Analysis of the peculiar shift of the low-frequency end of a variable photonic band gap

The effect of the variation of a rod’s dielectric constant on the photonic band gap in a two-dimensional square lattice structure photonic crystal is studied in this paper. The effects were calculated by FDTD algorithm and some peculiar variation properties were obtained. By consecutively changing the dielectric constant of the rod over certain wide ranges and fixing that of the background, the low-frequency end of the TM band gap in low frequency regions reveals very tiny shifts which to some extent can be treated as fixed. This is primarily due to the fact that the high-e region in the crystal is nearly unchanged, hence, the concentrated energy of the low frequency mode changes only slightly. This effect does not exist for materials whose dielectrics are varied over wide ranges. We propose an alternative method using 2D core-shell photonic crystals. The final results of the band calculation show that the gap maps of the core-shell cases closely match those of the ideal case. Such peculiar changes in the photonic band gap have wide application prospects. PACS 42.70.Qs; 78.20.Bh     

Design of sharp transmission filters using band-edge resonances in one-dimensional photonic crystal hetero-structures

This paper presents a design of sharp transmission filters using band edge resonance effects in a hetero-structure composed of one-dimensional photonic crystals with different periods. Assuming that the photonic crystals are made of identical pairs of transparent materials, the band-edge resonance occurs when the periods are distributed in a geometrical progression with a common ratio, r=r _c , where r _c is a known function of refractive-index modulation, incident angle and the polarization of light. The band-edge resonance results in sharp resonant peaks in the transmission spectrum, with the full width at half maximum of the peaks increasing with an increase in the number of unit cells in each photonic crystal. Furthermore, if M photonic crystals are used to construct the hetero-structure, M−1 resonant peaks with the spacing between kth (1<k<M) and (k−1)th peaks equal to the band gap of the kth photonic crystal form in the transmission spectrum.     

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.     

Band structures in nonlinear photonic crystal slabs

The finite-difference time-domain method was used to analyze band structures in two-dimensional Kerr-nonlinear photonic crystal slabs. A triangular lattice of circular air rods was considered. Results show red-shifting of the band structure due to the nonlinearity and the incident intensity. The red-shift of the band gap between the first and the second bands is maximal when the air rod radius is in the range 0.2a to 0.25a, where a is the period.     

The theory of cylindrical photonic wires

The energy modes for a photonic nanowire have been studied and calculated. We model our photonic crystals after Noda et al. (1999) [18] where logs of semiconductor material are stacked to produce photonic band gaps in both the near and far infrared regions. A nominal dispersion relation was adopted in order to achieve qualitatively useful results. Photonic wires were modeled in two schemes, each with two specific geometries. In the first scheme, a pillar of one photonic crystal is embedded in a larger photonic crystal to produce a wire. This pillar was modeled as having either a square or a circular cross-section. The photonic crystals considered consisted of varying proportions of Ga_xAl_1−xAs, so that the wire could be adjusted. The second scheme investigated was a dielectric material for the central pillar, rather than a photonic crystal. Again, circular and square cross sections were considered. It was found that many more modes fit into the near infrared band gap than the far infrared band gap, and that a circular cross-section permits fewer modes. Finally, a dielectric pillar allows for a wire which is physically much smaller than a wire with a photonic crystal in the middle. As many photonic devices include such wires, these qualitative results could be useful in their design.     

Band-structure properties of photonic superlattices

The band structure of a one-dimensional periodic array composed of two different layers of dimensions a and b characterized by refractive indices n ₁ and n ₂, respectively, is investigated. Refractive indices may take on positive as well as negative values. Within the Maxwell framework and using a transfer matrix technique for one dimensional periodic eigen-problems, we have determined a general equation, which governs the photonic band structure and the density of states (DOS) of one-dimensional photonic crystals. In addition to the well-known existence of the band gaps, we show that, depending on the width relationship b/a between the layer materials, super-lattices with null photonic band gap may exist and the conditions for such occurrences are established. Furthermore, we have been able to study the so-called 〈n〉 = 0 non-Bragg gap, ground ω₀, for which the average refraction felt by the propagating radiation is null. The text was submitted by the authors in English.     

Fabrication and optical properties of 3D composite photonic crystals of core-shell structures

Three-dimensional (3D) composite colloidal photonic crystals with SiO₂ core and ZnO shell were fabricated on borosilicate glass (BSG) substrate by a two-stage deposition method. Scanning electron microscopy (SEM) measurements show that both the pre-deposited SiO₂ and SiO₂/ZnO core-shell structures are oriented with their (1 1 1) axes parallel to the substrates. Optical measurement reveals that the periodic arrays exhibit a photonic band gap in the (1 1 1) direction. The optical properties of SiO₂/ZnO core-shell structures strongly depend on the size dispersions of colloidal spheres and the intrinsic defects in the sample.     

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     

由单负材料组成的一维对称型光子晶体中的隧穿模

由电单负材料A和磁单负材料B构成了一维对称型光子晶体,数值计算表明其带隙中出现了一隧穿模. 材料层数增加,隧穿模宽度急剧变窄,而其位置不变.隧穿模的位置和宽度对入射角的变化都不太敏感. 材料的几何厚度减小,隧穿模的位置蓝移,而其宽度不变. μ_A, ε_B增加,隧穿模的位置红移,宽度减小. 利用隧穿模的以上特性可以实现对电磁波传播的动态调控.     

对称型单负交替一维光子晶体的能带结构

构造了(AB)^N(BA)^N对称型两种单负材料交替一维光子晶体,利用传输矩阵法进行数值模拟.结果表明：这种单负交替对称型一维光子晶体具有一种特殊带隙结构,该带隙不敏感于入射角和晶格的无序性.在该带隙内出现了两个隧穿模,该隧穿模不敏感于入射角的改变和晶格的无序性,但能带及带隙内的隧穿模却敏感于晶格标度和周期数的变化;随着入射角的改变,带隙两侧的隧穿模趋于简并.这些特性对在利用此结构光子晶体设计双重超窄带滤波器时,具有一定的参考价值. 关键词： 光子晶体 单负材料 光子带隙     

Numerical analysis of a temperature sensor based on the photonic band gap effect in a photonic crystal fiber

In this paper we investigate, by the plane wave expansion method and an analytical model, the temperature effect on the photonic band gap fiber, and we report on a numerical demonstration of a temperature sensor based on the photonic band gap (PBG) shift in a solid core photonic crystal fiber (PCF) infiltrated with a high refractive index oil. The bandwidth and the position of the central wavelength of the band gap are the parameters of interests for our temperature sensing purpose. Simulation results were found to be in excellent agreement with the refractive index scaling law and the highest sensitivity of 3.21?nm/°C was achieved, and it will be even higher than the grating based sensors written in PCFs with similar structure.     

Geometrically distributed aperiodic circular photonic crystals with broad and isotropic photonic band gaps

In this paper, a new type of circular photonic crystal (CPC) with a geometrical distribution of concentric layers is presented. A broad and isotropic photonic band gap is achieved using this geometrically distributed CPC (GCPC). Also, the influence of the number of concentric layers to the overall band gap of GCPC is studied. It is demonstrated that the band gap broadens with a red shift when the number of concentric layers is increased. The reason for the red shift of the band gap is further investigated.     

Effect of anisotropy on the photonic band gap and surface polaritons of a one-dimensional single-negative photonic crystal

The effect of anisotropy on the photonic band structure and surface polaritons of a one-dimensional photonic crystal made of uniaxially anisotropic epsilon-negative (ε<0,μ>0) and mu-negative (ε>0,μ<0) metamaterials is theoretically investigated. Two different cases of uniaxially anisotropic epsilon-negative and mu-negative metamaterials are considered. It is found out that for one case of anisotropy, one-dimensional photonic crystal does not have any single-negative band gap. As a result, it can not support the surface polaritons. While, for another case, the structure shows single-negative band gaps. So, the surface polaritons can be excited at the interface of such a photonic crystal. However, these surface polaritons, unlike the isotropic case, are not omnidirectional and they are restricted to a limited rang of the propagation constant.     

Investigation of photonic band gap in a semiconductor-organic photonic crystal in ultraviolet region

We give a theoretical analysis of the photonic band gap in a one-dimensional semiconductor-organic photonic crystal containing a period of AlN/3-octylthiophenes (P3OT) bilayer. The band gap is investigated based on the reflectance calculated by using the transfer matrix method. It is shown that, in the ultraviolet region, there is a photonic band gap which is strongly dependent on the loss and the incident angle for the transverse electric and transverse magnetic waves. Additionally, we find the photonic band gap can be significantly widened in a ternary semiconductor-metal-organic one. The effect of distinct metal on the band gap is also illustrated.     

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     

光子晶体自准直光束偏振分束器

结合能带图和等频图分析,基于光子晶体自准直效应和光子带隙,设计了一种紧凑、高效的偏振分束器.时域有限差分法(FDTD)模拟表明,该设计可以在一个较大的频率范围f=0.268—0.278(c/a) 内实现TE模和TM模的高效(85%)、大角度(90°)分离.在光通讯波长λ=1.55 μm,该设计尺寸仅为9 μm×9 μm.这些特性使其在光通讯领域中具有重要的应用前景. 关键词： 光子晶体 偏振分束器 自准直     

A novel technique to measure the sucrose concentration in hydrogel sucrose solution using two dimensional photonic crystal structures

We propose a novel technique to measure the concentration of sucrose in PAm-hydrogel sucrose solution using two dimensional photonic crystal structures consists of air holes. PAm-hydrogel is an organic hydrogels, which is used as biomedical applications. The principle of measurement is based on the linear variation of photonic band gap with the change of dielectric constant of the solution infiltrated in air holes of photonic crystal structure. Plane wave expansion method is used to find the band gap and linear variation (R² = 0.9949) of photonic band gap with respect to sucrose concentration is observed. Besides this, an excellent linear variation (R² = 0.9949) of transmitted intensity of light with respect to sucrose concentration is also seen. Since the simulation is based on optical principle, it gives accurate results. This suggests the possible use of 2-D photonic crystal structure as a sucrose sensor. Experimental procedure for measuring the concentration of sucrose is also mentioned.     

一维函数光子晶体的研究

本文提出一种新型函数光子晶体, 其折射率是空间位置函数. 由费马原理, 我们给出光在一维、 二维和三维函数光子晶体中的运动方程, 以及一维函数光子晶体的色散关系、 带隙结构和透射率, 再利用传输矩阵理论研究函数光子晶体周期数、 入射角和介质层的厚度等对透射率和禁带结构的影响, 计算发现通过选择不同的折射率空间分布函数, 可以得到比传统光子晶体更宽或更窄的禁带结构. 这样为我们设计不同带隙结构的光子晶体提供理论依据.     

Optical properties of MgxZn1−xO nanowire photonic crystals

We investigate the optical properties of two-dimensional periodic arrays of well-aligned Mg_xZn_1−xO nanowires, i.e., Mg_xZn_1−xO nanowire photonic crystals. The nanowire photonic crystal can exhibit a photonic band gap in the visible range. As the mole fraction of Mg, x, increases, the edge frequencies of the band gap increase and the band gap size decreases. The characteristics of relative band gap and vacant point defect mode are also studied with varying x. From the finite-difference time-domain simulations, we show that the light extraction from nanowires can be controlled by varying the distance between optically excited nanowires and a waveguide, and the mole fraction of Mg. Controlling the light extraction from nanostructures can be useful in the implementation of nanoscale light emitting devices.