Shear Bloch waves and coupled phonon-polariton in periodic piezoelectric waveguides.

•Dispersion relation for SH waves in piezoelectric periodic waveguide is obtained.•Zero frequency stop bands, trapped modes, anomalous features are identified.•Extremal widths of the stop bands can be moved to the middle of the Brillouin zone.•At acoustic frequencies polaritons occur at wavelengths much larger than the cell.•Polaritons occur at wavelengths comparable with the unit cell at optic frequencies.