标题： 光子晶体中的半狄拉克色散关系 显示英文标题

标题： Semi-Dirac dispersion relation in photonic crystals

摘要： 半狄拉克锥指的是沿对称线呈线性而在垂直方向呈抛物线型的一种奇特色散关系。在这里，我证明由椭圆介电柱体组成的方形阵列的光子晶体能够在布里渊区中心产生这种特殊的色散关系。使用微扰方法可以评估线性斜率，并确认这种色散关系是一种半狄拉克类型。从边界有效介质理论计算出的有效介质参数不仅解释了在半狄拉克点处发生于等频率表面的意外拓扑转变，还提供了对该点性质的视角，即光子晶体在对称轴上表现为零折射率材料，但在垂直方向上则类似于光子带隙边缘的行为。 显示英文摘要

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.