Liapunov spectra for infinite chains of nonlinear oscillators

We argue that the spectrum of Liapunov exponents for long chains of nonlinear oscillators, at large energy per mode, may be well approximated by the Liapunov exponents of products of independent random matrices. If, in addition, statistical mechanics applies to the system, the elements of these random matrices have a distribution which may be calculated from the potential and the energy alone. Under a certain isotropy hypothesis (which is not always satisfied), we argue that the Liapunov exponents of these random matrix products can be obtained from the density of states of a typical random matrix. This construction uses an integral equation first derived by Newman. We then derive and discuss a method to compute the spectrum of a typical random matrix. Putting the pieces together, we see that the Liapunov spectrum can be computed from the potential between the oscillators.     

Taming Random Lasers through Active Spatial Control of the Pump

Active control of the spatial pump profile is proposed to exercise control over random laser emission. We demonstrate numerically the selection of any desired lasing mode from the emission spectrum. An iterative optimization method is employed, first in the regime of strong scattering where modes are spatially localized and can be easily selected using local pumping. Remarkably, this method works efficiently even in the weakly scattering regime, where strong spatial overlap of the modes precludes spatial selectivity. A complex optimized pump profile is found, which selects the desired lasing mode at the expense of others, thus demonstrating the potential of pump shaping for robust and controllable single mode operation of a random laser.     

A modal separation measurement technique for broadband noise propagating inside circular ducts

A measurement technique which separates broadband noise propagating inside circular ducts into the acoustic duct modes is developed. The technique is also applicable to discrete frequency noise. The acoustic modes are produced by weighted combinations of the instantaneous outputs of microphones spaced around the duct circumference. The technique is compared with the cross spectral density approach presently available and found to have certain advantages, and disadvantages. Considerable simplification of both the new technique and the cross spectral density approach occurs when no correlation exists between different circumferential mode orders. The properties leading to uncorrelated modes and experimental tests which verify this condition are discussed. The modal measurement technique-is applied to the case of broadband noise generated by flow through a coaxial obstruction (nozzle or orifice) in a pipe. Different circumferential mode orders are shown to be uncorrelated for this type of noise source.     

光纤中的电磁对偶变换与导波的模式分析

讨论了麦克斯韦方程在各向同性均匀电介质中的电磁对偶变换不变性,定义了电磁混合比,求出了对偶场的充要条件.把上述不变性和充要条件应用于阶跃光纤,分析其导波模式,证明在非轴对称情况下,阶跃光纤中不存在具有色散的受导简正模.存在的解只有临界折射模(n=n₂时的特解).求出了它的分立频谱.受导简正模只存在于轴对称情况中.以上结论与实验事实不矛盾,并由此解释了基模的特性 关键词： 光纤光学 光波导 电磁对偶变换 受导波     

The Random Phase Property and the Lyapunov Spectrum for Disordered Multi-channel Systems

A random phase property establishing in the weak coupling limit a link between quasi-one-dimensional random Schrödinger operators and full random matrix theory is advocated. Briefly summarized it states that the random transfer matrices placed into a normal system of coordinates act on the isotropic frames and lead to a Markov process with a unique invariant measure which is of geometric nature. On the elliptic part of the transfer matrices, this measure is invariant under the unitaries in the hermitian symplectic group of the universality class under study. While the random phase property can up to now only be proved in special models or in a restricted sense, we provide strong numerical evidence that it holds in the Anderson model of localization. A main outcome of the random phase property is a perturbative calculation of the Lyapunov exponents which shows that the Lyapunov spectrum is equidistant and that the localization lengths for large systems in the unitary, orthogonal and symplectic ensemble differ by a factor 2 each. In an Anderson-Ando model on a tubular geometry with magnetic field and spin-orbit coupling, the normal system of coordinates is calculated and this is used to derive explicit energy dependent formulas for the Lyapunov spectrum.     

Estimation of efficiency of vertical antenna arrays in underwater sound channels

The gain of the vertical antenna array in a randomly inhomogeneous ocean waveguide is numerically simulated on the assumption that the useful signal is generated by a finite set of mutually uncorrelated discrete spectrum modes and is received against the ocean noise background. It is shown that the choice of themost effective weight distribution of the array and the thus obtained gain strongly depend on both the modal spectra of the signal and noise and the number and position of the receiving elements in the channel. The critical factor is the mutual orthogonality of the waveguide modes at the array input, which indicates the possibility of specially arranging the elements for the known (expected) mode spectrum of the signal.     

Mean field of a low-frequency sound wave propagating in a fluctuating ocean

Statistical characteristics of low-frequency sound waves propagating over long distances in a fluctuating ocean are important for many practical problems. In this paper, using the theory of multiple scattering, the mean field of a low-frequency sound wave was analytically calculated. In these calculations, the ratio of the sound wavelength and the scale of random inhomogeneities can be arbitrary. Furthermore, the correlation function of inhomogeneities is expressed in terms of a modal spectrum (e.g., internal waves modes). The obtained mean sound field is expressed as a sum of normal modes that attenuate exponentially. It is shown that the extinction coefficients of the modes are linearly related to the spectrum of random inhomogeneities in the ocean. Measurements of the extinction coefficients can therefore be used for retrieving this spectrum. The mean sound field is calculated for both 3D and 2D geometries of sound propagation. The results obtained can be used to study the range of applicability of the 2D propagation model.     

Density of Eigenvalues of Random Normal Matrices

The relation between random normal matrices and conformal mappings discovered by Wiegmann and Zabrodin is made rigorous by restricting normal matrices to have spectrum in a bounded set. It is shown that for a suitable class of potentials the asymptotic density of eigenvalues is uniform with support in the interior domain of a simple smooth curve.     

一维随机激光器中准态模的饱和特性研究

针对随机激光器的半经典理论是应用电磁场时域有限差分法数值求解半经典随机激光模型方程组，基于半经典理论数值研究了一维随机激光器中准态模式的饱和特性，获得了不同准态模的空间分布和频谱分布图。计算结果分析显示：准态模式的某些特征参数如局域程度将会影响系统的饱和特性。利用这一结果，可以通过单频抽运方法选择具有低阈值、高饱和强度的准态模式作为整个激光系统的稳态输出模式。     

Possibility of observation of polaron normal modes at the far-infrared spectrum of acetanilide and related organics

We use a stationary and normal mode analysis of the semiclassical Holstein model in order to connect the low-frequency linear polaron modes to low-lying far-infrared lines of the acetanilide spectrum and through parameter fitting we comment on the validity of the polaron results in this system.     

Shot-noise-induced random telegraph noise in shuttle current

Random telegraph noise in the electric current produced by shot noise is predicted for an array of movable colloid particles by Monte Carlo and molecular dynamics calculations. The electron transport is attributed to the shuttle mechanism where moving colloid particles carry charges. The colloid-particle motion induced by the source-drain voltage shows periodic and/or quasiperiodic vibrations, and the current value depends on the vibration modes. Shot noise that is uncorrelated with the colloid-particle motion causes transitions between the periodic and quasiperiodic vibration modes, resulting in random switching between the current levels corresponding to the vibration modes.     

Highly sensitive bend sensor with hybrid long-period and tilted fiber Bragg grating

We demonstrate a new type of fiber optic bend sensor with a hybrid structure made up of a long period grating (LPG) and a tilted fiber Bragg grating (TFBG). The sensing mechanism is based on the spectrum of power transfers between the core and cladding modes from a TFBG located downstream from a LPG. We show that the curvature of a beam can be determined by the reflected power difference between the core mode and the recoupled cladding modes. We further provide design rules for the LPG and TFBG to optimize and linearize the sensor response. In addition, the temperature cross-sensitivities of this configuration are also investigated for two different types of fiber.     

Localized modes in orientation-disordered one-dimensional media with uniaxial scatterers

Localized modes in one-dimensional (1D) media with uniaxial scatterers that are assumed to be order in spatial location but disorder in spatial orientation of their optical axis are investigated. Based on the holistic effect model in random laser, I.e., the random laser is due to the interaction of the complex localized modes in active random media with local aperiodic quasi-structure with appropriate pump light, a physical model on this type of random media is found. Its disorder degree is defined by D = no/ne. Then, the typical transmission spectrum through the random media and the light field intensity distribution corresponding to the defect modes in photonic band-gap are calculated numerically by means of the transfer matrix method, and the condition that the localized mode appears is discussed. Results show that the medium disorder plays an important role in determining the lightwave state. The localized state appears when the medium disorder is strong enough, and a new mechanism creating random laser phenomenon is brought forward.     

散射颗粒分布对二维随机激光器腔内各模式的影响

采用时域有限差分法数值求解Maxwell方程组,分析了二维随机激光器中光波模式的频谱特性.计算表明,处于不同分布区域的散射颗粒对腔内不同模式的影响有很大差异,处于该模式空间分布区域的散射颗粒比区域外的颗粒对模式有更大的影响.这个特性是随机激光器所独有,并可以用来进行随机激光器的模式选择.     

Azimuthal-order variations of surface-roughness-induced mode splitting and scattering loss in high-Q microdisk resonators

We report an experimental observation of strong variations of quality factor and mode splitting among whispering-gallery modes with the same radial order and different azimuthal orders in a scattering-limited microdisk resonator. A theoretical analysis based on the statistical properties of the surface roughness reveals that mode splittings for different azimuthal orders are uncorrelated, and variations of mode splitting and quality factor among the same radial mode family are possible. Simulation results agree well with the experimental observations.     

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.     

无序介质激光的方向效应

无序介质激光是由该介质的非周期-类结构与相匹配的泵浦光场相互作用时其整体多重散射的干涉效应产生的.因此其局域模不仅与无序介质被泵浦的功率、面积有关,而且与方向有关.本文以ZnO粉末激光为例,运用传输矩阵的方法计算模拟了其局域模谱的方向效应.     

一种基于单水听器的浅海水下声源被动测距方法

针对浅海波导中宽带脉冲声源的被动测距问题,本文在群延迟理论的基础上,与warping变换处理相结合,提出了一种适用于浅海波导中宽带声源的单水听器被动测距方法.利用warping变换可以实现对脉冲声源接收信号各阶简正波的分离提取,对分离后的简正波进行时频分析处理可以得到各阶简正波到达时刻和频率之间的关系,即各阶简正波的频散曲线,从而得到任意两阶简正波到达接收水听器的时延差.海底相移参数P是描述海底地声参数的一个重要参量,包含了海底地声参数信息,在海底环境参数未知而P已知的情况下,利用P和简正波水平波数之间的关系可以求得任意两阶简正波的?S_(g,mn)(群慢差).根据群延迟理论,利用得到的任意两阶简正波的时延和?S_(g,mn)可实现利用单水听器对水下声源进行被动测距.本文提出的测距方法测量简单、计算方便,具有较强的实用意义.数值仿真和海上实验数据处理结果的测距误差都在10%以内,证明了该方法的有效性.     

Theoretical investigation on the threshold property of localized modes based on spectral width in two-dimensional random media

By use of the time dependent theory for random lasers, we make a comprehensive calculation on the spectrum intensity as well as the pump rate dependence of the peak intensity and the spectral width of localized modes in two-dimensional random media for both transverse electric and transverse magnetic polarization fashions. For any mode, there is a jump in the curve of the spectral width vs the pump rate. A method based on the trailing edge of the jump to determine the pump threshold of a mode is confirmed to be available and effective.     

全光纤干涉式结构中传感模式仿真分析

全光纤干涉式传感结构中包层模场与外界物理量作用,携带被感测信息,因此对包层模的研究是设计制作和提高该类传感器传感性能的关键.利用有限差分光束传播法获得传感光纤不同长度和不同芯径比时传感器对应的光谱,通过傅里叶变换获得其干涉频谱,计算出各主要参与干涉的包层模组的有效折射率,利用色散方程确定对应包层模.理论仿真结果显示,随着传感部分光纤长度增加,参与干涉的包层模式随之增加,并且向高阶模式变化,光谱变得稠密,是多阶包层模干涉的叠加,传感器输出干涉谱的自由光谱范围变小.随着输入光纤与传感光纤芯径比变化,会明显改变纤芯包层功率分布,同时,芯径比增大也会增加参与干涉的包层模种类和阶数.