Enlargement of complete two-dimensional band gap by using photonic crystal heterostructure

A two-dimensional photonic crystal heterostructure, which consists of two photonic crystals of a square lattice of circular columns with reverse dielectric configurations, is proposed. Photonic band gap properties are calculated using a plane-wave method and the transmission spectra are obtained. After optimization, the relative width of the complete band gap reached 13.8% based on the simple unit-cell shape and crystal lattice. The photonic crystal heterostructure opens up new ways of engineering photonic band gap materials and designing photonic crystal devices.     

Research of band gap properties based on two-dimensional photonic crystal with mixed shapes of rods

Two new structures of photonic crystals were designed. The band gap properties of photonic crystals with square and circular dielectric rods mixed arrangement are researched. The band gap properties of mixed shapes rods photonic crystal are calculated and compared with the crystals with square rods or round rods by using plane wave expansion method. Simulation results show that for the square lattice, mixed shapes of rods make the higher-order bands of TM modes moving toward the low frequency range. The gap bands’ widths and locations are between the parameters of square and round rods photonic crystal. In triangle lattice, a significant band gap is presented in photonic crystal with mixed shapes of rods in TE mode, while it is almost not presented in square and round rods crystals. The phenomenon of bands moving toward the low frequency range is also found in the triangle lattice mixed shapes rods photonic crystal. The reasons of the results in the vision were analyzed.     

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.     

Influence of the dielectric background on the quality factors of metallo-dielectric photonic crystals

The effect of varying the dielectric background on the quality factor of two-dimensional metallo-dielectric photonic crystals is theoretically studied. The studied metallo-dielectric photonic crystal consists of a square lattice of circular metallic rods embedded into a dielectric background with a defect rod on the center that creates resonant modes within the photonic band gap. The metal is modeled with the Drude dispersion relation. A combination of the finite-difference time-domain method together with a frequency filtering technique is used to estimate accurately the resonant frequencies and their quality factors. The results show that the quality factors increase with increasing background dielectric constant. If a dielectric background material such as Silicon is used instead of air, an enhancement in the quality factor of up to eight times can be achieved, depending on the resonant mode. We also show that, depending on the modes, there exists an optimal size for the defect rod that gives the maximum quality factor.     

Light confinement in 3D silicon doped with germanium (n-SixGe1−x) and silicon-on-insulator (SOI) photonic crystal structures

The numerical investigation of photonic band gaps (PBGs) for three-dimensional (3D) photonic crystals (PCs) of silicon doped with germanium (n-Si_xGe_1−x) and silicon-on-insulator (SOI) structures has been illustrated. The effect of germanium-doping (Ge-doping) concentration on the vertical confinement of the light and the band gap size has been presented. A 3D full vectorial plane wave was developed and employed to investigate design parameters of the 3D PC structure and to calculate dispersion relation for guided modes. Calculations of band structures for the triangular lattices of dielectric cylinders in air for quasi-3D PC structures have been performed.     

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.     

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。     

Surface phonon–polaritons in rectangular quantum wires of polar ternary mixed crystals

In this paper, the dispersion relations of surface phonon–polaritons in freestanding rectangular quantum wire systems of polar ternary mixed crystals are derived. The numerical calculations for Al_xGa_1−xAs and Zn_xCd_1−xSe quantum wire systems are performed. The results reveal that the frequencies of surface phonon–polariton modes are sensitive to the geometric structures of the quantum wires, the wave-vectors in z-direction, and the compositions of the ternary mixed crystal materials. The effects of the “two-mode” and “one-mode” behaviors of the ternary mixed crystals on the surface phonon–polariton modes are also discussed.     

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...     

Effect of the dielectric background on dispersion characteristics of metallo-dielectric photonic crystals

We theoretically study the effect of the dielectric background in two-dimensional metallo-dielectric photonic crystals. The metallo-dielectric photonic crystal consists of a square lattice of circular metallic rods embedded into a dielectric background. We calculate the photonic band structure by means of the plane wave method and the frequency-dependent finite-difference time-domain method. The transfer matrix method is used to obtain the reflectivity characteristics. Results show that the band structures shift toward lower frequencies and become flatter when the background dielectric constant increases. In addition, degeneracy can be broken and new gaps can be created in function of the dielectric background. We also found that the relative band gap width Δω/ω_g grows with increasing background dielectric constant and widths as large as 42.3% and 13.8% for the second and third band gaps can be achieved for ε_b = 9. We have investigated the origin of the new gap in these structures by studying the electric-field distribution at the band edges for the first five modes.     

Study on complete band gap of two-dimensional photonic crystal with quadrangular rods

The plane wave expansion method (PWM) was employed to study the relation between the photonic band gap (PBG) of 2D triangular lattice photonic crystal (PC) and the shapes of rods and dielectric constant. It is shown that the PBG of PC with quadrangular rods is the widest one, compared with the other case with cross section shapes of triangular, circular and hexagon under the same filling ratio, and a peak value appears when the side length ratio of l_x/l_y is equal to 1.21 approximately to any filling ratio. In the aspect of the effects of dielectric constant, the PBG width does not increase monotonically with the increase permittivity ?₂ of the background material to certain permittivity ?₁ of the quadrangular rods, but has a peak value instead. However, the larger the permittivity ?₁ is, the narrower the band width is and the lower the central frequency is, and the dispersion Δ? = ?₂ − ?₁ is larger also.     

用转移矩阵法数值研究二维正方介质柱光子晶体的传输特性

利用转移矩阵方法对二维正方介质柱光子晶体的传输特性进行了研究,数值计算研究了不同晶格、同一晶格柱体截面面积不同、放置方位角不同时光子晶体的传输特性。数值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,正方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对光子禁带有重要影响。数值研究表明在正方介质柱下设计宽平坦光子禁带时,可以首先考虑正方晶格结构,其次设法使柱体截面尽量大一些,最后可通过柱体放置方位角来微调光子禁带的宽度与中心频率以达到设计要求。     

Optical, thermal, dielectric and ferroelectric behaviour of sodium acid phthalate (SAP) single crystals

Sodium acid phthalate (SAP), an efficient semi-organic crystal having dimensions 17×8×2 mm³ has been grown from aqueous solution by slow evaporation technique at room temperature within the period of 2 weeks. The lattice parameters of the grown crystals were determined using single-crystal X-ray diffraction analysis. The presence of functional groups was estimated qualitatively by Fourier transform infrared (FTIR) analysis. The band gap energy was determined using optical absorption studies. The TG/DTA analysis reveals that the SAP crystal is thermally stable up to 141.6 °C. The dielectric constant and dielectric loss was studied as a function of frequency and the corresponding activation energy (E_a) has been calculated for the grown crystal. Scanning electron microscope studies enunciate the ferroelectric domain patterns of the SAP crystal. Ferroelectric property of the grown crystal was confirmed by hysteresis loop studies.     

介质柱型二维Triangular格子光子晶体的禁带特性

采用平面波展开法数值计算了空气背景中由圆形、正六边形和正方形介质柱构造的二维三角晶格光子晶体禁带结构,并研究了介质方柱旋转角度、介质折射率和填充比对完全光子禁带宽度的影响.结果表明,在低频区,介质方柱旋转17°时,出现最大完全光子禁带,且最大禁带宽度随介质折射率的变化较为稳定.在高频区,介质方柱旋转30°时,完全光子禁带宽度最大;且介质材料折射率n=2.2时即出现完全光子禁带,n=2.6时,完全光子禁带达到最大.     

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.     

Band gap studies of 2D photonic crystals with hybrid scatterers

Two-dimensional (2D) photonic crystals (PCs) of a square lattice with dielectric hybrid rods in air are proposed; these PCs consist of a square rod at the center of the unit cell and additional circular rods with their outermost edges against the middle of each side of the lattice unit cell. The band gap structures of PCs can be tailored and optimized by rotating the square rods and adding circular rods to the lattice unit cell. The variation of bands near the complete photonic band gap boundaries, due to some specific modes, is sensitive to certain structural parameters of the system. The results can be understood by analyzing the spatial energy distribution of the electromagnetic fields. Based on such a field analysis, a novel interpretative model is proposed. The PC can be fabricated easily and operated in the microwave region and, hence, should be suitable for applications in new microwave devices.     

二维复式晶格完全带隙光子晶体缺陷频率的分析

提出了一种具有完全带隙的二维复式晶格光子晶体,该晶体是在二维正方形格子中,旋转截面为正方形的柱子,同时在每个原胞中心引入圆形截面的柱子而形成的,并在其中引入点缺陷。运用平面波展开法并结合超晶胞理论分析此缺陷态光子晶体的频率特性。仿真结果表明,通过调节缺陷的尺寸、角度等结构参量,可以改变缺陷态频率的位置,使TE和TM模缺陷态频率一致,TE模和TM模同时谐振,处于缺陷态频率的入射光就能够完全耦合进点缺陷,具有较高的耦合效率。这种结构的复式晶格完全带隙光子晶体为制作完全带隙光子晶体谐振腔提供了理论基础。     

Tamm states and nonlinear surface modes in photonic crystals

We predict the existence of surface gap modes, known as Tamm states for electronic systems, in truncated photonic crystals formed by two types of dielectric rods. We investigate the energy threshold, dispersion, and modal symmetries of the surface modes, and also demonstrate the existence and tunability of nonlinear Tamm states in binary photonic crystals with nonlinear response.     

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     

二维函数光子晶体

光子晶体是由两种或两种以上不同介电常数材料所构成的周期性光学纳米结构.光子晶体结构可分为一维、二维和三维,其中二维光子晶体已成为研究的热点.可调带隙的二维光子晶体可以设计出新型的光学器件,因此,对它的研究具有重要的理论意义和应用价值.本文提出的二维新型函数光子晶体可以实现光子晶体带隙的可调性.所谓二维函数光子晶体,即组成它的介质柱的介电常数是空间坐标的函数,它不同于介电常数为常数的二维常规光子晶体.二维函数光子晶体是通过光折变非线性光学效应或电光效应使介质柱的介电常数成为空间坐标的函数.运用平面波展开法给出了TE和TM波的本征方程,由傅里叶变换得到二维函数光子晶体介电常数ε(r)的傅里叶变换ε(G),其傅里叶变换比常规二维光子晶体的复杂.计算发现当介质柱介电常数为常数时,其傅里叶变换与常规二维光子晶体的相同,因此二维常规光子晶体是二维函数光子晶体的特例.在此基础上具体研究了二维函数光子晶体TE波和TM波的带隙结构,其介质柱介电常数函数形式取为ε(r)=k·r+b,其中k,b为可调的参数.并与二维常规光子晶体TE波和TM波的带隙结构进行了比较,发现二维函数光子晶体与二维常规光子晶体TE波和TM波的带隙结构有明显的区别,二维函数光子晶体的带隙数目、位置以及宽度随参数k的变化而发生改变.从而实现了二维函数光子晶体带隙结构的可调性,为基于二维光子晶体的光学器件的设计提供了新的设计方法和重要的理论依据.