Characteristics of photonic bands generated by quadrangular multiconnected networks

In this paper, by means of the network equation and generalized dimensionless Floquet-Bloch theorem, we study the influences of the number of connected waveguide segments （NCWS） between adjacent nodes and the matching ratio of waveguide length （MRWL） on the photonic bands generated by quadrangular multiconnected networks （QMNs）, and obtain a series of formulae. It is found that multicombining networks （MCNs） and repetitive combining networks （RCNs） are equivalent to each other and they can all be simplified into the simplest fundamental combining systems. It would be useful for adjusting the number, widths, and positions of photonic bands, and would possess potential applications for the designing of all-optical devices and photonic network devices.     

Photonic band structures of two-dimensional photonic crystals with deformed lattices

Using the plane-wave expansion method, we have calculated and analysed the changes of photonic band structures arising from two kinds of deformed lattices, including the stretching and shrinking of lattices. The square lattice with square air holes and the triangular lattice with circular air holes are both studied. Calculated results show that the change of lattice size in some special ranges can enlarge the band gap, which depends strongly on the filling factor of air holes in photonic crystals; and besides, the asymmetric band edges will appear with the broken symmetry of lattices.     

Bragg waveguide grating as a 1d photonic band gap structure: COST 268 modelling task

Modal reflection, transmission and loss of deeply etched Bragg waveguide gratings were modelled by six European laboratories using independently developed two-dimensional (2D) numerical codes based on four different methods, with very good mutual agreement. It was found that (rather weak) material dispersion of the SiO₂/Si₃N₄ system does not significantly affect the results. The existence of lossless Floquet-Bloch modes in deeply etched gratings was confirmed. Based on reliable numerical results, the physical origin of out-of-plane losses of 1D or 2D photonic band gap structures in slab waveguides is briefly discussed.     

Bragg waveguide grating as a 1D photonic band gap structure: COST 268 modelling task

Modal reflection, transmission and loss of deeply etched Bragg waveguide gratings were modelled by six European laboratories using independently developed two-dimensional (2D) numerical codes based on four different methods, with very good mutual agreement. It was found that (rather weak) material dispersion of the SiO₂/Si₃N₄ system does not significantly affect the results. The existence of lossless Floquet–Bloch modes in deeply etched gratings was confirmed. Based on reliable numerical results, the physical origin of out-of-plane losses of 1D or 2D photonic band gap structures in slab waveguides is briefly discussed.     

含有理想导体的准分形结构光子晶体的能带

用时域有限差分方法计算了一组具有相似几何结构且包含理想金属材料的准分形光子晶体的能带.数值计算结果表明，这种准分形结构光子晶体具有绝对带隙，且带隙的宽度会 随着分形级数的增大而增大.同时，随着级数的增大，其能带在整体地趋向于高频端的同时，能带会被快速拉直而形成孤立的能级. 关键词： 光子晶体 带隙 分形     

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.     

两端有慢变结构的光子晶体的能带特性研究

研究了几种两端有慢变周期结构的光子晶体的能带特性，研究发现，通过在普能光子晶体两端添加适当的慢变周期结构，可以使光子晶体的光子禁带区向短波区或向长波区扩展，也可以同时向短波和长波两个区域扩展，与普通结构的光子晶体的光子禁带宽度相比，可以获得400％以上的禁带区宽度的拓展。     

Extreme narrow photonic passbands generated from defective two-segment-connected triangular waveguide networks

In this paper, we investigate the optical transmission properties of perfect and defective two-segment-connected tri- angular waveguide networks （2SCTWNs） and find that after introducing defects in networks, many groups of transparent extreme narrow photonic passbands （ENPPs） will be created in the middle of the transmission spectra, the number for each group and the group number of ENPPs can he adjusted by the matching ratios of waveguide length （MRWLs）, the number of defects, and the number of unit cells of 2SCTWNs. The influences of MRWL, number of defects, and number of unit cells on the number, width, and position of these ENPPs are researched and a series of quantitative rules and prop- erties are obtained. It may be useful for the designing of high-sensitive optical switches, wavelength division multiplexers, extreme-narrowband filters, and other correlative waveguide network devices.     

中红外波段硅基两维光子晶体的光子带隙

利用电化学腐蚀的方法制备了大多孔硅两维光子晶体.结构图形对称性为正方格子，其结构参数为正方形晶格周期a=44μm，正方形空气柱的边长l=2μm.并用显微红外光谱仪表征了光谱性质，揭示了所制备两维光子晶体样品的中红外波段光子的反射特性. 关键词： 光子晶体 光子带隙 反射谱 时域有限差分法     

Photonic band gap engineering in 2D photonic crystals

The polarization-dependent photonic band gaps (TM and TE polarizations) in two-dimensional photonic crystals with square lattices composed of air holes in dielectric and vice versa i.e., dielectric rods in air, using the plane-wave expansion method are investigated. We then study, how the photonic band gap size is affected by the changing ellipticity of the constituent air holes/dielectric rods. It is observed that the size of the photonic band gap changes with changing ellipticity of the constituent air holes/dielectric rods. Further, it is reported, how the photonic band gap size is affected by the change in the orientation of the constituent elliptical air holes/dielectric rods in 2D photonic crystals.     

Photonic band structure of three-dimensional colloidal crystals with field-induced lattice structure transformation

By utilizing the electrorheological effect, three-dimensional colloidal crystals can be produced, whose lattice structure can be changed from the body-centered-tetragonal lattice to other lattices under the application of electric fields. This paper calculates photonic band structures of such crystals with lattice structure transformation, and demonstrates the existence of complete band gaps for some intermediate lattices. Thus, it becomes possible to use the electrorheological effect to achieve photonic crystals with desired photonic gap properties resulting from tunable structures.     

手征材料构成的简立方光子晶体光子带结构计算——平面波法

发展了适于计算由手征材料组成的光子晶体的光子带结构的平面波法。在此基础上，研究了由手征材料组成的简立方光子晶体的光子带结构。计算表明：手征材料“球形原子”在电介质中排列所组成的科立方光子晶体和电介质“球形原子”在手征材料中排列所组成的简立方光子晶体，不仅都存在光子带隙，而且存在截止频率，在该频率以下的区域无传播模存在，本语文认了这种光子晶体的潜在应用。     

A ministop band in a single-defect photonic crystal waveguide based on silicon on insulator

This paper reports that a two-dimensional single-defect photonic crystal waveguide in the Г-K direction with triangular lattice on a silicon-on-insulator substrate is fabricated by the combination of electron beam lithography and inductively coupled plasma etching. A ministop band （MSB） is observed by the measurement of transmission characteristics. It results from the coupling between the two modes with the same symmetry, which is analysed from the stimulated band diagram by the effective index and the two-dimensional plane wave expansion methods. The parameter working on the MSB is the ratio of the radius of air holes to the lattice constant, fla. It is obtained that the critical τ/a value determining the occurrence or disappearance of MSB is 0.36. When τ/a is larger than or equal to 0.36, the MSB occurs. However, when τ/a is smaller than 0.36, the MSB disappears.     

A ministop band in a single-defect photonic crystal waveguide based on silicon on insulator

This paper reports that a two-dimensional single-defect photonic crystal waveguide in the \textit{$\Ga$-K} direction with triangular lattice on a silicon-on-insulator substrate is fabricated by the combination of electron beam lithography and inductively coupled plasma etching. A ministop band (MSB) is observed by the measurement of transmission characteristics. It results from the coupling between the two modes with the same symmetry, which is analysed from the stimulated band diagram by the effective index and the two-dimensional plane wave expansion methods. The parameter working on the MSB is the ratio of the radius of air holes to the lattice constant, $r/a$. It is obtained that the critical $r/a$ value determining the occurrence or disappearance of MSB is 0.36. When $r/a $ is larger than or equal to 0.36, the MSB occurs. However, when $r/a $ is smaller than 0.36, the MSB disappears.     

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。     

二维金属光子晶体的带结构研究

采用一种新的平面波展开法研究金属光子晶体的带结构，即在传统平面波展开法的基础上，将“原问题”拓展，引入一个“新问题”，通过求解“新问题”得到“原问题”的带结构，并论证了它们之间的关系.为了准确求解“新问题”，引入辅助函数，将其色散关系等价为一个积分微分本征方程，求解这个本征方程得到“新问题”的带结构，从而由此导出“原问题”的带结构.最后，以正方晶格二维金属光子晶体为例，进行数值计算，得到了满意的结果. 关键词： 金属光子晶体 平面波展开法 带结构 正方晶格     

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     

基元配置对二维光子晶体不同能带之间带隙的调节和优化

介绍一种方法来调节和优化二维光子晶体不同能带之间的带隙.在单胞中任意位置增加一个基元,可以调节不同能带之间的带隙.而且固定两个基元的最佳位置,调节两个基元柱体边长,可以找到一个合适的配置,使各自的带隙相对带宽达到更大值.同时结果也表明双基元情况下,不同能带之间带隙优化对系统对称性要求不同,频率越高处的带隙优化要求系统对称性越低. 关键词： 光子晶体 带隙 配置 对称性     

Non-Bragg band gaps and light manipulation of composite structures with metamaterials

A review is presented of various composite structures containing double-negative metamaterials or two types of single-negative metamaterials. In particular, non-Bragg band gaps arising from phase-compensation or tunneling effects and their manipulation of light are stressed. The non-Bragg band gaps that are robust against incident directions, thickness randomness and are easily tuned by changing the structural parameters can not only expand our ability in controlling the flow of light, but also provide new mechanisms for the design of photonic devices.