Abstract
In this study, a spring–mass physical model is proposed to study the complex band structure of a one-dimensional parity-time (PT)-symmetric local resonant phononic crystal. By solving the kinetic equations, the analytical solutions of the dispersion relation and effective mass are obtained. As is known, the infinite effective mass would appear at the resonant frequency in a Hermitian system without any gain or loss. Once the balanced gain and loss are added to form a PT-symmetric system, the infinite effective mass would become finite, and the exceptional points can be observed in the subwavelength realm. With the increase in gain and loss, exceptional points would coalesce and form a higher order one. The numerical simulations in a practical structure agree well with the analytical analysis. In addition, the simulated transmission/reflection spectrum and field distribution clearly demonstrate the anisotropic transmission resonances. Our investigation enriches the physical connotation of local resonant phononic crystals in non-Hermitian systems.
Highlights
Phononic crystals (PCs) are a class of artificial periodic composite materials that exhibit phononic bandgaps, which originate from the Bragg scattering of acoustic or elastic waves.1 In 2000, Liu et al.2 first proposed a conceptual realization of an acoustic metamaterial exhibiting local resonant bandgaps that were due to the resonance of the composite scatterer individually
All of the above interesting findings greatly promote the development of acoustic metamaterials, but most of them focused on Hermitian systems and the effective elastic parameters concerned are real
By analytically solving the kinetic equations, we investigated the evolution of exceptional points (EPs) and effective mass of the resonator
Summary
Phononic crystals (PCs) are a class of artificial periodic composite materials that exhibit phononic bandgaps (i.e., frequency regimes in which the acoustic or elastic waves cannot propagate), which originate from the Bragg scattering of acoustic or elastic waves. In 2000, Liu et al. first proposed a conceptual realization of an acoustic metamaterial exhibiting local resonant bandgaps that were due to the resonance of the composite scatterer individually. In 2000, Liu et al. first proposed a conceptual realization of an acoustic metamaterial exhibiting local resonant bandgaps that were due to the resonance of the composite scatterer individually. The wavelengths of local resonant bands are much longer than the lattice constant, and the crystal can be homogenized and will exhibit peculiar effective elastic parameters.. All of the above interesting findings greatly promote the development of acoustic metamaterials, but most of them focused on Hermitian systems and the effective elastic parameters concerned are real. Li et al achieved anisotropic transmission resonances in the PT-symmetric photonic crystal.. Notomi et al obtained the photonic topological insulating phase that is induced solely by gain and loss, and Fan et al found the topological edgegain effect in photonic PT-symmetric crystals.. The anisotropic transmission resonance phenomenon can be achieved in a finite-size practical structure
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