We study the uniqueness of solutions of Helmholtz equation for aproblem that concerns wave propagation in waveguides. The classicalradiation condition does not apply to our problem because theinhomogeneity of the index of refraction extends to infinity in onedirection. Also, because of the presence of a waveguide, some wavespropagate in one direction with different propagation constants andwithout decaying in amplitude.Our main result provides an explicit condition for uniqueness whichtakes into account the physically significant components,corresponding to guided and non-guided waves; this condition reducesto the classical Sommerfeld-Rellich condition in the relevant cases.Finally, we also show that our condition is satisfied by a solution,already present in literature, of the problem under consideration.
|Numero di pagine||24|
|Rivista||Mathematical Methods in the Applied Sciences|
|Stato di pubblicazione||Published - 2009|
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