The Airy<Subscript>1</Subscript> Process is not the Limit of the Largest Eigenvalue in GOE Matrix Diffusion

Using a systematic approach to evaluate Fredholm determinants numerically, we provide convincing evidence that the Airy₁-process, arising as a limit law in stochastic surface growth, is not the limit law for the evolution of the largest eigenvalue in GOE matrix diffusion.     

单模光纤中受激喇曼散射对调制不稳定性的影响

基于修正的非线性薛定谔方程，利用线性扰动理论和数值方法研究了单模光纤中的调制不稳定性.由于受激喇曼散射的作用，使得喇曼增益谱叠加到光纤中的调制不稳定性增益谱上.这样，原本调制稳定的光纤正常色散区也出现了调制不稳定性；而在反常色散区，随着初始功率的增加，常规的调制不稳定性增益谱的增益和频谱范围均增大，而喇曼增益谱的增益增大但其频谱范围基本不变，这样导致常规的不稳定区域逐渐侵入并最终掩盖喇曼增益区.数值模拟验证了解析结果的正确性，并证明了利用反常色散情形下的调制不稳定性可以产生超短脉冲序列，但这种脉冲序列的进一步传输将会出现喇曼孤子自频移现象.     

Spatiotemporal instability in dispersive nonlinear Kerr medium with a finite response time

We investigated the spatiotemporal modulation instability (MI) in a medium with a non-instantaneous Kerr response in which the nonlinear contribution to the refractive index is governed by a relaxing Debye type equation. The expression for the MI gain spectrum in non-instantaneous Kerr medium is obtained, which clearly reveals the influence of the finite time of the nonlinear response (relaxation effect) on the spatiotemporal MI. It is shown that, due to the relaxation effect, the spatiotemporal MI can appear for the case of anomalous dispersion and defocusing nonlinearity, while it cannot appear in instantaneous Kerr medium for the same case, and a new MI gain spectrum appears, adding to the conventional MI gain spectrum similar to that in an instantaneous Ker medium. In addition, the bandwidth of MI gain spectrum is extended and the maximum MI gain is reduced with increasing of the relaxation time. Interestingly, spatiotemporal MI can appear for any spatial frequencies in non-instantaneous Kerr medium for any combination of dispersion and nonlinearity. We have performed an experiment of MI in carbon disulfide (CS₂), a typical non-instantaneous Kerr medium, which shows quantitative agreement with the theoretical analyses.     

Modulation instability in silicon optical waveguide considering linear loss

Taking into account the linear loss of silicon-on-insulator (SOI) waveguide, modulation instability (MI) induced by combined effects of self-phase modulation and waveguide dispersions is investigated. The impacts of various parameters to gain spectra of MI are analyzed theoretically, and direct numerical simulation of nonlinear Schroedinger equation is performed as well. Results show that strong MI takes place even in the existence of low light power. The linear loss of waveguide obviously impacts gain spectra of MI, even within ultra-short propagation distance. The peak gain frequency and bandwidth of gain spectra decrease to 41.683% and 41.6879% of their maximum at propagation distance z = 5 mm, respectively.     

The influence of stochastic nonlinear gain variation on bright soliton transmission system

The model of stochastic nonlinear gain variation is built in the soliton transmission system. The influence of the stochastic nonlinear gain variation on the soliton transmission system is studied. The results show that the stochastic nonlinear gain variation apparently leads to the time jitters in arrival, degrades the capacity of soliton transmission system and the filter can suppress the influence well.     

用转移矩阵法研究LNN型非线性平面光波导

用转移矩阵法数值分析了芯区和衬底为非线性介质、覆盖层为线性介质结构平面光波导的传播特性,包括TM的模场分布和功率与有效折射率之间关系的分析.解析地表达了模式本征方程和功率分布,对非线性介质中电场强度与介质非线性系数的关系进行了研究.计算结果表明,TM的模场分布和功率与有效折射率及介质的非线性系数有关.     

电子结构方法中带结构特征值问题的统一视角

在(相对论)电子结构方法中,四元数矩阵特征值问题和计算激发能的线性响应(Bethe-Salpeter)特征值问题是两个经常出现的结构特征值问题. 尽管前一个问题已被十分仔细地研究,后一个问题在一般形式下,即不假设电子Hessian正定性的复矩阵情况,并没有得到完全的理解. 鉴于它们非常相似的数学结构,本文从一个统一的角度研究了这两个问题,揭示了它们特征向量的“李群”结构,为将来设计对角化算法和数值优化方法提供了一个统一的框架. 利用和处理四元数矩阵特征值问题相同的归约算法,本文给出了表征线性响应问题特征值(实数、纯虚、或复数)的充分必要条件. 这一结果可以看作是实矩阵情况下已知条件的自然推广.     

用于补偿增益窄化效应的Rugate滤波器设计

采用Rugate膜系理论,分别根据钛宝石和钕玻璃介质增益窄化的特点,合理选择补偿增益窄化的调制函数,优化设计出了分别用于补偿钛宝石系统和钕玻璃系统增益窄化效应的Rugate滤波器.由普通均匀多层膜的特征矩阵方法近似分析了设计出的Rugate滤波器的光谱响应,数值模拟了Rugate滤波器的光谱补偿效果.结果显示,能比较好的符合光谱补偿的要求,可以用作补偿增益窄化效应的光谱调制滤波器. 关键词： 超短脉冲 增益窄化 光谱补偿 Rugate滤波器     

Induced modulational instability in EDFAs in the presence of higher-order nonlinear and dispersive effects

We derive the dispersion equation for erbium doped fiber amplifiers (EDFAs), assuming the supplementary effects of time-derivative nonlinearities including intrapulse Raman scattering and self-steepening incorporated with third order dispersion and product of gain and square of dipole relaxation time parameter, in the extended form of nonlinear Schrödinger equation and investigate their impacts on gain and cut-off frequency of modulational instability (MI) in EDFAs. Also, the influences of those effects on instability of steady-state amplitude, in the form of generation of terahertz pulse train of femtosecond solitons from a weak-modulated signal by induced MI, are numerically simulated and discussed within EDFAs in normalized form.     

On generation of coherent structures induced by modulational instability in linearly coupled cubic-quintic Ginzburg-Landau equations

We study the properties of the coherent structures induced by the modulational instability (MI) of the two linearly coupled complex Ginzburg-Landau equations with both cubic and quintic terms, which in nonlinear optics can model ring lasers based on dual-core fibers. We obtain new stationary solutions different from the previous result and the analytic gain formula as function of the linear coupling constant and the model parameters. The fact that the system can be modulationally unstable for the vast region of the parameters space is demonstrated. The effects of the linear coupling constant on the evolution of a continuous wave under the MI are numerically investigated in the presence of the linear loss or gain. It is found that doubly asymmetric stable solitary pulses and stable breathers can be formed from the perturbed continuous waves state by the MI. The conditions for generating the periodic stable solitary pulses and fronts by the MI are identified by varying the linear coupling constant.     

Coherence resonance and stochastic synchronization in a nonlinear circuit near a subcritical Hopf bifurcation

We analyze noise-induced phenomena in nonlinear dynamical systems near a subcritical Hopf bifurcation. We investigate qualitative changes of probability distributions (stochastic bifurcations), coherence resonance, and stochastic synchronization. These effects are studied in dynamical systems for which a subcritical Hopf bifurcation occurs. We perform analytical calculations, numerical simulations and experiments on an electronic circuit. For the generalized Van der Pol model we uncover the similarities between the behavior of a self-sustained oscillator characterized by a subcritical Hopf bifurcation and an excitable system. The analogy is manifested through coherence resonance and stochastic synchronization. In particular, we show both experimentally and numerically that stochastic oscillations that appear due to noise in a system with hard excitation, can be partially synchronized even outside the oscillatory regime of the deterministic system.     

Relaxation in establishing a steady-state stochastic process with 1/<Emphasis Type="Italic">f</Emphasis> spectrum and low-frequency spike statistics

According to theory, fluctuations with a power spectrum inversely proportional to frequency (1/f processes) may arise when dissimilar phase transitions simultaneously take place in physical systems with intense white noise. In this work, relaxation effects in establishing a steady-state stochastic process with non-equilibrium phase transitions are described in terms of two nonlinear stochastic differential equations. The results thus obtained carry information on the statistics of large-scale low-frequency spikes. Step “forgetting” of initial conditions is noted. It is numerically shown that the distributions of the durations and maximal values of extreme low-frequency spikes have a power-type form.     

Modulational instability in the cubic-quintic nonlinear Schrödinger equation through the variational approach

The dynamics of nonlinear pulse propagation in an average dispersion-managed soliton system is governed by a constant coefficient nonlinear Schrödinger (NLS) equation. For a special set of parameters the constant coefficient NLS equation is completely integrable. The same constant coefficient NLS equation is also applicable to optical fiber systems with phase modulation or pulse compression. We also investigate MI arising in the cubic-quintic nonlinear Schrödinger equation for ultrashort pulse propagation. Within this framework, we derive ordinary differential equations (ODE’s) for the time evolution of the amplitude and phase of modulation perturbations. Analyzing the ensuing ODE’s, we derive the classical modulational instability criterion and identify it numerically. We show that the quintic nonlinearity can be essential for the stability of solutions. The evolutions of modulational instability are numerically investigated and the effects of the quintic nonlinearity on the evolutions are examined. Numerical simulations demonstrate the validity of the analytical predictions.     

Numerical study on multiple-pulse operation of passively modelocked stretched pulse fiber ring laser

We numerically study a stable multiple-pulse operation of passively modelocked stretched pulse fiber ring laser. The simulation results show that multiple pulses are formed with being triggered by radiation from a single pulse in a restricted parameter range. In order to obtain a better understanding of the effect of gain bandwidth and nonlinear gain on harmonic modelocking process of multiple-pulse operation, we analyze those effects in detail.     

Optical pulse evolution in the presence of a probe light in CW-pumped nonlinear fiber

We investigate theoretically and numerically the evolutions of optical pulses in the time domain due to modulation instability(MI), where CW pump accompanied with a probe is used as the input of nonlinear fiber. As the fiber length increases, we show that it exhibits beat frequency between the pump and the probe first when the probe lies outside the MI resonance region, and then gradually transforms into a pulse train resulting from spontaneous MI rather than induced MI. However, the regular pulse train is easier to generate in the whole fiber if the probe exists in MI resonance region,and the period of the pulse train is inversely proportional to the frequency spacing between the pump and the probe. It is emphasized that the pulse period can be adjusted only when the probe is in MI resonance region. The numerical simulations are in agreement with the theoretical results. The obtained results are guidable for generating and manipulating the optical pulse train in the fiber.     

Decomposing data sets into skewness modes

We derive the nonlinear equations satisfied by the coefficients of linear combinations that maximize their skewness when their variance is constrained to take a specific value. In order to numerically solve these nonlinear equations we develop a gradient-type flow that preserves the constraint. In combination with the Karhunen-Loève decomposition this leads to a set of orthogonal modes with maximal skewness. For illustration purposes we apply these techniques to atmospheric data; in this case the maximal-skewness modes correspond to strongly localized atmospheric flows. We have also checked that the results are statistically significant in spite of the finite length of the data. We show how these ideas can be extended, for example to maximal-flatness modes.     

Spatiotemporal optical modulation instability of coherent light in noninstantaneous nonlinear media

We report on the theoretical derivation and experimental observation of spatiotemporal modulation instability (MI) of a coherent light beam in noninstantaneous nonlinear media. We obtain analytically the MI growth rate as a function of the spatial and temporal frequencies of the perturbation and the material response time. In the experiment, we observe that the varying speed of the MI patterns increases with the decreased material response time. We also observe that increasing the material response time can arrest the MI, agreeing with our theoretical derivation.     

Nonlinear photonics with metallic nanostructures on top of dielectrics and waveguides

We review recent experimental and theoretical studies of the ultrafast and nonlinear optical response of metallic nanostructures on top of dielectric substrates and slab waveguides where plasmon hybridization is a key ingredient. In a first three-pulse all-optical control experiment a hybrid plasmonic mode is turned on or off only a few tens of femtoseconds after its excitation. A second experiment concentrates on the origin of the nonlinear response in a metallo-dielectric photonic crystal structure. We show that the shape of the nonlinear optical spectra provides unambiguous information about the nonlinear optical contribution of the metallic as well as the dielectric part of the structure. Furthermore, we discuss the influence of slow-light on the nonlinear response. All experimental results agree perfectly with numerical scattering matrix calculations as well as simulations based on a classical harmonic oscillator model.     

A Girsanov particle filter in nonlinear engineering dynamics

In this Letter, we propose a novel variant of the particle filter (PF) for state and parameter estimations of nonlinear engineering dynamical systems, modelled through stochastic differential equations (SDEs). The aim is to address a possible loss of accuracy in the estimates due to the discretization errors, which are inevitable during numerical integration of the SDEs. In particular, we adopt an explicit local linearization of the governing nonlinear SDEs and the resulting linearization errors in the estimates are corrected using Girsanov transformation of measures. Indeed, the linearization scheme via transformation of measures provides a weak framework for computing moments and this fits in well with any stochastic filtering strategy wherein estimates are themselves statistical moments. We presently implement the strategy using a bootstrap PF and numerically illustrate its performance for state and parameter estimations of the Duffing oscillator with linear and nonlinear measurement equations.     

KTP离子交换光波导及特性

报道了制备Ｚ－切ＫＴＰＲｂ／Ｂａ离子交换平面光波导的方法，给出了较理想的Ｒｂ和Ｂａ的ｍｏｌ％比，测量了光波导层的光损伤感度和晶格常数变化。实验结果表明：光损伤感度为１．２～２．３×１０－１０ｃｍ２／Ｊ，它与掺Ｂａ的含量和热退火工艺无关；晶格常数的变化为０．４２～０．２５％，它随着掺Ｂａ含量的增加而减少。