consider a two-dimensional configuration in which two parallel waveguides (of dif-
ferent 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 cut-off 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 cut-off
a single existence condition is derived, but for modes above this cut-off (but below
the second cut-off), 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.

## History

## School

- Science

## Department

- Mathematical Sciences

## Pages

276216 bytes## Publication date

2003## Notes

This pre-print has been submitted, and accepted, to the journal, Journal of Mathematical Physics [© American Institute of Physics]. The definitive version: LINTON, C.M and RATCLIFFE, K., 2004. Bound states in coupled guides. I. Two dimensions. Journal of Mathematical Physics, 45(4), pp. 1359-1379, is available at: http://jmp.aip.org/.## Language

- en