![]() ![]() ![]() We consider a non-resonant type metamaterial here since its working frequency range is considerably broader than that by resonant type metamaterials, ensuring stability and robustness in performance. Therefore, an extremely wide range of stiffness control, even covering the peculiar property of smaller normal stiffness than shear stiffness, is found achievable. In this arrangement, the slit length in particular has a significant effect on the relative ratio of effective shear stiffness to effective normal stiffness for the perpendicular material axis to the slits. The novelty of our metamaterial resides in the special “off-centered” slit arrangement, critical for the realization of polarization anomaly. In this paper, we first propose an elastic metamaterial the rectangular unit cell of which consists of off-centered double slits. Due to the classic paradigms for composite design, the required material property is not achievable as long as one uses natural ingredients 5, 6, 13. Unfortunately, the artificial realization of the anomaly in the composite form is quite difficult due to the peculiar anisotropic material property it requires smaller normal stiffness than shear stiffness for specific material axes while normal stiffness should be larger than shear stiffness for other material axes 5, 6, 7. Thus, the phenomenon has great potential for a variety of applications like retardation, filtering, controlling of scattering and radiation, tailoring of polarization state, and so on. The relative dispersion–not only frequency-dependent dispersion, but also spatial dispersion–properties can be reversed between the modes when we use the anomaly. To the best of our knowledge, the polarization anomaly is the one and only phenomenon that breaks the usual dispersion relation between the in-plane longitudinal and shear modes without any resonance scheme. Equivalently, it means that the (quasi-)longitudinal velocity is faster than (quasi-)shear velocity for usual solids. ![]() This is because normal stiffness governing the longitudinal mode is larger than shear stiffness governing the shear mode for usual solids even with strong anisotropy. Such behaviors are dilatation (volume change) and dilatation-less (shape change) deformations where their relative properties are restrictively tailorable. Unlike two orthogonal transverse modes in electromagnetics, however, the dissimilar, longitudinal and shear, modes in elasticity involve far different physical behaviors. For longitudinal and shear polarizations of elastic waves, similar phenomena may be employed to manipulate the relative dispersion property. Birefringence, dichroism, or Brewster angle effect, among others, are commonly used to tailor the polarization-dependent dispersion property. In the electromagnetic field, the precise control of the wave polarization state is desired for numerous applications including optical communications, spectroscopy, microscopy, etc 8, 9, 10, 11, 12. Polarization is an important wave characteristic of vector waves like electromagnetic and elastic waves. Considerable research in the past few decades have paid attention to the theoretical demonstration on the phenomenon, but no actual applications have been explored thus far due to the lack of natural materials exhibiting the desired phenomenon. It refers to the polarization transition from longitudinal to shear modes when the wavevector is moved along a certain equi-frequency contour (EFC) branch. Among others, the “polarization anomaly” is a very unusual phenomenon 1, 4, 5, 6, 7. The unique, complex nature of elastic waves in polarization manifests some interesting wave phenomena that cannot be found in other wave fields. The rich variety of polarizations, longitudinal and shear (transverse) in bulk media, and the strong coupling between the dissimilar modes are notable examples 1, 2, 3. Elastic waves possess distinct wave polarization characteristics that are different from electromagnetic and acoustic waves. ![]()
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