Wave-vector diagrams for two-dimensional photonic crystals

Photonic crystals exhibit band gaps, meaning that electromagnetic fields cannot propagate in them for specific ranges of wavelengths and directions. The calculation of band structure diagrams has been intensively studied and is now well understood. In contrast to that, so-called wave-vector diagrams (i.e. dispersion surfaces, depicting the loci of all relevant wave vectors at a fixed wavelength) are less known and used. In principle, they show how the effective index of the structure depends on the direction of propagation. A method to calculate explicitly wave-vector diagrams for two-dimensional photonic crystals is derived which leads finally to quadratic eigenvalue problems. Results for square and triangular lattices are presented and some applications are discussed.     

Beyond butterflies—the diversity of biological photonic crystals

When biological photonic crystals are discussed, butterfly photonic crystals are often cited as representative; in fact, numerous diverse biological photonic crystals exist and butterfly photonic crystals have several quirks when compared with others, with the consequence that considering them typical is in many ways unhelpful. In this paper, we give an overview of biological photonic crystals and discuss their typical features, specifically with regard to their periodicities, geometries, chemical compositions, the wavelengths they reflect and their band gaps. The low refractive index contrast and low mean refractive index: a universal feature of biological photonic crystals compared with artificial ones is highlighted and attention is drawn to their comparatively complex band diagrams.     

修正的频域有限差分法在二维金属光子晶体分析中的应用

与介质光子晶体相比,金属光子晶体的带隙特性在毫米波和亚毫米波波段有着重要的应用价值.基于Yee网格的频域有限差分法推导得出的本征模方程,求解后能方便而又可靠地得出介质光子晶体的带隙图和场分布.但由于金属与介质的本质差异,该方法不能直接应用于金属光子晶体.文中引入了金属表面边界条件,推导了二维金属周期结构的光子带隙本征模方程.通过数值计算,得出了不同晶格结构（正方/三角格子）下两种模式（TE/TM）的全禁带特性,并与介质周期结构的禁带特性进行对比,分析了金属周期结构在模式选择和器件集成方面的优点.     

修正的频域有限差分法在二维金属光子晶体分析中的应用

与介质光子晶体相比,金属光子晶体的带隙特性在毫米波和亚毫米波波段有着重要的应用价值.基于Yee网格的频域有限差分法推导得出的本征模方程,求解后能方便而又可靠地得出介质光子晶体的带隙图和场分布.但由于金属与介质的本质差异,该方法不能直接应用于金属光子晶体.文中引入了金属表面边界条件,推导了二维金属周期结构的光子带隙本征模方程.通过数值计算,得出了不同晶格结构（正方/三角格子）下两种模式（TE/TM）的全禁带特性,并与介质周期结构的禁带特性进行对比,分析了金属周期结构在模式选择和器件集成方面的优点. 关键词： 金属光子晶体 频域有限差分法 全禁带     

Surface electronic structure of SnO2(110)

We report theoretical investigations on the surface electronic structure of the (110)-face of SnO₂, a semiconductor of rutile bulk structure. Starting with a tight binding Hamiltonian for the bulk, we determine the surface electronic structure using the scattering theoretic method. As results we obtain the surface bound states, the surface resonances and the wave-vector resolved surface layer densities of states. The dominant features are two backbond states in the stomach gap of the main valence band and two Sn-s derived states in the lower conduction band region. In the upper valence band region, only weak resonances occur, like in other materials with relatively strong ionicity.     

一维光子晶体反常折射的数值分析

分析了一维光子晶体中产生反常折射的原因,根据波向量图对光在其中传播的方式做了定性的分析.根据一维光子晶体中具有波频率与波向量之间明确解析表达式的特点,指出利用此关系式能方便地对光在其中的传播方式进行深入的分析.利用这种方法,文中分析了光在其中传播的一些性质.指出光的偏移性质与角度和频率密切相关.     

Numerical study on characteristic of two-dimensional metal/dielectric photonic crystals

An improved plan-wave expansion method is adopted to theoretically study the photonic band diagrams of twodimensional(2D) metal/dielectric photonic crystals.Based on the photonic band structures,the dependence of flat bands and photonic bandgaps on two parameters(dielectric constant and filling factor) are investigated for two types of 2D metal/dielectric(M/D) photonic crystals,hole and cylinder photonic crystals.The simulation results show that band structures are affected greatly by these two parameters.Flat bands and bandgaps can be easily obtained by tuning these parameters and the bandgap width may reach to the maximum at certain parameters.It is worth noting that the hole-type photonic crystals show more bandgaps than the corresponding cylinder ones,and the frequency ranges of bandgaps also depend strongly on these parameters.Besides,the photonic crystals containing metallic medium can obtain more modulation of photonic bands,band gaps,and large effective refractive index,etc.than the dielectric/dielectric ones.According to the numerical results,the needs of optical devices for flat bands and bandgaps can be met by selecting the suitable geometry and material parameters.     

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。     

Exciton--polaritons in ternary mixed crystals

In this paper the bulk exciton polaritons in ternary mixed crystals (TMCs) are investigated in the Born--Huang approximation. The numerical results of the polariton frequencies as functions of the wave-vector and the compositions for ternary mixed crystals Al电震荡 三重混合晶体 激子 电磁学polariton, exciton, ternary mixed crystalProject supported partly by PhD Progress Foundation of Higher Education Institutions of China (Grant No~20040126003) and the Natural Science Foundation of Inner Mongol of China (Grant No~200408020101).2006-10-08In this paper the bulk exciton polaritons in ternary mixed crystals （TMCs） are investigated in the Born-Huang approximation. The numerical results of the polariton frequencies as functions of the wave-vector and the compositions for ternary mixed crystals AlxGa1-xAs, CdxZn1-xSe, and AlxGa1-xN are obtained and discussed. The new dispersion characteristics for exciton-polaritons in TMC systems are found in comparison with binary crystals. The splitting of the two branches of exciton-polariton frequencies varies nonlinearly with the composition of TMCs and has a minimum in the long-wavelength range.     

First-principles calculations of structural, electronic, optical and elastic properties of magnesite MgCO3 and calcite CaCO3

Detailed ab initio calculations of the structural, electronic, optical and elastic properties of two crystals - magnesite (MgCO₃) and calcite (CaCO₃) - are reported in the present paper. Both compounds are important natural minerals, playing an important role in the carbon dioxide cycling. The optimized crystal structures, band gaps, density of states diagrams, elastic constants, optical absorption spectra and refractive indexes dependence on the wavelength all have been calculated and compared, when available, with literature data. Both crystals are indirect band compounds, with calculated band gaps of 5.08 eV for MgCO₃ and 5.023 eV for CaCO₃. Both values are underestimated by approximately 1.0 eV with respect to the experimental data. Although both crystals have the same structure, substitution of Mg by Ca ions leads to certain differences, which manifest themselves in noticeable change in the electronic bands profiles and widths, shape of the calculated absorption spectra, and values of the elastic constants. Response of both crystals to the applied hydrostatic pressure was analyzed in the pressure range of phase stability, variations of the lattice parameters and characteristic interionic distances were considered. The obtained dependencies of lattice constants and calculated band gap on pressure can be used for prediction of properties of these two hosts at elevated pressures that occur in the Earth's mantle.     

Correlations between electronic energy bands spin splitting and magnetic profile symmetry of magnetic superlattice

We have theoretically investigated the energy band structures of two typical magnetic superlattices formed by perpendicular or parallel magnetization ferromagnetic stripes periodically deposited on a two-dimensional electron gas (2DEG), where the magnetic profile in the perpendicular magnetization is of inversion anti-symmetry, but of inversion symmetry in parallel magnetization, respectively. We have shown that the energy bands of perpendicular magnetization display the spin-splitting and transverse wave-vector symmetry, while the energy bands of the parallel magnetization exhibit spin degeneration and transverse wave-vector asymmetry. These distinguishing spin-dependent and transverse wave-vector asymmetry features are essential for future spintronics devices applications.     

Polaritonic stop-band transparency via exciton-biexciton coupling in CuCl

Radiation is almost completely reflected within the exciton-polariton stop band of a semiconductor, as in the typical case of CuCl. We predict, however, that a coherently driven exciton-biexciton transition allows for the propagation of a probe light beam within the stop band. The phenomenon is reminiscent of electromagnetically induced transparency effects occurring in three-level atomic systems, except that it here involves delocalized electronic excitations in a crystalline structure via a frequency and wave-vector selective polaritonic mechanism. A well-developed transparency, favored by the narrow linewidth of the biexciton, is established within the stop band where a probe pulse may propagate with significant delays. The transparency window can be controlled via the pump beam detuning and intensity.     

毛细管中柱对称类面心结构胶体晶体的光谱特性

用体积浓度为30% 的低分散二氧化硅小球悬浮液注入毛细管中自组织生长成胶体晶体. 实验测量了这种胶体晶体的透射谱. 测量结果显示这种胶体晶体的透射谱的柱对称性. 在垂直毛细管轴向的平面内，谱带结构不随光的入射角度变化，测得光谱在径向转360°保持不变. 在含毛细管轴的平面内，在与毛细管轴向夹角越小的方向，谱带越紫移；在垂直毛细管轴方向有最红的带隙. 测量得的光谱结果表明这种毛细管内的胶体晶体结构是柱对称的, 胶体晶体中密排面平行于毛细管的管壁. 另外，此柱对称的胶体晶体比低浓度制作的体心胶体晶体稳定. 这种轴向对称性的光子带隙特性将带来许多潜在的应用. 关键词： 光子晶体 胶体晶体 光子带隙 透射光谱 毛细管     

Optical properties and electronic structure of fluorite and corundum

The complete sets of 12 fundamental optical functions for fluorite crystals in the range 5–39 eV and corundum crystals in the range 2–30 eV are determined from the experimental and theoretical spectra known for certain of these functions. The main features and generalities of these functions are revealed. A theoretical analysis of the optical spectra obtained is performed using the known theoretical band diagrams and the spectra of ?₂.     

Applications of the finite difference mode solution method to photonic crystal structures

The finite difference waveguide mode solution method, which has been popularly employed in the study of waveguide modes on various optical and dielectric waveguides, is utilized to calculate the modal characteristics of photonic crystal fibers (PCFs) and planar photonic crystal waveguides and the band diagrams of two-dimensional photonic crystals. Vector guided modes on both PCFs based on the total internal reflection guiding mechanism ('holey fibers') and those resulting from photonic band gap effect are accurately computed, with their effective indexes and field distributions compared with other methods. Calculated dispersion of a single-core holey fiber and coupled-power behavior of a two-core holey fiber are found to agree with measured results. For applications to band diagram calculation and planar photonic crystal waveguide analysis, the finite difference scheme is modified simply by imposing suitable periodic boundary condition. Numerical results for air-column crystals and dielectric-rod crystals are both found to agree well with calculations using other methods.     

Simulations of the intermediate bandwidth fluctuations in nanostructured PV

The size dispersion and distributions of quantum dot nanoparticles (sizes from 2–5 nm) embedded in the active region of the intermediate band solar cells are important to reach the high efficiencies. An optimized size and regularity can increase the efficiency due largely to avoided non-radiative transitions which can originate from the fluctuations in the bandwidth of the intermediate layer. In this work, we propose all the energy band diagrams possible in the formation of such a cell. Five equivalent band diagrams of the cells with different size dispersions and regularity of quantum dots are considered and compared with the reported experimental profiles in the literature. Furthermore, the degree of the size fluctuation is considered by proposing a fluctuation degree for the band gap and sub-band gaps of the cell. These proposed profiles and the fluctuation theory are exploited to consider the experimental data reported in literature. The optimized size dispersion will increase the photocurrent of the cell. We believe that every quantum dot solar cell will fall into one of the proposed band diagrams. This approach gives foresight to the theoretical studies of such devices and expectation from the energy band structure and band widths since it considers the fluctuation of the band widths for the intermediate band separately.     

基于三角晶格光子晶体谐振腔的双通道解波分复用器

提出了一种基于三角晶格二维光子晶体解波分复用器。该器件主体由线缺陷波导、环形谐振腔及点缺陷微腔构成。使用平面波展开法研究了线缺陷波导的特性,给出了线缺陷波导的能带图,对局部器件微调后进行大量的性能仿真以及对整体器件进行性能仿真,选择合适的器件参数,并使用时域有限差分法研究了不同波长的光在解波分复用器中的传输特性,并给出了电场分布图。仿真结果表明,该种结构可以实现波长分别为1271nm和1291nm两种光波的解波分复用。采用6个额外的介质柱,提高了环形腔的透射率;并通过在入射波导的入射口处增加三对介质柱,提高了波导的出射效率,从而整体上提高了双通道解波分复用器的输出效率。     

平面波展开法计算二维磁振子晶体带结构

磁振子晶体是光子晶体或声子晶体在磁性材料领域内的替代品,是近来的一个研究热点. 本文提出了磁振子晶体领域内的一种平面波展开法,其较传统的平面波展开法能节约一半以上的计算时间. 采用此方法,数值计算了由Fe/EuO二种铁磁材料构成的二维磁振子晶体带结构. 数值计算结果表明,在一定的体积填充率下,有自旋波带隙的出现;影响磁振子晶体带隙结构形成的主要因素是有效场中的交换作用场,其他作用场的影响相对很小. 关键词： 磁振子晶体 带隙 平面波展开法     

Gap kinematic Frenkel biexciton

A general dispersion equation is derived determining the wave-vector dependence of the energy of a bound kinematic Frenkel biexciton, previously discovered by the author, in crystals of arbitrary symmetry. A solution of this equation shows that, in crystals of a certain symmetry, bound gap Frenkel biexcitons can exist, the isolated terms of which lie in the gap between the components of the Davydov multiplet of unbound two-exciton states. In crystals with two monomers in the unit cell, these terms lie in the gap between two low-frequency components of the Davydov multiplet and are not in resonance with the central component, in contrast to what was observed in previously investigated crystals of higher symmetry. Besides, the biexcitons discovered in this work have a finite, rather than zero, dispersion, although their bandwidth is extremely small. The bound biexcitons also have some other specific features followed from the dispersion relation.     

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.