New Shear Horizontal (SH) Surface Acoustic Waves Propagating at the Interface Between Two Elastic Half-Spaces

It is commonly agreed that shear horizontal (SH) surface acoustic waves cannot exist on an elastic half-space or at the interface between two different elastic half-spaces. However, in this paper (inspired by the newly developed elastic meta materials) we will show that SH surface elastic waves can propagate at the interface between two elastic half-spaces, providing that one of them is a metamaterial half-space with a negative elastic compliance $S_{44}(\omega)$ . In addition, if $S_{44}(\omega)$ changes with frequency $\omega$ as the dielectric function $\mathcal{E}(\omega)$ in Drude's model of metals, then the proposed SH ultrasonic waves can be considered as an acoustic analogue of Surface Plasmon Polariton (SPP) electromagnetic waves propagating at the metal-dielectric interface. Analytical expressions for the dispersion equation, phase and group velocities of the new SH elastic surface wave were developed. The newly discovered SH elastic surface wave inherits many of extraordinary properties of SPP electromagnetic waves such as: strong subwavelength concentration of the wave field in the proximity of the guiding interface, low phase and group velocity etc. Therefore, the proposed new SH ultrasonic surface waves can potentially be used in: a) near-field subwavelength acoustic imaging, b) acoustic sensors with extremely large mass sensitivity, c) wave trapping (zero group and energy velocity) and d) non-reciprocal and topological waveguides.