Tuning the band gap of self-assembled superparamagnetic photonic crystals in colloidal magnetic fluids using external magnetic fields

The model of tunable superparamagnetic photonic crystals self-assembled in colloidal magnetic fluids under externally applied magnetic fields is established. The mechanisms, which are in charge of the tunability of the band gaps with magnetic fields are clarified. The band structures of the triangularly-arrayed two-dimensional photonic crystals with limited heights of magnetic columns are calculated with the experimental data of structures and refractive indices in the literatures. The field-dependent properties of the first band gaps are gained for the z-odd and z-even modes, respectively. Simulation results indicate that the mid frequencies of the first band gaps of the z-odd modes can be easily tuned by the external magnetic fields, while those of the z-even modes bear relatively weak dependence on the external magnetic fields. Simultaneously, the first band gaps of both kinds of modes become wide along with the increase of the magnetic fields. The results presented in this work give a guideline for realizing the tunable photonic crystals with magnetically colloidal materials and magnetic stimuli.     

可见光波段SiO2/CdSe一维光子晶体及缺陷模的研究究

采用SiO2/CdSe构建了可见光波段一维光子晶体结构,并在其中引入LiTaO3缺陷层。利用传输矩阵法,分析了电磁波在无缺陷与含LiTaO3缺陷层两种光子晶体中的带隙结构,系统地研究了缺陷层参数对光子晶体可见光波段带隙结构的影响规律。计算结果表明：LiTaO3的引入,有利于带隙宽度的增加,调整缺陷层结构参数,缺陷模的位置可在不同颜色区域出现,如红光、黄光等缺陷模。该结构有望用于制作可见光波段的滤波器。     

含负折射率材料的一维光子晶体的光学传输特性

采用光学传输矩阵方法,模拟研究了由正折射率材料和负折射率材料交替组成的一维光子晶体的光学传输特性.计算了这种含负折射率材料的一维光子晶体的透射谱和色散关系.结果表明,在正入射时,含负折射率材料的光子晶体的带隙要比传统的光子晶体要大得多,并具有狭窄的透射带,从光学薄膜理论的色散关系出发解释了形成上述现象的原因.讨论了在不同的偏振模式下,光以中心波长入射时,反射率随着入射角度的变化关系.发现含负折射率材料的一维光子晶体具有更好的角度特性,可以用来实现对中心波长的全方位反射.     

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     

Dispersion properties of two-dimensional plasma photonic crystals with periodically external magnetic field

Dispersion properties of two types of two-dimensional periodically magnetized plasma array structures with square lattices have been investigated by using plane wave expansion method. It is found that two different regions of flatbands and photonic band gaps occur in the TE polarization due to the external magnetic field. The two types of system can be seen as a kind of unusual plasma photonic crystals. The results show that not only the location of flatbands but also the position and bandwidth of photonic band gaps can be tuned by external magnetic field. The cutoff frequency decreases as external magnetic field increases. The edge of two different of flatbands regions and cutoff frequency shift downward to lower frequencies obviously with increasing plasma collision frequency, while they shift upward to higher frequencies notably with increasing plasma frequency. The filling factor has little effect on the location of flatbands regions. The width of flatbands regions and photonic band gaps are almost unchanged by increasing filling factor, but the number of ominidirectional photonic band gap for type-1 structure plasma photonic crystals can be effectively controlled by adjusting filling factor. It is worth to be noted that the first band gaps above the cutoff frequencies in Г–X and Г–M direction for two types of PPCs can be modulated by the parameters as mentioned above, and the relative bandwidth of band gap in Г–X direction is wider than the one in Г–M direction. The results may provide theoretical instructions to design new tunable photonic crystals devices.     

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.     

Control of photonic band gaps in one-dimensional photonic crystals

The photonic band gaps in one-dimensional photonic crystals (PCs) are theoretically investigated. A new method to broaden the photonic band gaps is introduced. Based on the similar method, a kind of photonic crystals is constructed to generate photonic band gaps with proportioned central frequencies. This technology can be used for designing nonlinear PCs for harmonic generation.     

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。     

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.     

Temperature dependence of photonic crystals based on thermoresponsive magnetic fluids

The influence mechanisms of temperature on the band gap properties of the magnetic fluids based photonic crystals are elaborated. A method has been developed to obtain the temperature-dependent structure information (A_sol/A) from the existing experimental data and then two critical parameters, i.e. the structure ratio (d/a) and the refractive index contrast (Δn) of the magnetic fluids photonic crystals are deduced for band diagram calculations. The temperature-dependent band gaps are gained for z-even and z-odd modes. Band diagram calculations display that the mid frequencies and positions of the existing forbidden bands are not very sensitive to the temperature, while the number of the forbidden bands at certain strengths of magnetic field may change with the temperature variation. The results presented in this work give a guideline for designing the potential photonic devices based on the temperature characteristics of the magnetic fluids based photonic crystals and are helpful for improving their quality.     

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 gaps structure and semi-Dirac point of two-dimensional function photonic crystals

Two-dimensional function photonic crystals, in which the dielectric constants of medium columns are the functions of space coordinates , are proposed and studied numerically. The band gaps structures of the photonic crystals for TE and TM waves are different from the two-dimensional conventional photonic crystals. Some absolute band gaps and semiDirac points are found. When the medium column radius and the function form of the dielectric constant are modulated, the numbers, width, and position of band gaps are changed, and the semi-Dirac point can either occur or disappear. Therefore,the special band gaps structures and semi-Dirac points can be achieved through the modulation on the two-dimensional function photonic crystals. The results will provide a new design method of optical devices based on the two-dimensional function photonic crystals.     

Investigation of one-dimensional photonic crystals composed of dispersive materials

One-dimensional photonic crystals (1DPCs) composed of dispersive materials (including negative refractive index materials, negative μ materials, and negative ? materials) are proposed. The dependence of the band gaps on the angle of incidence and thickness scale are investigated by using the transfer matrix method. Simulation results show that the band gaps of these dispersive material 1DPC are insensitive to the thickness scale. The defect modes of these doped 1DPCs behave specially when the thickness of the defect layer, the angle of incidence and the thickness scale of PC change.     

金属插层对C60/AlN一维光子晶体带隙的影响

利用传输矩阵方法,研究了金属Ag插层对C60/AlN一维光子晶体带隙宽度以及反射率的影响.结果表明：在C60与AlN之间插入Ag组成的［C60/Ag/AlN］n一维光子晶体,与未插入Ag层相比可使带隙增宽73.91%,最大反射率提高到91.01% .该结构可望用于制作紫外线波段的宽带反射镜.     

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.     

Physics and applications of photonic crystals

In this article, we investigate how the photonic band gaps and the variety of band dispersions of photonic crystals can be utilized for various applications and how they further give rise to completely novel optical phenomena. The enhancement of spontaneous emission through coupled cavity waveguides in a one-dimensional silicon nitride photonic microcrystal is investigated. We then present the highly directive radiation from sources embedded in two-dimensional photonic crystals. The manifestation of novel and intriguing optical properties of photonic crystals are exemplified experimentally by the negative refraction and the focusing of electromagnetic waves through a photonic crystal slab with subwavelength resolution.     

Anisotropic photonic crystals: Generalized plane wave method and dispersion symmetry properties

This article presents a generalized vector plane wave expansion method, applicable to isotropic and anisotropic periodic dielectric media of arbitrary geometry and dimension. The influence of anisotropic material orientation on the symmetry properties of photonic crystal dispersion surface is discussed. It is shown that the overall Brillouin zone symmetry is formed by the intersection of the photonic crystal lattice symmetry and the symmetry determined by the anisotropic material orientation. This work explains how to define the irreducible Brillouin zone of a two-dimensional anisotropic photonic crystal and demonstrates that doing it correctly allows one to avoid erroneous results, when calculating band gap diagrams of anisotropic photonic crystals. With the help of the methods presented, the possibility of controlling the band gaps of anisotropic photonic crystals by means of external electric field is shown.     

Optics of Photonic Crystals

In this article, a general theoretical framework to describe and analyze the optical properties of photonic crystals is presented. In addition to the analytical treatment of their optical response based on the method of Green’s function, numerical tools to calculate the dispersion relations and the eigenfunctions of the radiation field, transmission spectra, localized midgap modes, and lasing threshold are introduced and applied to some typical examples. Group theory to analyze the symmetry of the eigenmodes is also introduced, and the existence of uncoupled modes that cannot be excited by external plane waves is shown. The presence of the enhancement effect of nonlinear optical processes and stimulated emission due to the small group velocity which is easily realized in the photonic crystals is pointed out, and the possibility of low-threshold lasing in the photonic crystals is discussed.     

Synthesis and photonic band gap characterization of high quality photonic crystal heterostructures

High quality photonic crystal heterostructures with a thin titania planar defect layer between its two constitutional photonic crystals were fabricated and their structural and optical properties were analyzed. The results suggest that the thin planar defect layer is beneficial to separate the two constitutional photonic crystals from each other and to reduce the roughness of the interface. The quality of the resulting photonic crystal heterostructures is improved largely and the main features of the photonic band gaps of the two constitutional photonic crystals are inherited. The predominant optical quality of these heterostructures (e.g. deep double photonic band gaps and steep photonic band edges) may afford new flexibility and functionality for engineered photonic behavior in practical devices such as late-model light-operated switches.     

二维八重准晶有机光子晶体平板的光学传播特性

采用时域有限差分法研究了二维八重准晶有机光子晶体的光传输特性,重点分析了光束在聚苯乙烯空气柱平板结构和聚苯乙烯介质柱结构中的透射特性与光局域特性。研究结果表明,即使在低折射率对比度的情况下,两种完整八重准晶平板结构中均出现了可见光波段的光子带隙和本征模,且光子带隙中心位置随着平板厚度的增大而红移。当在两种准晶结构中引入缺陷微腔时,带隙内的缺陷模产生位置和波长红移特性随着微腔结构的变化规律明显不同,这种差异性是由两种物理机制(即光子晶体缺陷能级变化与微腔所支持的驻波条件)共同作用的结果。这一研究结果将为实验制备有机准晶发光器件提供一定的理论基础。