New Torsional Surface Elastic Waves in Cylindrical Metamaterial Waveguides for Sensing Applications

In this paper, we demonstrate that torsional surface elastic waves can propagate along the curved surface of a metamaterial elastic rod (cylinder) embedded in a conventional elastic medium. The crucial parameter of the metamaterial rod is its elastic compliance s44(1)ω, which varies as a function of frequency ω analogously to the dielectric function εω in Drude's model of metals. As a consequence, the elastic compliance s44(1)ω can take negative values s44(1)ω<0 as a function of frequency ω. Negative elastic compliance (s44(1)ω<0) enables the emergence of new surface states, i.e., new types of surface elastic waves. In fact, the proposed torsional elastic surface waves can be considered as an elastic analog of Surface Plasmon Polariton (SPP) electromagnetic (optical) waves propagating along a metallic rod (cylinder) embedded in a dielectric medium. Consequently, we developed the corresponding analytical equations, for the dispersion relation and group velocity of the new torsional elastic surface wave. The newly discovered torsional elastic surface waves exhibit virtually all extraordinary properties of their electromagnetic SPP counterparts, such as strong subwavelength concentration of the wave energy in the vicinity of the cylindrical surface (r=a) of the guiding rod, very low phase and group velocities, etc. Therefore, the new torsional elastic surface waves can be used in: (a) near-field subwavelength acoustic imaging (super-resolution), (b) acoustic wave trapping (zero group and phase velocity), etc. Importantly, the newly discovered torsional elastic surface waves can form a basis for the development of a new generation of ultrasonic sensors (e.g., viscosity sensors), biosensors, and chemosensors with a very high mass sensitivity.