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Bound states in coupled guides. I. Two dimensions.

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posted on 01.08.2005, 11:20 by Christopher LintonChristopher Linton, Keith Ratcliffe
Bound 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.



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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:



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