We study the uniqueness of solutions of Helmholtz equation for a problem that concerns wave propagation in waveguides. The classical radiation condition does not apply to our problem because the inhomogeneity of the index of refraction extends to infinity in one direction. Also, because of the presence of a waveguide, some waves propagate in one direction with different propagation constants and without decaying in amplitude. We provide an explicit condition for uniqueness for rectilinear waveguides, which takes into account the physically significant components, corresponding to guided and non-guided waves; this condition reduces to the classical Sommerfeld-Rellich condition in the relevant cases. By a careful asymptotic analysis we prove that the solution derived by Magnanini and Santosa (SIAM J. Appl. Math. 2001; 61:1237-1252) for stratified media satisfies our radiation condition.

A radiation condition for uniqueness in a wave propagation problem for 2-D open waveguides / G. Ciraolo, M. R. - In: MATHEMATICAL METHODS IN THE APPLIED SCIENCES. - ISSN 0170-4214. - 32:10(2009), pp. 1183-1206.

A radiation condition for uniqueness in a wave propagation problem for 2-D open waveguides

G. Ciraolo;
2009

Abstract

We study the uniqueness of solutions of Helmholtz equation for a problem that concerns wave propagation in waveguides. The classical radiation condition does not apply to our problem because the inhomogeneity of the index of refraction extends to infinity in one direction. Also, because of the presence of a waveguide, some waves propagate in one direction with different propagation constants and without decaying in amplitude. We provide an explicit condition for uniqueness for rectilinear waveguides, which takes into account the physically significant components, corresponding to guided and non-guided waves; this condition reduces to the classical Sommerfeld-Rellich condition in the relevant cases. By a careful asymptotic analysis we prove that the solution derived by Magnanini and Santosa (SIAM J. Appl. Math. 2001; 61:1237-1252) for stratified media satisfies our radiation condition.
electromagnetic fields; wave propagation; Helmholtz equation; optical waveguides; uniqueness of solutions; radiation condition
Settore MAT/05 - Analisi Matematica
2009
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/675150
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