On the basis of the linear response theory, we calculate the components of the electromagnetic propagator of a non-magnetic system, consisting of alternating superconductor–dielectric slabs of different thicknesses in the case when one of the layers breaks the translational symmetry. The photonic band structure and the corresponding power spectra are studied from the poles and the imaginary part of the electromagnetic propagator. It is shown that as the magnitude of the in-plane wave vector rises, the frequency of the lowest localized mode increases and the highest-frequency localized mode decreases. On the other hand, for a fixed in-plane wave vector it is shown that there appear additional modes in the band gap.