Holographic design of hexagonal photonic crystals of irregular columns with large full band gap

The shape and size of the dielectric columns or particles (“atoms”) of photonic crystals (PhCs) formed by holographic lithography are determined by the isointensity surfaces of the interference field; consequently the PhCs’ photonic band gap (PBG) properties are closely related to their fabrication design. Here we have proposed a new structure of two-dimensional (2-D) hexagonal lattice with irregular columns, which can yield a 2-D complete relative band gap of 24.0% in case of the dielectric columns of ε = 13.6 in air, about 27% increase compared with that of the same lattice with regular triangular columns. This band gap size is among the largest for all the possible 2-D PhCs reported until now. The relationship between band gap properties of resultant structure and the specific fabrication conditions such as structure design and the choice of optimum intensity threshold and filling ratio are systematically discussed. The optical design for making this structure by two exposures is explained. This work may demonstrate the unique feature and advantages of photonic crystals made by holographic method and provide a guideline for their design and experimental fabrication.     

Absolute photonic band gaps in a two-dimensional photonic crystal with hollow anisotropic rods

The plane-wave expansion method is used to calculate photonic band gaps for two structures with hollow anisotropic tellurium (Te) rods. Both structures are found to have absolute band gaps at the low- and high-frequency regions. Compared with the photonic crystal with solid Te rods, the photonic crystal with hollow Te rods has a large absolute band gap at the high-frequency region: for the triangular lattice of oval hollow Te rods, there is an absolute band gap of 0.058w_e (w_e=2πc/a), and for the square lattice of square hollow Te rods, there is an absolute band gap of 0.056w_e.     

一种衍生于三角晶格的二维光子晶体

通过在二维三角晶格中引入三个完全相同的介质圆柱构成了一种全新结构的光子晶体,并对其光子能带进行了频域计算.借助数值方法分析了填充率对光子能带的影响,结果表明,在一定填充率下,这种二维光子晶体对于E偏振和H偏振都存在很宽的带隙,而且还可以获得一个窄完全带隙.     

Photonic band gaps in two-dimensional photonic crystals of core-shell-type dielectric nanorod heterostructures

A new type of two-dimensional photonic crystal (PC) called core-shell-type PC composed of a nanorod heterostructure array in a square or triangular lattice such that a dielectric nanorod is covered by a thin interfacial layer is studied. Using the plane-wave numerical expansion method, we study the modification of the band gap spectrum when the nanorods are covered by other material, and reveal that the photonic band gap is considerably enhanced in size for both square and triangular lattice. The effects of structural parameters on the band gaps are also studied. The results show that there exist optimal parameters to open large gaps, and TE (Transverse-electric) band gaps are favored in a triangular lattice.     

Two-dimensional absolute photonic band gaps in the visible

The most promising two-dimensional photonic crystals are the graphite lattice of dielectric rods in air background and the triangular lattice of air holes in dielectric background. In this paper, we compare their convenience in achieving structures which inhibit the propagation of visible electromagnetic waves. For visible waves, etching is difficult because the structure period must be smaller than the light wavelength. Furthermore, the semiconductor materials whose electronic band gap does not absorb any optical waves have little dielectric constant, which reduces photonic band gap widths. We show, using the Plane Wave Method and the Transfer Matrix Method, that the triangular structure is not appropriate because its gap is too narrow and its dimensions are too small for fabrication. On the other hand, wider gaps and larger dimensions that should be etched easily in wide gap semiconductors make graphite a much more suitable structure.     

Absolute band gaps of a two-dimensional triangular-lattice dielectric photonic crystal with different shapes

Absolute band gaps of a two-dimensional triangular-lattice photonic crystal are calculated with the finite-difference time-domain method in this paper.Through calculating the photonic band structures of the triangular-lattice photonic crystal consisting of Ge rods immersed in air with different shapes,it is found that a large absolute band gap of 0.098 (2c/a) can be obtained for the structures with hollow triangular Ge rods immersed in air,corresponding to 19.8% of the middle frequency.The influence of the different factors on the width of the absolute band gaps is also discussed.     

类蜂窝状结构完全带隙二维光子晶体

通过在二维三角晶格中引入两个完全一样的介质圆柱构成了类蜂窝状结构光子晶体,并对其光子能带进行了频域计算。借助数值方法分析了介质柱位置改变对光子能带的影响,计算结果表明,这种类蜂窝状结构二维光子晶体可以产生很宽的带隙,而且在一定填充率下,可以通过调整介质柱的位置使完全光子带隙达到最大化。     

Improvement of absolute band gaps in 2D photonic crystals by anisotropy in dielectricity

Two-dimensional (2D) photonic band gaps (PBG) structure fabricated from anisotropic dielectric is studied by solving Maxwell's equations with use of plane-wave expansion method. Numerical simulations show that absolute photonic band gaps can be substantially improved in two dimensional square and triangular lattices of cylinders by introducing anisotropy in material dielectricity. Owing to different refractive indices for electromagnetic waves with E- and H-polarization, the quasi-independent adjustment of band gaps for the E- and H-polarization modes can be implemented by uniaxial crystals with their extraordinary axis parallel to the cylinders. Large absolute band gaps can be created for uniaxial cylinders in air with a positive anisotropy. In the case of air holes in background uniaxial dielectric with even a weak negative anisotropy, the absolute band gap can be increased 2-3 times. Large absolute band gap can also be obtained in other complex configurations of uniaxial and biaxial materials and this enables a full exploitation of potential utilization for anisotropic materials available in nature. Such a mechanism of band gap adjustment should open up a new scope for designing band gaps in 2D PBG structures. Received 26 January 1999     

一类粗锐复合结构光子晶体的完全带隙研究

通过研究发现粗锐组合的二维复式结构光子晶体的完全带隙宽度和带隙结构随结构粗锐尺寸灵敏地改变. 而其粗锐复合结构的复合错位对带隙宽度影响不大. 对二维复式正方格子和二维复式三角格子的研究结果表明：二维复式正方格子的粗锐尺寸选择恰当时其完全带隙的带宽可大于１8％. 二维复式三角格子中的粗锐尺寸选取可导致出现单、双完全带隙两种情况. 本文给出了反映其变化规律的关系曲线. 关键词： 光子晶体 光子能隙 复式结构     

Photonic band gaps structure properties of two-dimensional function photonic crystals

The tunable two-dimensional photonic crystals band gap, absolute photonic band gap and semi-Dirac point are beneficial to designing the novel optical devices. In this paper, tunable photonic band gaps structure was realized by a new type two-dimensional function photonic crystals, which dielectric constants of medium columns are functions of space coordinates. However for the two-dimensional conventional photonic crystals the dielectric constant does not change with space coordinates. As the parameter adjustment, we found that the photonic band gaps structures are dielectric constant function coefficient, medium columns radius, dielectric constant function form period number and pump light intensity dependent, namely, the photonic band gaps position and width can be tuned. we also obtained absolute photonic band gaps and semi-Dirac point in the photonic band gaps structures of two-dimensional function photonic crystals. These results provide an important theoretical foundation for design novel optical devices.     

三角形复式晶格的光子带结构研究

设计了一种三角形复式晶格结构的光子晶体，在该类晶体中，电介质圆柱在空气中的排列存在Ｅ偏振和Ｈ偏振的光子带隙重叠区，称之为绝对光子带隙；而空气圆孔在电介质中的排列时，虽然Ｅ偏振和Ｈ偏振均分别存在光子带隙，但不存在绝对光子带隙。同时利用晶体的光子带结构研究了有效长波介电常数，所得结果与静电理论吻合。     

由球形原子构成的多种周期性介电结构的光子能带计算

采用矢量平面波方法计算了由球形空气原子构成的体心立方结构和六角密堆结构的光子能带，两种结构下都看到了贯通整个布里渊区的禁带。本文预言周期性介电结构的最大折射率调制度和最大禁带宽度对应于同样的原子体积分数，而且这个最佳的原子体积分数是结构无关的。文中还计算了由各向异性介电小球构成的面心立方结构的光子能带并看到了禁带，这与各向同性介电小球构成的面心立方结构很不相同。     

二维三角柱光子晶体的传输特性

利用时域有限差分方法对二维三角介质柱光子晶体的传输特性进行了研究,计算了不同晶格、同一晶格柱体截面面积不同、放置方位角不同、入射波入射方向不同时光子晶体的传输特性。结果表明:光子禁带的宽度与中心频率和晶格结构有很大关系,三角晶格更易形成平坦光子禁带,柱体截面面积大,则形成的禁带较宽,在其他因素相同的条件下柱体放置的方位角在一定范围内对光子禁带有重要影响;对不同入射方向时光子晶体的传输特性的研究结果表明,在低频范围内,入射角对禁带宽度和中心频率没有任何影响,在高频段,透射率随入射角变大而降低。研究结果为实验上制作三角柱光子晶体器件提供了重要的理论依据。     

磁导率对二维蜂窝结构光子晶体带隙的影响

利用平面波展开法对二维六角晶格结构磁性光子晶体的带隙特性进行了研究，给出其能带结构分布图，并与非磁性介质构成的光子晶体进行了比较.结果表明，由磁性材料构成的光子晶体更易出现带隙，磁导率对带隙结构影响很大.空气背景磁性散射子情况，磁导率增加较小时，二个绝对光子带隙宽度逐渐减小，直至消失.继续增加磁导率，在较低频率范围内出现一个绝对光子带隙，占空比逐渐加大，且最佳填充系数基本保持不变.磁性背景空气散射子，类似地在较低频率范围内也出现了一个绝对光子带隙.磁性背景非磁性散射子与空气背景磁性散射子情况相似.     

Band structure of photonic crystal fibers with silica rings in triangular lattice

The characteristics of the cladding band structure of air-core photonic crystal fibers with silica rings in triangular lattice are investigated by using a standard plane wave method. The numerical results show that light can be localized in the air core by the photonic band gaps of the fiber. By increasing the air-filling fraction, the band gap edges of the low frequency photonic band gaps shift to shorter wavelength, whereas the band gap width decreases linearly. In order to make a specified light fall in the low frequency band gaps of the fiber, the interplay of the silica ring spacing and the air-filling fraction is also analyzed. It shows that the silica ring spacing increases monotonously when the air-filling fraction is increased, and the spacing range increases exponentially. This type fiber might have potential in infrared light transmission.     

二维光子晶体禁带特性研究

采用平面波展开法对二维光子晶体分别在E和H极化下的带隙进行了计算. 考虑了填充比、晶格结构、介电常数对最大绝对帯隙的影响. 结果表明,不论是正方晶格还是三角晶格,TM模在介质柱型光子晶体中更容易形成带隙;TE模在空气孔型光子晶体中更容易形成带隙. 填充比一定,最大绝对帯隙宽度并非随着介电常数增大总是增大,而是存在一个峰值. 相对介电常数一定,最大绝对帯隙宽度随填充比的变化也存在一个峰值. 不论空气孔型还是介质柱型结构,三角晶格比正方晶格更容易形成帯隙. 关键词： 平面波展开法 TE模 TM模 最大绝对帯隙     

正三角形晶格金属柱光子带隙结构

采用有限差分法分析了正三角形晶格金属柱光子带隙(PBG)结构中TE模式的色散特性,导出了全局带隙分布图, 探讨了一套系统的设计指定本征频率PBG结构的方法。结果表明,金属柱半径与晶格常数的比值越小,越有利于PBG谐振腔的圆波导耦合输出。说明了类比圆柱波导设计回旋管的可能性。     

Creation of tunable absolute bandgaps in a two-dimensional anisotropic photonic crystal modulated by a nematic liquid crystal

Photonic crystals (PCs) have many potential applications because of their ability to control light-wave propagation. We have investigated the tunable absolute bandgap in a two-dimensional anisotropic photonic crystal structures modulated by a nematic liquid crystal. The PC structure composed of an anisotropic-dielectric cylinder in the liquid crystal medium is studied by solving Maxwell's equations using the plane wave expansion method. The photonic band structures are found to exhibit absolute bandgaps for the square and triangular lattices. Numerical simulations show that the absolute bandgaps can be continuously tuned in the square and triangular lattices consisting of anisotropic-dielectric cylinders by infiltrating nematic liquid crystals. Such a mechanism of bandgap adjustment should open up a new application for designing components in photonic integrated circuits.     

三维光子晶体典型结构完全禁带的最佳参数理论分析

基于平面波展开法，理论分析了晶格结构、填充率、介电常数比等因素对fcc，diamond，woodpile三种三维光子晶体典型结构完全禁带的影响.三种结构中，fcc结构由于高对称性导致的能级简并，只适用于密堆积排列的反蛋白石结构；diamond结构非常容易产生高带隙率的完全禁带，并且可以通过调节多项参数得到所需的完全禁带；woodpile结构参数调节范围比较宽，为实验制备带来方便.对于不同的三维光子晶体结构，随着介电常数比的增大，完全禁带的宽度和带隙率也会随着增大.还发现了一些以前未引起注意的现象. 关键词： 三维光子晶体 完全禁带 介电常数比 带隙率 平面波展开法     

二维斜三角晶格光子晶体完全带隙研究

在二维正三角晶格光子晶体的基础上,通过改变晶体的晶格基矢构造了一种全新的周期结构。该周期结构的最小周期单元不再是传统意义上的等边三角形,而是一种更为优化的斜三角形结构。利用平面波展开法理论模拟了二维斜三角晶格光子晶体完全带隙的情况,发现所设计结构的完全带隙宽度是二维正三角晶格光子晶体完全带隙宽度的4.3 2倍。分析了介质柱宽度,介质柱旋转角度以及相对介电常数对所构造结构的完全带隙的影响,所得结果对二维光子晶体的理论研究和实际应用有所帮助。为任意角度的二维光子晶体集成波导的研究和制作提供了理论基础。