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arXiv 1312.0201physics.optics
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光子晶体中的半狄拉克色散关系

Semi-Dirac dispersion relation in photonic crystals

Ying Wu

摘要:

半狄拉克锥是指一种特殊类型的色散关系,它沿对称线是线性的,但在垂直方向上是二次的。在这里,我证明了一个光子晶体组成的一个正方形阵列的椭圆形介质柱能够产生这种特定的布里渊区中心的色散关系。一个微扰方法被用来评估的线性斜率,并确认色散关系是一个半狄拉克型。从边界有效介质理论计算的有效介质参数不仅解释了在半狄拉克点处发生的等频表面中的意外拓扑转变,它们还提供了对该点处的性质的透视,其中光子晶体沿对称轴表现为零折射率材料,但在垂直方向上类似于光子带边缘。

英文摘要:

A semi-Dirac cone refers to a peculiar type of dispersion relation that is linear along the symmetry line but quadratic in the perpendicular direction. Here, I demonstrate that a photonic crystal consisting of a square array of elliptical dielectric cylinders is able to produce this particular dispersion relation in the Brillouin zone center. A perturbation method is used to evaluate the linear slope and to affirm that the dispersion relation is a semi-Dirac type. Effective medium parameters calculated from a boundary effective medium theory not only explain the unexpected topological transition in the iso-frequency surfaces occurring at the semi-Dirac point, they also offer a perspective on the property at that point, where the photonic crystal behaves as a zero-refractive-index material along the symmetry axis but functions like at a photonic band edge in the perpendicular direction.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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