石墨烯中的弹道电荷输运与超材料周期介质结构中的光传播：比较研究
Ballistic charge transport in graphene and light propagation in periodic dielectric structures with metamaterials: a comparative study
摘要：
我们探讨了含有左手材料的周期性层状介质的光学性质。这项研究是基于光在超材料中的传播和石墨烯中的电荷传输之间的几个类比。我们推导出这两个问题等价的条件，即，当相应的波函数重合时的方程和边界条件。我们发现，光子带隙结构的周期性系统交替的左手和右手的电介质板包含类似的狄拉克点在石墨烯中的带电准粒子的能谱中的圆锥奇点。这种奇异性的区域结构的无限系统引起相当不寻常的性质，在有限的样品中的光传输。在一个富有洞察力的数值实验（高斯光束通过正常和亚稳态的混合堆叠的传播）中，我们同时证明了四个狄拉克点引起的异常：（i）在禁止频率处强度的扩散样衰减，（ii）光束的聚焦和散焦，（iii）光束的横向位移的情况下，和（iv）Zitterbewegung效应的空间模拟。所有这些现象都发生在平均折射率为非零的介质中，并且可以通过改变样品的几何和电磁参数或光的频率和偏振来调谐。
英文摘要：
We explore the optical properties of periodic layered media containing left-handed metamaterials. This study is based on several analogies between the propagation of light in metamaterials and charge transport in graphene. We derive the conditions for these two problems become equivalent, i.e., the equations and the boundary conditions when the corresponding wave functions coincide. We show that the photonic band-gap structure of a periodic system built of alternating left- and right-handed dielectric slabs contains conical singularities similar to the Dirac points in the energy spectrum of charged quasiparticles in graphene. Such singularities in the zone structure of the infinite systems give rise to rather unusual properties of light transport in finite samples. In an insightful numerical experiment (the propagation of a Gaussian beam through a mixed stack of normal and meta-dielectrics) we simultaneously demonstrate four Dirac point-induced anomalies: (i) diffusion-like decay of the intensity at forbidden frequencies, (ii) focusing and defocussing of the beam, (iii) absence of the transverse shift of the beam, and (iv) a spatial analogue of the Zitterbewegung effect. All of these phenomena take place in media with non-zero average refractive index, and can be tuned by changing either the geometrical and electromagnetic parameters of the sample,or the frequency and the polarization of light.
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