  We study the essential spectra of formally self-adjoint elliptic systems on
doubly periodic planar domains perturbed by a semi-infinite periodic row of
foreign inclusions. We show that the essential spectrum of the problem consists
of the essential spectrum of the purely periodic problem and another component,
which is the union of the discrete spectra of model problems in the infinite
perturbation strip; these model problems arise by an application of the partial
Floquet-Bloch-Gelfand transform.
