Dirac锥外例外点的生成环
Spawning rings of exceptional points out of Dirac cones
摘要：
狄拉克锥是石墨烯和拓扑绝缘体的许多独特电子性质的基础，它的能带结构--两个在一个点接触的锥形带--也已经被波导阵列中的光子、光晶格中的原子以及通过偶然简并实现。狄拉克锥的形变经常揭示出有趣的性质;一个例子是量子霍尔效应，恒定的磁场将狄拉克锥分解成孤立的朗道能级。一个看似无关的现象是例外点，也被称为宇称时间对称性破缺点，其中两个共振在位置和宽度上都重合。例外点会导致违反直觉的现象，如损耗引起的透明性，单向传输或反射，以及反向泵浦依赖性或单模操作的激光器。这两个研究领域实际上是相互联系的：在这里我们发现了狄拉克锥演化成例外点环的能力，我们称之为“例外环”。“我们在光子晶体平板中实验证明了这一概念。对光子晶体平板的角分辨反射测量表明，反射率峰由偶然简并而遵循狄拉克锥的锥形能带结构，而系统的复本征值则变形为一个被特殊环包围的二维平坦带.这种变形是由偶极和四极共振的不同辐射率引起的，其作用类似于宇称时间对称系统中的损耗和增益。我们的研究结果表明，存在于任何开放系统中的辐射可以从根本上改变其物理性质的方式，以前预计只有在物质的损失和增益的存在。
英文摘要：
The Dirac cone underlies many unique electronic properties of graphene and topological insulators, and its band structure--two conical bands touching at a single point--has also been realized for photons in waveguide arrays, atoms in optical lattices, and through accidental degeneracy. Deformations of the Dirac cone often reveal intriguing properties; an example is the quantum Hall effect, where a constant magnetic field breaks the Dirac cone into isolated Landau levels. A seemingly unrelated phenomenon is the exceptional point, also known as the parity-time symmetry breaking point, where two resonances coincide in both their positions and widths. Exceptional points lead to counter-intuitive phenomena such as loss-induced transparency, unidirectional transmission or reflection, and lasers with reversed pump dependence or single-mode operation. These two fields of research are in fact connected: here we discover the ability of a Dirac cone to evolve into a ring of exceptional points, which we call an "exceptional ring." We experimentally demonstrate this concept in a photonic crystal slab. Angle-resolved reflection measurements of the photonic crystal slab reveal that the peaks of reflectivity follow the conical band structure of a Dirac cone from accidental degeneracy, whereas the complex eigenvalues of the system are deformed into a two-dimensional flat band enclosed by an exceptional ring. This deformation arises from the dissimilar radiation rates of dipole and quadrupole resonances, which play a role analogous to the loss and gain in parity-time symmetric systems. Our results indicate that the radiation that exists in any open system can fundamentally alter its physical properties in ways previously expected only in the presence of material loss and gain.
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