电磁波在周期介质中的传播及二维光子晶体的光子带结构

光子晶体是光学与凝聚态物理交叉的新领域,也是近年来应用物理学的一个重要研究领域,它是一种由介电常数高的(低的)介质在另一种介电常数低的(高的)背景介质中周期排列所组成的人造多维周期结构材料,能够产生光子带隙。频率落在带隙内的光在晶体里沿任何方向都不能传播,因而具有能够抑制原子、分子的自发辐射等诱人的光电子学特性,在基础研究和实际应用上都有着巨大的潜力。本文在这一领域里进行了富有成效的研究,获得了很好的结果。主要有:(1)利用平面波展开方法来计算二维光子晶体的带隙结构。首先,我们设计正方晶胞的二维光子晶体模型。设x₃方向为介质柱的轴方向,二维周期结构在x₁-x₂平面上。晶胞的晶格常数为a,半径为r,介质柱和空气柱的介电常数分别为ε_a=17和ε_b=1,a>2r。设计的核心思想是通过降低光子晶体结构的对称性,消除光子能带在晶体的布里渊区高对称点上的本征简并。(2)对于二维光子晶体的电磁波理论及周期介质中的Bloch波解做了详细的推导,给出了光子晶体中禁带存在的理论依据。同时以正方格子晶格的二维光子晶体为例,验证了电介质在空气圆孔中的排列存在E偏振和H偏振的光子带隙重叠区,称为绝对光子带隙。对于二维的光子晶体,两种本征偏振模式的光子能带结构可以独立地调节,以实现两者的光子带隙的最优重叠, 从而大大提高了二维光子晶体的完全带隙宽度。     

Band gaps of two-dimensional photonic crystal structure using conjugated polymer (3-octylthiophenes)

The possibility of using conjugated polymer (3-octylthiophenes, P3OT) as two-dimensional (2D) photonic band gap crystals was investigated. The different aspects were examined of the absolute photonic band gap (PBG) formation for 2D photonic crystals (PCs) consisting of P3OT pillars in air. The formation of PBG was exhibited and confirmed by a calculation of transfer matrix method (TMM). It was found that P3OT triangular structure could be good candidate for absolute inhibition of reflection in ultraviolet frequency region for given orientation.     

Photonic Band Gap in Two-Dimensional Anisotropic Photonic Crystal with Rectangular Bars

Photonic band gap (PBG) in two-dimensional (2D) anisotropic photonic crystal (PC) constructed of rectangular bars has been numerically studied by using Transfer Matrix Method (TMM). The results show that the PBG is bounded by the lower band edge of TE wave and the upper band edge of TM wave. Its width simply increases with increasing of shape parameter . It reaches a maximum value as the structure degenerates into its 1D counterpart, due to the complete overlapping of gaps in TE and TM waves. The anisotropy in PC structure results in the transmission anisotropic property. One can design the PBG structures in different incident directions to match their application demand.     

大带隙二维三角格子光子晶体结构参数的优化设计

光子晶体结构设计优化是理论研究的一个重要内容.运用平面波展开法对圆柱、方柱及正六边柱构造的二维三角格子光子晶体的禁带进行仿真计算,讨论了介质材料分别为GaAs、Si和Ge情况下,柱子形状、旋转角度、填充比的变化对完全光子禁带的影响.发现:对于二维三角格子光子晶体,相对于介质柱,空气柱更易获得完全光子禁带;而相对于圆柱及...     

Diffractionless flow of light in all-optical microchips

We introduce the concept of a hybrid 2D-3D photonic band gap (PBG) heterostructure which enables both complete control of spontaneous emission of light from atoms and planar light-wave propagation in engineered wavelength-scale microcircuits. Using three-dimensional (3D) light localization, this heterostructure enables flow of light without diffraction through micron-scale air waveguide networks. Achieved by intercalating two-dimensional photonic crystal layers containing engineered defects into a 3D PBG material, this provides a general and versatile solution to the problem of "leaky modes" and diffractive losses in integrated optics.     

二维单斜点阵光子晶体的第一布里渊区及带隙计算

二维单斜点阵光子晶体在光学聚焦器件及光子晶体波导中有重要的应用价值，详细讨论了二维单斜点阵光子晶体的第一布里渊区及带隙计算，并与常规方法计算得出的二维正三角形晶格光子晶体的带隙结构进行了比较.最后讨论了临界条件下二维单斜点阵光子晶体的带隙结构，证明了本方法的有效性.     

Arrangements of four beams for any Bravais lattice

A single geometric model based on a new concept of a reciprocal primitive pyramid (RPP) in reciprocal space is proposed for investigation of relationships between any three-dimensional (3D) lattice and arrangements of four beams (AFBs) that produce the lattice. A ternary linear equation set, described for the one-to-one correspondence between a RPP and AFB, can readily reveal all AFBs for the same lattice (AFBSLs). Quantitative AFBs for bcc and fcc real lattices are illustrated to show that various AFBSLs can modulate the properties of a photonic bandgap (PBG) both by tuning the lattice constant and by changing the lattice-point shape. This fact may yield the appropriate AFB for a complete 3D PBG with the desired center wavelength. The nonuniqueness of AFBSLs can provide abundant choices for persons who plan interference experiments, especially for holographic fabrication of 3D photonic crystals (PCs).     

Two-dimensional Si photonic crystals on oxide using SOI substrate

Two-dimensional photonic crystals (2D-PhCs) on oxide can be easily incorporated into photonic integrated circuits. Although an asymmetrical structure (air/PhC/oxide) is advantageous in terms of ease of fabrication, it has been pointed out that such a structure may have no photonic band gap (PBG). To clarify the characteristics of the asymmetrical structure, we calculated the band structure using the three-dimensional (3D) FDTD method and measured the transmission characteristics of a fabricated 2D Si-PhC on oxide. The calculations show that we can use a quasi-PBG even in an asymmetrical structure when the PhC thickness satisfies the single-mode condition. The measured transmission characteristics correspond to the calculated band structure and reveal the existence of a quasi-PBG. These results show that the asymmetrical 2D Si-PhC-on-oxide structure can be applied to various optical devices.     

基于太极形介质柱六角光子晶体禁带特性研究

提出了一种新型的非对称性散射体的二维六角晶格光子晶体结构–-太极形介质柱光子晶体. 利用平面波展开法从理论研究这种光子晶体结构的能带特性以及结构参数对完全禁带的影响. 研究表明:散射体对称性的打破, TE模和TM模能带宽度和数目都会有所增加, 有益于获得更宽的完全禁带以及更多条完全禁带.通过参数优化, 发现在ε = 17, R=0.38 μm, r=0.36R, θ = 0° 时, 获得最大完全带隙宽度0.0541(ωa/2πc); 在ε = 16, R=0.44, r=0.2R, θ = 0°时, 光子晶体完全带隙数目最多达到8条. 关键词： 光子晶体 禁带 平面波展开     

Absolute photonic band gaps of two-dimensional square-lattice photonic crystals with Taiji-shaped dielectric rods

A novel structure of two-dimensional (2D) square-lattice photonic crystal (SLPC) composed of Taiji-shaped dielectric rods imbedded in air is constructed and the properties of absolute photonic band gap (PBG) are theoretically analyzed in both the number and width by Plane Wave Expansion Method (PWM). By comparing the absolute PBGs in 2D SLPCs consisting of four shapes of rods with different symmetries (circle, button, semicircle and Taiji) at the same filling ratio, we find that both the number and width of absolute PBG significantly increase with the breaking of scatterer's symmetry, and the Taiji-shaped rods with the poorest symmetry can attain both the most number and the largest width of absolute PBGs. Additionally, we also study the influence of dielectric constant ε and three geometric parameters of Taiji-shaped scatterer on the absolute PBG and discover that the SLPC with Taiji-shaped rods can generate at most nine absolute PBGs and the largest absolute PBG with the width 0.0485 (ωa/2πc).