We prove that there are no non-zero square-integrable solutions to a
two-dimensional Helmholtz equation in some unbounded inhomogeneous domains
which represent junctions of stratified media. More precisely, we consider
domains that are unions of three half-planes, where each half-plane is
stratified in the direction orthogonal to its boundary. As for the well-known
Rellich uniqueness theorem for a homogeneous exterior domain, our result does
not require any boundary condition. Our proof is based on half-plane
representations of the solution which are derived through a generalization of
the Fourier transform adapted to stratified media. A byproduct of our result is
the absence of trapped modes at the junction of open waveguides as soon as the
angles between branches are greater than $\pi$/2.

Questo articolo esplora i giri e le loro implicazioni.

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