非线性三原子链状超晶格的能带退化与演化
Band degeneration and evolution in nonlinear triatomic chain superlattices
摘要：
非线性超晶格表现出独特的功能，允许波操纵。强非线性超晶格的能带结构和带隙的物理机制及其演化过程一直是人们关注的焦点。本文建立了强非线性超晶格模型（三原子模型），通过解析和数值方法研究了典型非线性能带结构的演化过程。我们发现，强非线性超晶格表现出特殊的能带退化和分岔，并伴随着单胞内的振动模式转移。在考虑模式转移的情况下，阐明了不同模型下能带退化的演化过程和物理机制。所观察到的退化可能会发生位移，分叉，缩短，合并或消失的色散曲线，所有这一切都取决于耦合的非线性元件的安排。同时，单位晶胞的尺寸减小，同时带隙的频率范围和机制（布拉格和局部共振）发生变化。这些发现回答了非线性周期结构、非线性晶体和非线性超材料研究中的一些基本问题，引起了广大物理学界的兴趣
英文摘要：
Nonlinear superlattices exhibit unique features allowing for wave manipulations. Despite the increasing attention received, the underlying physical mechanisms and the evolution process of the band structures and bandgaps in strongly nonlinear superlattices remain unclear. Here we establish and examine strongly nonlinear superlattice models (three triatomic models) to show the evolution process of typical nonlinear band structures based on analytical and numerical approaches. We find that the strongly nonlinear superlattices present particular band degeneration and bifurcation, accompanied with the vibration mode transfer in their unit cells. The evolution processes and the physical mechanisms of the band degeneration in different models are clarified with the consideration of the mode transfer. The observed degeneration may occur as the shifting, bifurcating, shortening, merging or disappearing of dispersion curves, all depending on the arrangement of the coupled nonlinear elements. Meanwhile, the dimension of the unit cell reduces, alongside changes in the frequency range and mechanisms (Bragg and local resonance) of the bandgaps. These findings answer some foundamental questions peritinent to the study of nonlinear periodic structures, nonlinear crystals and nonlinear metamaterials, which are of interest to the broad community of physics
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