Spatial solitons in photonic lattices with large-scale defects

We address the existence,stability and propagation dynamics of solitons supported by large-scale defects surrounded by the harmonic photonic lattices imprinted in the defocusing saturable nonlinear medium.Several families of soliton solutions,including flat-topped,dipole-like,and multipole-like solitons,can be supported by the defected lattices with different heights of defects.The width of existence domain of solitons is determined solely by the saturable parameter.The existence domains of various types of solitons can be shifted by the variations of defect size,lattice depth and soliton order.Solitons in the model are stable in a wide parameter window,provided that the propagation constant exceeds a critical value,which is in sharp contrast to the case where the soliton trains is supported by periodic lattices imprinted in defocusing saturable nonlinear medium.We also find stable solitons in the semi-infinite gap which rarely occur in the defocusing media.     

二维非晶光子材料的缺陷态

应用多重散射方法计算了二维介质柱构成的非晶光子材料的缺陷态。在非晶光子材料中抽掉不同位置的圆柱会产生频率不同的缺陷模，但缺陷模的能量都是非常局域的，能量基本上集中在以缺陷波长1／3为半径的圆内。这表明非晶光子材料中形成的缺陷模不仅具有周期性光子晶体的缺陷模的强局域化特征，同时缺陷模更富于变化。     

弹性波通过一维复合材料系统的透射性质

提出了不同结构的一维弹性波复合材料系统模型,包括一维周期结构声子晶体、标准Fibonacci准周期结构声子晶体、广义Fibonacci准周期结构声子晶体以及完全无序结构的复合材料系统. 采用模式匹配理论法,数值计算了弹性波通过一维复合材料系统的透射系数. 计算结果表明,利用特殊的准周期结构声子晶体可获得比周期结构声子晶体更宽的带隙范围,准周期结构排列的复合材料系统相当于在周期结构中引入了缺陷体一样,带隙内出现了丰富的局域模式. 对弹性波/声波在复合材料系统中局域态性质的研究有助于弹性波/声波滤波器、导波器 关键词： 弹性波复合材料 局域化     

基于频域变换的MEMS声学薄膜缺陷检测算法

The micro-electro-mechanical system (MEMS) acoustic film has extremely high requirements for tape-out, storage and packaging environments, and its surface defects will affect the quality and performance of MEMS devices. The image defects detection is an effective non-contact optical detection means that can effectively improve the yield rate of MEMS production. However, the periodic structure texture of the MEMS devices surface will interfere with defect detection. A acoustic film defect detection algorithm based on frequency domain transformation was proposed. By calculating the gradient distribution of spectrogram and establishing the Boolean mask, the dominant frequency components corresponding to the periodic structure texture were eliminated. The residual spectrograms were subjected to a Fourier inversion to reconstruct the defect images. The reconstructed images were decomposed by single-layer Haar wavelet to obtain the low-frequency sub-band image and the defect information was extracted by simple threshold segmentation. The defect detection effects of different types of MEMS acoustic film were showed. The experimental results show that it is reasonable to set the zoom constant in the range of 0.7~1.0.     

Spatial and frequency domain effects of defects in 1D photonic crystal

The aim of this paper is to present the analysis of influence of defects in 1D photonic crystal (PC) on the density of states and simultaneously spontaneous emission, in both spatial and frequency domains. In our investigations we use an analytic model of 1D PC with defects. Our analysis reveals how presence of a defect causes a defect mode to appear. We show that a defect in 1D PC has local character, being negligible in regions of PC situated far from the defected elementary cell. We also analyze the effect of multiple defects, which lead to photonic band gap splitting.     

大小周期正方格子复合结构的光子带隙特性

把具有宽完全带隙的粗锐复合的周期常数为a的二维正方格子再与周期常数为a₂的大周期简单正方格子复合，发现大周期正方格子起缺陷作用.并发现当a₂<5a时,缺陷态明显地随入射角度变化.此变化随a₂的增大而减少.用FDTD方法计算了其透射和反射谱,结果表明缺陷峰透射率与a₂的大小成反比.另外还发现: 缺陷峰结构与大周期正方格子的圆柱直径的关系曲线与a₂关系不大.通过调节大周期正方格子的圆柱的直径，可获得单 关键词： 光子晶体 光子能隙 复式结构 缺陷态     

含有多缺陷的一维光子晶体的完全透射及应用

计算了具有多缺陷且相对中间缺陷具有镜像对称结构的一维光子晶体的透射谱。在光子晶体的禁带中得到了多个完全透射峰且对称性地分布于禁带中心频率两侧。缺陷相距较近时，禁带中心不存在透射峰。所有透射峰都敏感地依赖于中间缺陷的折射率。     

THREE-SPACE-HARMONIC INTERACTION IN DOUBLY SINUSOIDAL PERIODIC MEDIA

Three-space-harmonic (3SH) interaction in doubly sinusoidal periodic (DSP) medium is investigated. Associated physical effects such as additional gap, defect state, and indirect gaps, are theoretically and numerically revealed. This simple DSP model can facilitate the understanding and utilizing of a series of effects in rather complicated periodic structures with additional defect or modulation.     

Localization of electromagnetic and acoustic waves in random media. Lattice models

We consider lattice versions of Maxwell's equations and of the equation that governs the propagation of acoustic waves in a random medium. The vector nature of electromagnetic waves is fully taken into account. The medium is assumed to be a small perturbation of a periodic one. We prove rigorously that localized eigenstates arise in a vicinity of the edges of the gaps in the spectrum. A key ingredient is a new Wegner-type estimate for a class of lattice operators with off-diagonal disorder.     

多个单负材料缺陷一维光子晶体的孪生缺陷模

分析了含有多个单负材料缺陷层的一维光子晶体中缺陷模的性质。在两种单负(负介电常量或负磁导率)材料交替堆叠形成的一维光子晶体中,掺入了多个周期排列的单负材料缺陷层,得到在该光子晶体的零有效相位(zero-effective phase)带隙内存在孪生缺陷模。通过改变缺陷的数目或缺陷层的厚度,可调节缺陷模的频率间隔,但缺陷模的数目总保持为两个。计算结果显示,该孪生缺陷模的频率对入射角度的依赖较弱;随着入射角度的改变,缺陷模频率的相对改变量总保持在0.03以下。此外,对应缺陷模频率的电场在该光子晶体中传播时,将被强烈地局域在缺陷层与周期结构的交界面上。     

Stability and instability of nonlinear defect states in the coupled mode equations—Analytical and numerical study

Coupled backward and forward wave amplitudes of an electromagnetic field propagating in a periodic and nonlinear medium at Bragg resonance are governed by the nonlinear coupled mode equations (NLCME). This system of PDEs, similar in structure to the Dirac equations, has gap soliton solutions that travel at any speed between 0 and the speed of light. A recently considered strategy for spatial trapping or capture of gap optical soliton light pulses is based on the appropriate design of localized defects in the periodic structure. Localized defects in the periodic structure give rise to defect modes, which persist as nonlinear defect modes as the amplitude is increased. Soliton trapping is the transfer of incoming soliton energy to nonlinear defect modes. To serve as targets for such energy transfer, nonlinear defect modes must be stable. We therefore investigate the stability of nonlinear defect modes. Resonance among discrete localized modes and radiation modes plays a role in the mechanism for stability and instability, in a manner analogous to the nonlinear Schrödinger/Gross-Pitaevskii (NLS/GP) equation. However, the nature of instabilities and how energy is exchanged among modes is considerably more complicated than for NLS/GP due, in part, to a continuous spectrum of radiation modes which is unbounded above and below. In this paper we (a) establish the instability of branches of nonlinear defect states which, for vanishing amplitude, have a linearization with eigenvalues embedded within the continuous spectrum, (b) numerically compute, using Evans function, the linearized spectrum of nonlinear defect states of an interesting multiparameter family of defects, and (c) perform direct time-dependent numerical simulations in which we observe the exchange of energy among discrete and continuum modes.     

A General Framework for Localization of Classical Waves: II. Random Media

We study localization of classical waves in random media in the general framework introduced in Part I of this work. This framework allows for two random coefficients, encompasses acoustic waves with random position dependent compressibility and mass density, elastic waves with random position dependent Lamé moduli and mass density, electromagnetic waves with random position dependent magnetic permeability and dielectric constant, and allows for anisotropy. We show exponential localization (Anderson localization) and strong Hilbert–Schmidt dynamical localization for random perturbations of periodic media with a spectral gap. This revised version was published online in July 2006 with corrections to the Cover Date.     

数值研究含有负折射率材料的一维光子晶体的带隙特性

由修正后的传输矩阵理论研究了由单负材料构成的一维光子晶体的带隙特性。发现了此结构的光子晶体中同时存在着全方位带隙和布拉格带隙,且发现A、B层厚度等比例变化时全方位带隙非常稳定;当引入缺陷时,全方位带隙里的缺陷态将随入射角度、A层和B层同比例缩放的变化相对稳定,而布拉格带隙里的缺陷态在频谱域内变化很大。     

Band gaps and defect modes in periodically structured waveguides

This work examines a simple one-dimensional acoustic band gap system made from a diameter-modulated waveguide. Experimental and theoretical results are presented on perfectly periodic waveguide arrays showing the presence of band gaps--frequency intervals in which the transmission of sound is forbidden. The introduction of defects in the perfect periodicity leads to narrow frequency transmission bands--defect states--within the forbidden band gaps. The circular cross-section waveguide system is straightforward to simulate theoretically and experimental results demonstrate good agreement with theory. The experimental transmission of the periodic waveguide arrays is measured using an impulse response technique.     

三组元声子晶体中的缺陷态

运用基于平面波的超元胞方法，研究作为缺陷引入的第三组元材料(四氯化碳、水)对二维二组元声子晶体(水/水银，四氯化碳/水银)带结构的影响.结果表明，二组元声子晶体在引入第三组元点缺陷/线缺陷后，在原来的带结构中会出现缺陷态/带，原带隙的位置、宽度变化不大；缺陷态/带频率主要受第三组元材料物性参数的影响；这些缺陷态都是局域化的.因此，在具有宽带隙的二组元体系中引入适当的第三组元点缺陷/线缺陷，让缺陷态/带频率落在二组元体系的带隙中，就可以形成特殊的滤声态/波导态.声子晶体的这一特性对于声波/弹性波的传播和新的声学应用具有重要意义. 关键词： 声子晶体 三组元 点缺陷 线缺陷     

Excitation of defect modes from the extended photonicband-gap structures of 1D photonic lattices

This paper stuides numerically the model equation in a one dimensional defective photonic lattice by modifying the potential function to a periodic function. It is found that defect modes (DMs) can be regarded as Bloch modes which are excited from the extended photonic band-gap structure at Bloch wave-numbers with k x = 0. The DMs for both positive and negative defects are considered in this method.     

Optoacoustic diagnostics of absorbing media

We have calculated the intensities of ultrasonic waves excited by counter-propagating light waves of different frequencies and scattered by spherical defects in absorbing isotropic media. We have analyzed the intensity of the scattered sound as a function of the scattering angle and the position of the defect relative to the entry face of the acoustic waveguide. We have shown that for hollow spherical defects, the intensity of the scattered sound tends toward zero for scattering angles close to 90o, and for significantly smaller angles for dense inclusions. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 73, No. 5, pp. 686–689, September–October, 2006.     

A General Framework for Localization of Classical Waves: I. Inhomogeneous Media and Defect Eigenmodes

We introduce a general framework for studying the localization of classical waves in inhomogeneous media, which encompasses acoustic waves with position dependent compressibility and mass density, elastic waves with position dependent Lamé moduli and mass density, and electromagnetic waves with position dependent magnetic permeability and dielectric constant. We also allow for anisotropy. We develop mathematical methods to study wave localization in inhomogeneous media. We show localization for local perturbations (defects) of media with a spectral gap, and study midgap eigenmodes.     

Observations of defect propagation in [100]-oriented opal-type photonic crystals

Charged colloidal suspensions have been used as experimental models for the study of crystal nucleation. Here we propose that the technique of template-assisted colloidal self-assembly can be used to visualize the effects of defect propagation in atomic crystal films produced using epitaxial growth. Templates with periodic line defects were used to grow [100]-oriented three-dimensional photonic crystals by means of the template-assisted colloidal self-assembly method, aided by capillary and gravitational forces. The defect propagation in the [100]-oriented photonic crystal was observed using scanning electron microscopy, both at the surface of the crystal and on cleaved facets. This method is useful in the understanding of defect propagation in the growth of colloidal films on templates - and the same approach may also prove useful for the understanding of atomic crystal growth on substrates with defects. Additionally, the deliberate incorporation of line defects may prove valuable as a way of introducing waveguide channels into three-dimensional photonic crystals.     

相位失配弹性平板复合波导中的缺陷态*

为了在弹性波波导中实现缺陷态的调控,该文基于相位失配原理设计了一种周期性平板波导结构。以正弦边界弹性波导为例,通过连接具有不同相位的两段波导结构,形成了弹性板中不同程度的缺陷,并分析了其谱带特性和能量局域化特征。结果表明,禁带中存在两个不同模式的缺陷态,其以透射峰形式出现并随着相位的改变产生频移。与此同时,两个缺陷态在空间上对应的应力场和位移场分布也具有不同的模态特征。该文提出的复合弹性波导缺陷态调控方法,不仅为研究弹性波与结构之间的内在联系提供了关键的理论支持,也为实际弹性波探测器件的设计提供重要参考。