Elastic spectra for a structurally chiral finite slab

We consider an artificial helical solid whose lattice vectors rotate around a given axis when displacing along such an axis; emulating the texture of a cholesteric liquid crystal. We analyze the general case of a local crystal symmetry for which the stiffness parameter values are such that the longitudinal and transverse elastic waves are coupled, causing the system to exhibit simultaneously two types of band gaps. Here, we calculate analytically for the first time, the elastic spectra of a structurally chiral elastic slab whose helical axis is normal to the sample borders, made with a finite number of periods; when elastic longitudinal and transverse circularly polarized waves impinge the slab. The outstanding features of the mentioned bandgaps are the following. One exhibits a circularly discriminatory behavior, in which only the right circularly polarized waves are reflected, whereas the left circularly polarized waves pass practically without change. The other band gap converts longitudinal incident waves in right circularly polarized reflected waves and vice versa.