  We study the spectrum of the Helmholtz equation in a two-dimensional infinite
waveguide, containing a weak heterogeneity localized at an internal point, and
obeying Dirichlet boundary conditions at its border. We prove that, when the
heterogeneity corresponds to a locally denser material, the lowest eigenvalue
of the spectrum falls below the continuum threshold and a bound state appears,
localized at the heterogeneity. We devise a rigorous perturbation scheme and
derive the exact expression for the energy to third order in the heterogeneity.
