Dirac 点附近亚波长区域中的波包传播

Honeycomb-lattice Minnaert bubbles

The ability to manipulate the propagation of waves on subwavelength scales is important for many different physical applications. In this paper, we consider a honeycomb lattice of subwavelength resonators and prove, for the first time, the existence of a Dirac dispersion cone at subwavelength scales. As shown in [H. Ammari et al., A high-frequency homogenization approach near the Dirac points in bubbly honeycomb crystals, arXiv:1812.06178], near the Dirac points, honeycomb crystals of subwavelength resonators has a great potential to be used as near-zero materials. Here, we perform the analysi…

Wave packets in Honeycomb Structures and Two-Dimensional Dirac Equations

In a recent article [10], the authors proved that the non-relativistic Schrödinger operator with a generic honeycomb lattice potential has conical (Dirac) points in its dispersion surfaces. These conical points occur for quasi-momenta, which are located at the vertices of the Brillouin zone, a regular hexagon. In this paper, we study the time-evolution of wave-packets, which are spectrally concentrated near such conical points. We prove that the large, but finite, time dynamics is governed by the two-dimensional Dirac equations.

亚波长机制下的广义蜂窝结构材料

Generalized Honeycomb-structured Materials in the Subwavelength Regime

本文研究含六个夹杂物的广义蜂窝结构材料，利用层势理论证明在额外对称性下第2至第5能带存在双重狄拉克锥，并分析收缩与扩张两种变形导致谱隙打开及其拓扑差异。

Wave packet dynamics in slowly modulated photonic graphene

Mathematical analysis on electromagnetic waves in photonic graphene, a photonic topological material which has a honeycomb structure, is one of the most important current research topics. By modulating the honeycomb structure, numerous topological phenomena have been observed recently. The electromagnetic waves in such a media are generally described by the 2-dimensional wave equation. It has been shown that the corresponding elliptic operator with a honeycomb material weight has Dirac points in its dispersion surfaces. In this paper, we study the time evolution of the wave packets spectrally …

Wave packets in the fractional nonlinear Schrödinger equation with a honeycomb potential

In this article, we study wave dynamics in the fractional nonlinear Schrödinger equation with a modulated honeycomb potential. This problem arises from recent research interests in the interplay between topological materials and nonlocal governing equations. Both are current focuses in scientific research fields. We first develop the Floquet-Bloch spectral theory of the linear fractional Schrödinger operator with a honeycomb potential. Especially, we prove the existence of conical degenerate points, i.e., Dirac points, at which two dispersion band functions intersect. We then investigate the d…

一维空间中狄拉克粒子的渐近动量

Asymptotic Momentum of Dirac Particles in One Space Dimension

研究自由狄拉克方程引导的自旋半波包粒子的轨迹，证明大时间下波函数近似为反向传播的两个波包叠加，粒子渐近动量和能量恒定，且负能量粒子速度与动量反向。