正方介质柱光子晶体中异常传输现象研究

Anomalous Propagation in Photonic Crystals with Square Rods

研究了电磁波在二维正方介质柱光子晶体中的传输,发现处于第一频带部分带隙的电磁波在不同界面切割方向上不同角度入射时可分别产生全反射及复杂异常折射现象如自准直现象、负折射现象.首先利用平面波展开法从理论上研究正方介质柱正方晶格光子晶体的频带结构及等频线,然后通过时域有限差分法来仿真研究光子晶体在第一频带部分带隙的传输特性.当光子晶体的界面切割沿着ΓX方向时,由于光子晶体内无本征模能够被有效地激发,入射波束被完全反射,这与光子带隙导致的全反射具有本质的不同;当光子晶体的界面切割方向沿着ΓM时,归因于其扁平的等频线,一定角度范围内入射的波束在光子晶体内几乎沿同方向传输即产生自准直现象.

The propagation of electromagnetic wave was investigated in two-dimensional photonic crystals （PCs） which are formed by square dielectric rods arranged in a square lattice. Total reflection and complicated anomalous refractions, such as the self-collimating phenomenon and negative refraction,were found in the first partial band gap when the interface of the PCs is changed and the incident angles are different. The plane wave expansion method was used to calculate and analyze the photonic band structure as well as the equifrequency contours （EFCs）. The numerical simulations using the finite-difference timedomain （FDTD） method were used to investigate the propagation properties of the electromagnetic wave in the first partial band gap. When the interface of the PCs is along the direction of ГX,the incident beams are reflected totally,because none of the eigen-modes in the PCs could be excited, and the total reflection is different in nature from that resulted from band gap. If the interface turns to ГM,due to its flat EFCs the incident beams with different angles in a certain rang refract nearly in the same direction in the PCs, that is, the self-collimating phenomena occurs.