Elastic wave localization in two-dimensional phononic crystals with one-dimensional random disorder and aperiodicity

The band structures of in-plane elastic waves propagating in two-dimensional phononic crystals with one-dimensional random disorder and aperiodicity are analyzed in this paper. The localization of wave propagation is discussed by introducing the concept of the localization factor, which is calculated by the plane-wave-based transfer-matrix method. By treating the random disorder and aperiodicity as the deviation from the periodicity in a special way, three kinds of aperiodic phononic crystals that have normally distributed random disorder, Thue-Morse and Rudin-Shapiro sequence in one direction and translational symmetry in the other direction are considered and the band structures are characterized using localization factors. Besides, as a special case, we analyze the band gap properties of a periodic planar layered composite containing a periodic array of square inclusions. The transmission coefficients based on eigen-mode matching theory are also calculated and the results show the same behaviors as the localization factor does. In the case of random disorders, the localization degree of the normally distributed random disorder is larger than that of the uniformly distributed random disorder although the eigenstates are both localized no matter what types of random disorders, whereas, for the case of Thue-Morse and Rudin-Shapiro structures, the band structures of Thue-Morse sequence exhibit similarities with the quasi-periodic (Fibonacci) sequence not present in the results of the Rudin-Shapiro sequence.     

光脉冲通过含有色散与增益型缺陷的一维光子晶体的传播

研究了光脉冲通过含有色散和增益型缺陷的一维光子晶体的传播行为.缺陷的色散与增益性质用Lorentz振子模型描述.随着振子强度的变化，脉冲峰的传播呈现极慢光速和超光速的传播行为，但能量速度小于真空中的光速c.脉冲峰的超前与落后是各Fourier分量在介质中获得了不同的相移和幅度改变后重新相干叠加的结果. 关键词： 光子晶体 缺陷 光脉冲传播 能量速度     

Propagation of circularly polarized waves in one-dimensional bragg structures (magnetophotonic crystals)

A theory of electromagnetic wave propagation in structures formed by alternating magnetic and dielectric layers is proposed. Models of macroscopically thick and atomically thin layers magnetized perpendicular to their plane are considered. Transfer matrices of circularly polarized waves and characteristics of light propagation in periodic magnetic structures under normal incidence are obtained by the self-consistent electrodynamic Green’s function method in analytic form. The results obtained are employed to analyze linear-in-magnetization magneto-optical effects in the transmittance and reflectance spectra of one-dimensional magnetic Bragg structures called magnetophotonic crystals. For structures of finite thickness, Faraday rotation and other observable magneto-optical quantities are shown to vary appreciably in the spectral region of the stop bands of a magnetophotonic crystal. This is paralleled by a substantial enhancement of the magnetic-fieldinduced modulation of the reflectance of light polarized in the analyzer plane.     

Eigenwaves in one-dimensional photonic crystals with gain

The dispersion characteristics of a one-dimensional photonic crystal are analyzed in detail on the basis of the exactly solvable Kronig-Penney model for the particular case of a periodic system consisting of an infinite number of insulator-air layers arranged in the direction of propagation of radiation. An analytical solution is obtained, and the behavior of eigenwaves near the edges of the photonic band is thoroughly studied. The behavior of roots on a complex plane is qualitatively analyzed with the use of approximate dispersion characteristics obtained via expanding the solution of the wave equation in series in terms of the harmonics of the lattice spacing. It is shown that, despite the amplifying properties of the material, no gain in the photonic band gap is present, because of the interference quenching of waves.     

Delocalization in one-dimensional tight-binding models with fractal disorder

In the present work, we investigated the correlation-induced localization-delocalization transition in the one-dimensional tight-binding model with fractal disorder. We obtained a phase transition diagram from localized to extended states based on the normalized localization length by controlling the correlation and the disorder strength of the potential. In addition, the transition of the diffusive property of wavepacket dynamics is shown around the critical point.     

具有二阶和三阶非线性一维光子晶体中的耦合模孤子

研究同时具有二阶和三阶非线性的一维光子晶体中的耦合孤子动力学.从Maxwell方程出发,利用多重尺度法,导出了光学整流场与两个基频电场包络的非线性耦合模方程组,给出了耦合模方程组的孤子解.结果表明,由于二阶非线性导致的光学整流场对基频电场有调制作用,使得两个基频电场分量可以呈现为亮孤子亮孤子、暗孤子暗孤子及亮孤子-暗孤子对 当两个基频电场的振动频率趋于光子晶体频带的带边频率时,光学整流场消失     

具有二阶和三阶非线性一维光子晶体中的耦合模孤子

研究同时具有二阶和三阶非线性的一维光子晶体中的耦合孤子动力学. 从Maxwell方程出发,利用多重尺度法,导出了光学整流场与两个基频电场包络的非线性耦合模方程组,给出了耦合模方程组的孤子解. 结果表明,由于二阶非线性导致的光学整流场对基频电场有调制作用,使得两个基频电场分量可以呈现为亮孤子-亮孤子、暗孤子-暗孤子及亮孤子-暗孤子对;当两个基频电场的振动频率趋于光子晶体频带的带边频率时,光学整流场消失.     

Order-disorder transition in one-dimensional system with disorder in composition

The influence of structural inhomogeneity onto order-disorder transitions in 1D systems is considered in the scope of the Potts-like model with many-particle interactions. The helix-coil transition in DNAs, heterogeneous by hydrogen bonding energy, is considered as an example. The microcanonical method is employed to evaluate the free energy. The secular equation for the heteropolymer is constructed. Both the melting temperature and interval of DNA melting are obtained. In the limit of small difference between inverse melting temperatures of poly(A-T) and poly(G-C), the coincidence with classical results is obtained.     

一维分子晶体中的极化子

本文从量子化的Holstein模型出发,运用相干态展开法和能量极小原理,通过实施连续近似得到了一维分子晶体模型处于基态的极化子满足的非线性薛定谔方程及其定态孤子解、基态能量、晶格位移,其结果与Holstein T[1].从半经典理论所得的结果完全一致,因此相干态展开方法在处理与极化子有关的其他物理问题中是一种非常有效的方法.     

Wave localization in two-dimensional porous phononic crystals with one-dimensional aperiodicity

The localization properties of in-plane elastic waves propagating in two-dimensional porous phononic crystals with one-dimensional aperiodicity are initially analyzed by introducing the concept of the localization factor that is calculated by the plane-wave-based transfer-matrix method in this paper. The band structures characterized by using localization factors are calculated for different phononic crystals by altering matrix material properties and geometric structure parameters. Numerical results show that the effect of matrix material properties on wave localization can be ignored, while the effect of geometric structure parameters is obvious. For comparison, the periodic porous system and Fibonacci system with rigid inclusion are also analyzed. It is found that the band gaps are easily formed in aperiodic porous system, but hard for periodic porous system. Moreover, compared with aperiodic system with rigid inclusion, the wider low-frequency band gaps appear in the aperiodic porous system.     

一维长程关联无序系统的局域性

研究了在紧束缚近似下,由de Moura和Lyra提出的一维长程关联无序模型的局域性. 分布在［-W/2,W/2］区间的格点位能,其关联函数〈ε_iεj〉的傅里叶变换满足S(k)∝k^-α,其中关联强度α>0. 利用participation ratio不仅证实了在α>2和W<4 关键词： 安德森局域化 长程关联 扩展态     

Photonic gap vanishing in one-dimensional photonic crystals with single-negative metamaterials

The properties of photonic band gap in one-dimensional photonic crystals composed of single-negative metamaterials are studied theoretically. Our study shows that the photonic gap will vanish at a certain incident angle when both the phase-match and impedance-match conditions are satisfied simultaneously, suggesting that the bandwidth and location of the photonic gap are strongly dependent on the incident angle and polarization. However, the photonic gap will not vanish and may become insensitive to the incident angle when the two match conditions cannot be met. Our study also shows that losses in metamaterials have little effect on the properties of the photonic gap.     

飞秒脉冲激光1维强度调制的传输特性

实验研究了飞秒激光干涉条纹在CS2介质中传输的增长率与条纹间隔以及增长率与中心峰值强度的关系。结果发现,在非线性介质中传输的１维干涉调制特别是当其调制频率位于中心光强对应的最快增长频率附近时,随着传输距离的增加调制场迅速获得增长,将高斯光束分裂成多根峰值强度很高的带状细丝。相应的数值模拟与实验结果具有较好的一致性。     

飞秒脉冲激光1维强度调制的传输特性

实验研究了飞秒激光干涉条纹在CS2介质中传输的增长率与条纹间隔以及增长率与中心峰值强度的关系。结果发现,在非线性介质中传输的1维干涉调制特别是当其调制频率位于中心光强对应的最快增长频率附近时,随着传输距离的增加调制场迅速获得增长,将高斯光束分裂成多根峰值强度很高的带状细丝。相应的数值模拟与实验结果具有较好的一致性。     

Vectorial coupled—mode solitons in one—dimensional photonic crystals

We study the dynamics of vectorial coupled-mode solitons in one-dimensional photonic crystals with quadratic and cubic nonlinearities. Starting from Maxwell's equations, the vectorial coupled-mode equations for the envelopes of two fundamental-frequency optical mode and one low-frequency mode components due to optical rectification are derived by means of the method of multiple scales. A set of coupled soliton solutions of the vectorial coupled-mode equations is provided. The results show that a modulation of the fundamental-frequency optical modes occurs due to the optical rectification field resulting from the quadratic nonlinearity. The optical rectification field disappears when the frequency of the fundamental-frequency optical fields approaches the edge of the photonic bands.     

Floquet-bloch waves in bound one-dimensional photonic crystals

Floquet-Bloch waves in a bound one-dimensional photonic crystal are considered. It is shown that a single Floquet-Bloch wave can be excited in a one-dimensional photonic crystal located between two homogeneous media. An exact solution of the wave equation corresponding to this case is represented in the form of a set of heterogeneous waves. For the case of incidence of the plane wave from a homogeneous medium on a bounded one-dimensional photonic crystal, the functions for the reflection and transmission coefficients are obtained based on the exact solution of the wave equation. It is shown that the transmission function for the one-dimensional photonic crystal has a form similar to that for the traditional Fabri-Perot interferometer and is determined by the interference of the Floquet-Bloch waves excited in the crystal. The evolution of the amplitude profile of the decaying Floquet-Bloch waves and the reflection spectrum of the bounded one-dimensional photonic crystal are considered in the first-order forbidden band.     

Anomalous dispersion in one-dimensional plasma photonic crystals

The anomalous dispersion in one-dimensional plasma photonic crystals (1-DPPCs) is studied. The width of band pass and band gap are compressed, the phase velocity decreases and the cup-off frequency comes close to the frequency of plasma when EM wave oblique incidence on 1-DPPCs. The band gaps are affected by the thickness of plasma, the dielectric constant of the dielectric material, the plasma density and the angle of incidence. Superluminal negative group velocity is discovered in this study. This character is interesting for scientists and may have a potential application.     

Mobility in a one-dimensional disorder potential

In this article the one-dimensional, overdamped motion of a classical particle is considered, which is coupled to a thermal bath and is drifting in a quenched disorder potential. The mobility of the particle is examined as a function of temperature and driving force acting on the particle. A framework is presented, which reveals the dependence of mobility on spatial correlations of the disorder potential. Mobility is then calculated explicitly for new models of disorder, in particular with spatial correlations. It exhibits interesting dynamical phenomena. Most markedly, the temperature dependence of mobility may deviate qualitatively from Arrhenius formula and a localization transition from zero to finite mobility may occur at finite temperature. Examples show a suppression of this transition by disorder correlations.Dedicated to Professor H. Wagner on the occasion of his 60th birthday     

Negative refraction in one-dimensional plasma photonic crystals

We have theoretically explored the negative refraction (NR) in one-dimensional plasma photonic crystals (PCs) consisting of plasma and dielectric materials. By using the transfer matrix method and Bloch theorem, we have studied the group velocity and we have obtained the NR in plasma PCs with the help of the group velocity. The results show that plasma PCs can also exhibit the NR although they have a periodically modulated positive permittivity ? and permeability μ. It is also shown that the NR in plasma PCs exhibits difference behaviour in different frequency regions, ω < ω_p and ω > ω_p, respectively. The parameter dependence of the effects is also examined and discussed.