非晶光子晶体中的光子局域化

利用多重散射方法计算并研究了二维光子晶体随着无序度变化的光子局域化.通过控制方形单元随机旋转角度以控制光子晶体的无序度.研究发现，随着无序度的增加光子通带的透过率逐渐降低，而光子禁带中的透过率逐渐上升，即无序导致的局域化逐渐由光子带边向光子禁带中心和光子通带的中心扩展.而且光子通带中的平均透过率随无序度的增加呈e指数下降. 关键词： 非晶 光子晶体 无序 光子局域     

单轴应力对一维镜像光子晶体光子局域态透射峰的影响

利用传输矩阵法研究了镜像异质三周期一维光子晶体中的光子局域态随单轴应力发生变化的特性. 对于镜像异质三周期光子晶体, 由于其镜像结构, 破坏了光子晶体的有序性, 产生了一个缺陷态, 使其在较宽的光子禁带中心有一个光子局域态透射峰. 研究表明: 当对镜像异质三周期光子晶体施加单轴应力时, 其中的光子局域态透射峰会随着应力的改变而发生剧烈的变化. 当外部微弱的机械应力施加到光子晶体上时, 对光子晶体形成一个拉伸应变, 拉伸应变引起光子晶体结构的变化, 进而大幅度影响光子局域态透射峰的透射率.结果表明: 透射峰的透射率明显受单轴应力的影响. 这些特性可为用此结构的光子晶体设计超高灵敏度压力传感器提供理论参考. 关键词： 光子晶体 单轴应力 光子局域态 传输矩阵     

Ray Modes in Random Gap Systems

A disordered photonic crystal with spectral degeneracies in the form of Dirac nodes is considered. Disorder can create a random gap at the Dirac nodes, which leads to the formation of random edge modes. We study the distribution of these edge modes and find from symmetry considerations that the discrete anisotropy of the photonic crystal is spontaneously broken for the propagation of photons from a local photon source. This effect can be understood as the spontaneous creation of a ray mode or as the creation of a one‐dimensional waveguide in a two‐dimensional photonic crystal through strong random scattering. The phenomenon must be distinguished from Anderson localization of photons in a single band crystal and can be considered as angular localization, since it creates geometric states rather than confining the photons to an area of the size of the localization length. The propagation of the photon intensity is described by a Fokker‐Planck equation, whose drift term is determined by the spectrum of the photonic crystal near the Dirac node.     

Slight disorder effects in two dimensional photonic crystal structures

In the actual manufacturing process of photonic crystal structure, unavoidable error can generate slight disorder which may influence the performance of photonic crystal based device. In this work, randomly distributional disorders are applied to the air holes in the photonic crystal structure. Based on this, we investigate the influence of the slight disorder on the photonic crystal band structure and the performance of photonic crystal based devices (waveguide and slab cavity). The studies indicate that the slight disorder provides small influence on the band structure of the photonic crystal. But, the random disorder in photonic crystal waveguide may increase transmission loss obviously when the wavelength of the light and the distribution of disorder break the balance of multiple interferences. Also, the slight disorder can reduce the Q factor of the photonic crystal cavity at a certain degree. The studies may provide some useful guides for further photonic crystal device research.     

The ballistic dimer resonance in the one-dimensional disordered photonic crystals

The propagation of electromagnetic waves in one-dimensional disordered dielectric layer stack is studied theoretically using the transfer matrix formalism. The presence of the dimer unit cells inside a host photonic crystal, as the intentionally short range disorder correlation, provides predicted dimer resonances, leading to the break down of the Anderson localization. However while suitably adjusting the intrinsic defect unit cell parameters (i.e. the defect dielectric constants), the light can be transmitted on larger localization length through a ballistic canal, opening up possibilities for performing better tailored ballistic optical filters. Moreover, by increasing the rate of disorder (i.e. the defects concentration and/or the length of the system) the quality of the transmission around the ballistic resonance can be improved with the smoother corresponding allowed mini bands.     

Disorder-induced localization of light near edges of nonlinear photonic lattices

We investigated the influence of edges and corners on the Anderson localization of light in disordered two-dimensional photonic lattices that are optically induced in nonlinear saturable photorefractive media. A systematic quantitative study of gradual transition from corner to bulk Anderson localization in truncated two-dimensional photonic lattices was carried out. We analyzed numerically the localization at several corners and edges of the square and triangular photonic lattices and compared them with the localization in bulk medium. We found that, for strong disorder, corners and edges effectively suppress Anderson localization, as compared to the bulk, but to a varying degree.     

Extrinsic optical scattering loss in photonic crystal waveguides: role of fabrication disorder and photon group velocity

Formulas are presented that provide clear physical insight into the phenomenon of extrinsic optical scattering loss in photonic crystal waveguides due to random fabrication imperfections such as surface roughness and disorder. Using a photon Green-function-tensor formalism, we derive explicit expressions for the backscattered and total transmission losses. Detailed calculations for planar photonic crystals yield extrinsic loss values in overall agreement with experimental measurements, including the full dispersion characteristics. We also report that loss in photonic crystal waveguides scales inversely with group velocity, at least, thereby raising serious questions about future low-loss applications based on operating frequencies that approach the photonic band edge.     

Numerical test of the theory of pseudo-diffusive transmission at the Dirac point of a photonic band structure

It has recently been predicted that a conical singularity (=Dirac point) in the band structure of a photonic crystal produces an unusual 1/L scaling of the photon flux transmitted through a slab of thickness L. This inverse-linear scaling is unusual, because it is characteristic of radiative transport via diffusion modes through a disordered medium - while here it appears for propagation of Bloch modes in an ideal crystal without any disorder. We present a quantitative numerical test of the predicted scaling, by calculating the scattering of transverse-electric (TE) modes by a two-dimensional triangular lattice of dielectric rods in air. We verify the 1/L scaling and show that the slope differs by less than 10% from the value predicted for maximal coupling of the Bloch modes in the photonic crystal to the plane waves in free space.     

介质层厚度无序对Bragg微腔模式的影响

采用本征模展开法(EME)结合完全匹配层（PML）边界条件,研究了由TiO2和SiO2复合膜结构组成的平面光子晶体Bragg微腔的模式特性,分析了介质厚度无序对微腔模式的调制以及入射角对局域长度的影响.结果表明,若光束正入射,带边局域长度要大于禁带局域长度,随着无序度的增加光子通带的透过率逐渐降低,而禁带的透过率逐渐上升.当无序度较小时,局域长度随随机度的变化在带边和禁带内表现出相反的规律.当无序度较大时,局域长度不仅和随机度、带隙有关,还受到材料的影响;若光束斜入射,TE模的局域长度要远小于TM模对应的值,且其最小值向短波方向移动。此外,入射角和膜层数的变化都会导致局域长度的起伏.     

时变磁化等离子体光子晶体光子局域态分析

采用磁化等离子体的分段线形电流密度卷积(Piecewise Linear Current Density Recursive Convolution,PLCDRC)时域有限差分(Finite-Different Time-Domain,FDTD)算法研究了具有单一缺陷层一维时变磁化等离子体光子晶体的光子局域态特性。以高斯脉冲为激励源,用算法公式所得的电磁波透射系数来讨论了等离子体上升时间对其缺陷模的影响。结果表明,改变等离子体上升时间和密度可以获得不同的缺陷模。     

Dielectric matrices with air cavities as a waveguide photonic crystal

Frequency dependences of the transmission coefficient of a microwave photonic crystal that represents a structure containing alternating layers of ceramic material (Al₂O₃) with a relatively large number of cavities and foam plastic are studied in the presence and absence of distortions of the periodicity of a photonic structure. The frequency dependences of the transmission coefficient can be analyzed using a model of effective medium that makes it possible to consider the interaction of electromagnetic wave and photonic crystal using a transfer matrix of a 1D photonic crystal. The band character of the frequency dependence of the transmission coefficient of the photonic crystal related to the periodicity of the photonic crystal in the transverse plane for the waveguide with a standard cross section is not manifested in a certain range of material permittivities.     

Propagation in one-dimensional crystals with positional and compositional disorder

Propagation in perturbed one-dimensional phononic or photonic crystals, with bothcompositional and positional disorder, is considered. The coherent potential approximationis used to obtain the band structure and the Floquet normal form of theperiodic-on-average perturbed crystal, which is modified differently with respect to thetwo kinds of disorder. For finite size crystals, the transmission amplitude is calculatedand compared to direct numerical simulations and to an estimate based on localizationlength. The transmission spectrum is found to be better described using the fullexpression of the Floquet modes of the disordered, but periodic on average, medium.     

Expectation-based approach for one-dimensional randomly disordered phononic crystals

An expectation-based approach to the statistical theorem is proposed for the one-dimensional randomly disordered phononic crystal. In the proposed approach, the expectations of the random eigenstates of randomly disordered phononic crystals are investigated. In terms of the expectations of the random eigenstates, the wave propagation and localization phenomenon in the random phononic crystal could be understood in a statistical perspective. Using the proposed approach, it is proved that for a randomly disordered phononic crystal, the Bloch theorem holds in the perspective of expectation. A one-dimensional randomly disordered binary phononic crystal consisting of two materials with the random geometry size or random physical parameter is addressed by using the proposed approach. From the result, it can be observed that with the increase of the disorder degree, the localization of the expectations of the eigenstates is strengthened. The effect of the random disorder on the eigenstates at higher frequencies is more significant than that at lower frequencies. Furthermore, after introducing the random disorder into phononic crystals, some random divergent eigenstates are changed to localized eigenstates in expectation sense.     

Photonic Scattering on a Trimer with <Emphasis Type="Italic">PT</Emphasis>-Symmetry

We analyze photonic scattering on a trimer with PT symmetry, where the photon propagates in an array of cavities. In the system, a passive and an active cavity couple to another cavity without loss and gain simultaneously, which is in the middle of the cavity array. Such three cavities can be regarded as the scattering target coupling to the unlimited number of cavities from two directions respectively. Our approach is to use the Schrödinger equation to calculate the reflection coefficient and transmission coefficient, and then let photonic transmission spreads from gain or loss cavity. It shows that the scattering of the photon is closely associated with the PT symmetric characteristic of the dynamics of the system. The atom’s modulation on the photonic transmission is also investigated. We found that the scattering center can behave as a photonic switch, which could be used potentially to control the photonic transmission.     

一维无序结构光子晶体的能带特性研究

通过引入结构参数a，深入研究了具有无序结构的一维二元光子晶体的能带特性。研究发现，无序结构有效拓宽了光子带隙，与均匀结构相比，拓宽率达到200％以上；无序一维光子晶体表现出从可见到红外很宽区域的高反射特性。本文还计算和分析了入射角和无序度D对光子晶体带隙的影响。     

Eigenstate statistics and optical properties of one-dimensional disordered photonic crystals

Optical eigenstates in one-dimensional disordered photonic crystals were studied. The threshold disorder level was established below which the probability of appearance of an eigenstate at the photonic bandgap center is negligible. The threshold is reached when the relative fluctuation in the optical lengths of the structure periods becomes equal to the square root of one-third of the relative bandgap width. The dependence of the ensemble-averaged structure transmission coefficient on the fluctuation of the period optical length has a break corresponding to the threshold fluctuation.     

Luminescence spectra of a cholesteric photonic crystal

The transmission and luminescence spectra of a cholesteric photonic crystal doped with an organic dye are measured. The density of photon states is calculated using the material parameters obtained from the comparison of the experimental and theoretical spectra. The shape of the luminescence spectra is modified with respect to the density of photon states owing to the difference in the structure of the normal modes of the photonic crystal near the short-wavelength and long-wavelength edges of the photonic quasi-band gap upon the “pushing” of the photon states from the gap and to the nonvanishing orientation ordering of the luminescent molecules. The luminescence spectrum calculated taking into account the chiral structure of the photonic crystal agrees with the experimental spectrum.     

Model study on disordered one-dimensional microstructures

Using a finite Kronig-Penney model the localization behavior is studied as a function of disorder and sample size for individual realizations as well as for ensembles. There is a number of effects typical for small disordered systems: e.g. level repulsion is found to be connected with resonant delocalization, and there is a pronounced N-odd/N-even effect in the transmission coefficient. Opposite to the thermodynamic limit the ensemble shows weakest fluctuation in the average transmission coefficient rather than in the average localization length. The 3-dimensional extension of the model which still behaves one-dimensional, demonstrates the importance of spatial correlations in addition to disorder strength.     

Loss analysis of air-core photonic crystal fibers

By using a multipole moment approach, we analyze the loss of an air-core photonic crystal fiber and demonstrate that it is possible reduce the transmission loss that is due to photon radiation leakage through the photonic crystal cladding to a level below 0.01 dB/km, with eight rings of air holes. An analogy is drawn between air-core photonic crystal fiber modes and Bragg fiber modes. The influence of material absorption in the silica glass is discussed.     

Structure of light scattering spectra in opal photonic crystals

Spectra of light losses are studied at a fixed angle of incidence of a collimated beam on the surface of an opal anisotropic photon crystal at various observation angles. It is shown that the structure of the forward-and backscattered light spectra is connected with the existence of several directional photonic forbidden bands. It is demonstrated that back scattering is enhanced and forward scattering is suppressed in the frequency region of photonic forbidden bands. It is suggested that a scattering band associated with photon localization at the photonic gap edge is observed.