  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.
  Our main result provides an explicit condition for uniqueness 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.
  Finally, we also show that our condition is satisfied by a solution, already
present in literature, of the problem under consideration.
