Kiełczyński Piotr, Wieja Krzysztof, Balcerzak Andrzej
Institute of Fundamental Technological Research, Polish Academy of Sciences, ul. Pawińskiego 5B, 02-106 Warsaw, Poland.
Sensors (Basel). 2024 Dec 29;25(1):143. doi: 10.3390/s25010143.
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.
在本文中，我们证明了扭转表面弹性波可以沿着嵌入常规弹性介质中的超材料弹性杆（圆柱体）的曲面传播。超材料杆的关键参数是其弹性柔顺性s44(1)ω，它随频率ω的变化类似于德鲁德金属模型中的介电函数εω。因此，弹性柔顺性s44(1)ω作为频率ω的函数可以取负值s44(1)ω<0。负弹性柔顺性（s44(1)ω<0）使得能够出现新的表面态，即新型的表面弹性波。实际上，所提出的扭转弹性表面波可以被视为沿着嵌入电介质中的金属杆（圆柱体）传播的表面等离激元极化激元（SPP）电磁（光学）波的弹性类似物。因此，我们推导了新的扭转弹性表面波的色散关系和群速度的相应解析方程。新发现的扭转弹性表面波几乎展现出其电磁SPP对应物的所有非凡特性，例如在引导杆的圆柱表面（r = a）附近波能量的强烈亚波长集中、非常低的相速度和群速度等。因此，新的扭转弹性表面波可用于：（a）近场亚波长声学成像（超分辨率），（b）声波捕获（零群速度和相速度）等。重要的是，新发现的扭转弹性表面波可为开发具有非常高的质量灵敏度的新一代超声传感器（例如粘度传感器）、生物传感器和化学传感器奠定基础。
