Trifurcation of band-gap structure and coexistence of lattice-like states and critical states in piezoelectric period-doubling superlattices

We study the propagation of electromagnetic wave in piezoelectric period-doubling superlattices with using the generalized 4 × 4 transfer matrix method, and the dynamics of electromagnetic wave and acoustic wave is treated on equal footing. The band-gap structure trifurcates, which is understood within the framework of perturbation theory under periodic boundary condition. The uncoupled phononic branch of field distributions is Bloch-wave-like. For the coupled polaritonic branch, the lattice-like field distributions, for which Thue-Morse sequence is famous, also manifest in this piezoelectric period-doubling system and coexist with critical states. They can be characterized as extended if the superlattice size considered is large enough. In fact, our study suggests that such lattice-like field distributions are common phenomena in piezoelectric superlattices irrespective of lattice types and depend only on the frequency and domain widths, they reflect the intrinsic symmetry of the transfer matrices for the particular domain setting and frequency. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2007