Twist defects in helical sonic structures

We analyze theoretically both the acoustic wave propagation in periodic media made of anisotropic materials whose stiffness tensor is uniformly rotating along a given axis $x_3$ and the defect mode produced by twisting about $x_3$ one part of the helical structure with respect to the other. Within the Bragg band of the periodic structure, the twist defect gives rise to a resonant mode that is a superposition of two standing waves: one localized with $\exp \left(-\gamma |x_3|\right)$ dependence centered at the defect and the other extended over the whole sample. The ratio between the amplitudes of the localized and nonlocalized waves depends sharply on both the twist angle and the elastic anisotropy, and can assume huge values. The defect mode and the resonance frequency ${\omega }_0$ are defined by fully analytical and very simple expressions. Finally, we discuss how around ${\omega }_0,$ a finite sample acts as a frequency filter for circularly polarized shear waves, whose bandwidth can be changed by many orders of magnitude by varying the sample thickness, the twist angle, or the elastic anisotropy.