Analysis of photonic band gaps in a two-dimensional photonic crystal with centrifugal core-shell rods

The absolute photonic band gap (PBG) in two-dimensional (2D) photonic crystal with excentric core-shell rods is studied in this paper. The core rod shifts away from the core-shell rod center, and its position is decided by two new introduced parameters — the shift angle θ and the offset ρ. We use the FDTD algorithm to calculate the photonic bands of the photonic crystal, and analyze how the offset and shift angle affect the photonic bang gap of excentric core-shell photonic crystal for different core rod size. It has been shown that the variation of the photonic band gap is quite peculiar.     

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。     

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.     

基于横向磁光效应磁化等离子体光子晶体的光子带隙特性

通过外加与电磁波传播方向垂直的磁场来调控等离子体光子晶体的光子带隙结构。采用时域有限差分方法数值分析了由本征层为等离子体层和其他电介质材料层交替堆叠而成的磁化等离子体光子晶体的光子带隙结构和频谱特性。数值结果表明,光子晶体中等离子体的介电常数随着外磁场大小的变化而改变,从而使磁化等离子体光子晶体的带隙特性在一定的频率范围相应地得到调节。     

在高频区存在巨带隙的长方晶格二维光子晶体

本文利用降低光子晶体的对称性来提高绝对禁带宽度, 提出两种长方结构长方介质柱二维光子晶体, 用快速平面波展开法研究其高频区的带结构.经参数优化发现, 长方晶格包含一套介质柱时, 最大绝对禁带宽度Δω为0.1265ωe（ωe=2πc/a, a为晶格常数, c为光速）, 绝对禁带中心频率ωmid为1.9256ωe, Δω/ωmid=6.6%; 当长方晶格包含两套介质柱时, 最大绝对禁带宽度为0.203ωe, 绝对禁带中心频率为1.8597ωe, Δω/ωmid=10.9%.     

基于法拉第效应磁化等离子体光子晶体FDTD分析

通过增加外磁场来调控等离子体光子晶体的光子带隙结构,采用时域有限差分算法分析了由本征层为磁化等离子体层和其他电介质材料层交替堆叠而成的磁化等离子体光子晶体的光子带隙结构,数值模拟中采用完全匹配层吸收边界条件以防止边界的反射。由于外磁场的法拉第磁光效应,使等离子体的介电常数随着外磁场的变化而改变。数值结果表明,等离子体光子晶体的带隙特性在一定的频率范围相应地得到调节,实现了频率低于等离子体频率的电磁波也能在等离子体中传播。     

具有复介电常量二维光子晶体的特性研究

采用平面波展开法,通过数值模拟研究了具有复介电常量的二维光子晶体的能带结构和光传输特性,重点讨论介电常量的虚部为负值情形时对传输特性的影响。研究表明由于光子带隙的存在有效地抑制了频率位于带隙内光的自发辐射。当在介质中掺入具有增益特性的杂质时,即使两种介质的介电常量相差很小,在靠近光子带隙边缘,出现了较强的受激辐射放大。通常在带隙的边缘处,光子晶体的群速度较小,而激光阈值正比于群速度的平方,当群速度很小时,激光阈值将大大减小。这为实现零阈值激光器提供了基础,也为制作光放大微器件提供了一个有益的理论参考。     

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通过增加外磁场来调控等离子体光子晶体的光子带隙结构,采用时域有限差分算法分析了由本征层为磁化等离子体层和其他电介质材料层交替堆叠而成的磁化等离子体光子晶体的光子带隙结构,数值模拟中采用完全匹配层吸收边界条件以防止边界的反射。由于外磁场的法拉第磁光效应,使等离子体的介电常数随着外磁场的变化而改变。数值结果表明,等离子体光子晶体的带隙特性在一定的频率范围相应地得到调节,实现了频率低于等离子体频率的电磁波也能在等离子体中传播。     

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.     

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     

一维Al/SrF2低温超导体-电介质光子晶体能带结构

基于二流体电子模型和平面波展开法,计算了一维Al/SrF2超导体-电介质光子晶体的能带结构.结果表明:随着超导层厚度的增加,第一光子带隙中心频率和截止频率均发生蓝移,且第一带隙宽度逐渐增加到一个峰值后又逐渐变窄.更重要的是,在低于临界温度的超低温环境中,温度的微小变化,对该类光子晶体的带隙宽度、中心频率以及截止频率均有...     

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。     

Position calculation of the frequency band gap in the finite photonic crystal with multiple alternations using boundary element method

In this paper, the wave transmission from finite photonic crystals with multiple alternations is investigated using boundary element method (BEM). Since that, in these structures the alternation is not in all directions of space; the investigations of the frequency band gap with desired accuracy are not practical by analytical methods. Also, the frequency dispersion of dielectric rods is an effective parameter in photonic crystals, which this effect in our calculations has been considered. Due to the high capabilities of the BEM, the transmitted wave spectrum in the photonic crystal is calculated by changing the geometrical and optical parameters of the photonic crystal and applying more alternation in its structure and the position and width of the frequency band gap is investigated. Then, it is assumed that the photonic crystal with an arbitrary angle is rotated around the axis which is perpendicular on the crystal cross section and then, it is irradiated with a plan wave. The band gap of the photonic crystals with the desired structure, desired rotation angle and multiple alternations have been solved. Very low information volume, high speed and accuracy during the calculation and useable for any desired structures are the characteristics of this method.     

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.     

Band gap extension in honeycomb lattice two-dimensional plasma photonic crystals in the presence of dissipation

We investigate two types of honeycomb lattice two-dimensional plasma photonic crystals that possess large photonic band gaps in the presence of dissipation. We obtain a clear insight into the band structures and find imaginary parts of the eigenvalue band structure at the symmetry points display discontinuous behaviour when the filling factor of plasma in type-1 structure is low. Further more, we show how the photonic band gaps are affected by the normalized plasma frequency, radius of cylinder, dielectric constant and collision frequency. Our results demonstrate the band gap extension by increasing normalized plasma frequency in both type structures and radius of plasma cylinders in type-1 structure. The width of band gaps could also be enlarged by decreasing dielectric cylinder's radius. The bands shift toward lower frequencies when relative dielectric constant increases in both two types. These results may provide theoretical instructions to design new optoelectronic devices.     

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.     

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.     

Pressure, temperature and plasma frequency effects on the band structure of a 1D semiconductor photonic crystal

In this work using the transfer-matrix formalism we study pressure, temperature and plasma frequency effects on the band structure of a 1D semiconductor photonic crystal made of alternating layers of air and GaAs. We have found that the temperature dependence of the photonic band structure is negligible, however, its noticeable changes are due mainly to the variations of the width and the dielectric constant of the layers of GaAs, caused by the applied hydrostatic pressure. On the other hand, by using the Drude's model, we have studied the effects of the hydrostatic pressure by means of the variation of the effective mass and density of the carriers in n-doped GaAs, finding firstly that increasing the amount of n-dopants in GaAs, namely, increasing the plasma frequency, the photonic band structure is shifted to regions of higher frequencies, and secondly the appearance of two regimes of the photonic band structure: one above the plasma frequency with the presence of usual Bragg gaps, and the other, below this frequency, where there are no gaps regularly distributed, with their width diminishing with the increasing of the plasma frequency as well as with the appearance of more bands, but leaving a wide frequency range in the lowest part of the spectrum without accessible photon states. Also, we have found characteristic frequencies in which the dielectric constant equals for different applied pressures, and from which to higher or lower values the photonic band structure inverts its behavior, depending on the value of the applied hydrostatic pressure. We hope this work may be taken into account for the development of new perspectives in the design of new optical devices.     

光子晶体理论应用于光纤布拉格光栅的研究

将光纤布拉格光栅近似为一维光子晶体，研究光栅的能带结构和光学传输特性。利用平面波展开法对光子晶体进行理论研究，将研究方法移植到光纤布拉格光栅上，并对其进行数值分析，得到光栅的传输特性。研究表明，光栅反射谱有多个反射峰，峰值中心频率是基频的整数倍，而且峰值处存在光子带隙，反射峰带宽对应光子带隙宽度，中心频率和带宽随光栅长度、高介电常量材料占空比、调制深度而变化。结果与传统的耦合模理论一致。     

Light exiting from real photonic band gap crystals is diffuse and strongly directional

Any photonic crystal is in practice periodic with some inevitable fabricational imperfections. We have measured angle-resolved transmission of photons that are multiply scattered by this disorder in strongly photonic crystals. Peculiar non-Lambertian distributions occur as a function of frequency: due to internal diffraction, wide angular ranges of strongly reduced diffuse transmission coincide with photonic stop bands, while enhancements occur for directions outside stop gaps. We quantitatively explain the experiment with a model incorporating diffusion and band structure on equal footing. We predict that in the event of a photonic band gap, diffuse light at frequencies near band gap edges can exit only along isolated directions. Angle-resolved diffuse transmission appears to be the photonic equivalent of angle-resolved photoelectron spectroscopy.