Origin of folded bands in metamaterial crystals

Recently it has been found numerically that the spectra of metamaterial crystals may contain pairs of bands which disappear inside the Brillouin zone. We observe that the wave equations for such systems are essentially non-Hermitian, but PT-symmetric. We show that the real-frequency spectra correspond to PT-symmetric solutions of the wave equation. At those momenta in the Brillouin zone where apparently no solutions exist, there appear pairs of complex-frequency solutions with spontaneously broken PT symmetry.