双包层Er-Yb共掺光纤放大器上能级粒子数分布研究

基于速率方程和功率传播方程, 数值分析了双包层Er-Yb共掺光纤放大器在波长为972nm的泵浦光作用下, 分别采用三种不同泵浦方式, 其Er3+和Yb3+上能级粒子数分布情况. 数值结果表明,Er3+上能级粒子数分布受信号功率影响作用大, 激发率基本保持在50％以上; Yb3+上能级粒子数分布受泵浦功率影响作用大, 激发率基本保持在10％以下, 该结论对双包层Er-Yb共掺光纤放大器的性能研究具有一定指导意义.     

双程掺镱光纤放大器的增益特征及优化

比较了掺钕光纤和掺镱光纤对1064 nm光放大的特点.基于速率方程和传输方程,数值分析了在915 nm泵浦下双程掺镱光纤放大器的增益特征,并且和传统的单程放大进行了比较.分析了信号光和泵浦光,以及粒子数沿着光纤方向的分布特点.最后对双程掺镱光纤放大器进行了优化.     

掺镱光纤放大器泵浦脉宽优化

为抑制低重复频率高能脉冲光纤主振荡功率放大(MOPA)系统的放大自发辐射(ASE)效应,达到脉冲泵浦的最佳放大效果,需要对泵浦脉宽进行优化。基于求解速率方程和功率传输方程,理论研究了脉冲泵浦下掺镱光纤放大器上能级粒子数密度、光纤内存储能量、正反向放大自发辐射的瞬态响应。在给定的泵浦功率、光纤长度、纤芯面积和掺杂数密度等参数下,数值计算得到的优化泵浦脉宽为793 s。此外,实验测定了ASE的建立时间; 通过调节泵浦脉宽,测定了脉冲泵浦下掺镱光纤放大器的放大效果,实验中得到的泵浦脉宽的优化值为800 s,证明了数值模拟的正确性。     

宽带碲基掺铒光纤放大器多信道增益竞争的仿真分析

对新型宽带碲基掺铒光纤放大器(EDTFA)多信道间的增益演变关系进行了理论仿真。仿真结果表明:EDTFA多信道间的增益存在着一个竞争过程,竞争的强弱取决于碲基掺铒光纤内的能级粒子数分布;当上能级粒子数处于反转分布态时,具有较大的发射截面与吸收截面差值的波长信道拥有相对较大的竞争优势,可获得相对较高的信号增益;当上能级粒子数处于未反转分布态时,具有较大的发射截面与吸收截面比值的波长信道拥有相对较大的增益竞争优势。     

沿传输方向掺杂浓度渐变掺铒光纤放大器的研究

本文在分析了均匀掺杂分布式掺饵光纤放大器的基础上,提出了沿传输方向掺杂浓度线性单调下降(单变),和线性降升结合(两变)的两种渐变型分布式掺饵光纤放大器,并用传输方程研究和比较了透明传输和最佳掺杂浓度下,均匀、单变和两变型三种放大器中的信号和噪音的传输特性及放大器的噪音指数、信噪比、临界泵浦功能和最佳泵浦周期等特性.     

利用杜哈梅尔方法近似求解EDF的自发辐射特性

掺铒光纤(EDF)中的自发辐射噪声是影响掺铒光纤放大器(EDFA)工作性能和掺铒光纤激光器(EDFL)的起振特性的重要因素。自发辐射与泵浦方式紧密相关,研究脉冲泵浦下EDF的自发辐射具有重要的学术意义。从速率方程出发,建立了任意波形脉冲泵浦下EDF自发辐射的能级粒子数分布所满足的一元二阶变系数微分方程。由于没有封闭形式的解析解,采用杜哈梅尔方法,将泵浦脉冲波形进行分时段描述,每个小时段都有解析解,从而得到了自发辐射的平均功率表达式。分析结果表明,随着泵浦功率的增大,ASE的输出波形更接近泵浦光的波形,且泵浦光的毛刺对于ASE噪声的影响较小。     

掺镱光纤放大器增益特性的理论分析

在引入光场与掺杂分布的重叠因子及忽略放大自发辐射(ASE)和光纤损耗的情况下,通过求解掺Yb3+光纤放大器(YDFA)的能级速率方程和光传输方程,得到了在稳态条件下YDFA的速率-传输方程组的解,推导出了泵浦阈值、放大器增益、最佳光纤长度的表达式.研究了泵浦光、信号光、掺杂浓度、最佳光纤长度、最佳光纤长度下增益之间的内在联系.最后对数值模拟结果进行了分析和讨论.     

掺铒光纤激光器输出特性的研究

根据掺铒光纤激光器的速率方程,对线性腔连续掺铒光纤激光器的输出特性进行了详细的理论分析,得到了980 nm泵浦的掺铒光纤激光器在稳态条件下的解析表达式.利用数值模拟结果对光纤激光器的上下能级粒子数和泵浦功率沿光纤长度分布以及泵浦阈值、斜率效率等进行了分析和讨论,并进行了980 nm泵浦的掺铒光纤激光器的实验,实验证明:光纤激光器的阈值与理论计算基本一致.     

沿传输方向掺杂浓度渐变掺铒光纤放大器的研究

本文在分析了均匀掺杂分布式掺饵光纤放大器的基础上，提出了沿传输方向掺杂浓度线性单调下降（单变），和线性降升结合（两变）的两种渐变型分布式掺饵光纤放大器，并用传输方程研究和比较了透明传输和最佳掺杂浓度下，均匀、单变和两变型三种放大器中的信号和噪音的传输特性及放大器的噪音指数、信噪比、临界泵浦功能和最佳泵浦周期等特性．     

FEMLAB在模拟掺镱双包层光纤放大器脉冲放大特性的应用1

应用FEMLAB软件模拟掺镱双包层光纤放大器的脉冲放大特性.计算了在915 nm前向抽运下，光纤放大器中的上能级粒子数，抽运光和放大自发辐射在光纤中的稳态分布,以及高斯脉冲和方波脉冲的输出、能量及增益特性.与文献上的结果进行比较证明了该程序的有效性.     

GENERALIZATION OF AN INVERTIBLE TRANSFORMATION AND EXAMPLES OF ITS APPLICATIONS

Recently we highlighted the remarkable nature of an explicitly invertible transformation, we reported some generalizations of it and examples of its expediency in several mathematical contexts: algebraic and Diophantine equations, dynamical systems (with continuous and discrete time), nonlinear PDEs, analytical geometry, functional equations. In this paper we report a significant generalization of this approach and we again illustrate via some analogous examples its expediency to identify problems which appear far from trivial but are in fact explicitly solvable.     

On the problem of one-dimensional disordered chain

Conclusion Some properties of a one-dimensional disordered homogeneous chain were studied in this paper. Using standard techniques of probability theory, expressions for the frequency distribution function (2) and the localization length (6) were derived. Having considered only pair correlations between atoms, both these expressions contained only one unknown function — the joint probability distribution of the massm _n and the ratiot _n ^± = –ku _n±1/u _n which could be found as a solution of the integral equation (5). Our approach to the problem was applied on the ideal lattice and the lattice with low concentration of impurities. In these cases the solutions of the integral equation (5) reduced to the functional form (7) were found analytically. Using these solutions, old well-known results for ( ²) and the local vibration of impurities were derived by this method.Derivation of all equations in this paper is straightforward from the equations of motion. The quantities we deal with have a clear physical meaning, which facilitated, for instance to find the solutions of functional equation (7) in the special case of the ideal crystal. This is what we consider to be the advantages of our approach.     

<Emphasis Type="Italic">N</Emphasis> = 1, 2 supersymmetric non-local gas equation

In this paper we study the supersymmetrization of the N = 1 and N = 2 nonlocal gas equation. We show that this system is bi-Hamiltonian. While the N = 1 supersymmetrization allows the hierarchy of equations to be extended to negative orders (local equations), we argue that this is not the case for the N = 2 supersymmetrization. In the bosonic limit, however, the N = 2 system of equations lead to a new coupled integrable system of equations. Presented at the International Colloquium “Integrable Systems and Quantum Symmetries”, Prague, 16–18 June 2005.     

Regge behaviour of distribution functions and t and x-evolutions of gluon distribution function at low-x

In this paper, t and x-evolutions of gluon distribution function from Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution equation in leading order (LO) at low-x are presented assuming the Regge behaviour of quarks and gluons at this limit. We compare our results of gluon distribution function with MRST 2001, MRST 2004 and GRV 1998 parametrizations and show the compatibility of Regge behaviour of quark and gluon distribution functions with perturbative quantum chromodynamics (PQCD) at low-x. We also discuss the limitations of Taylor series expansion method used earlier to solve DGLAP evolution equations in the Regge behaviour of distribution functions.      

Equation of state and initial temperature of quark gluon plasma at RHIC

In gold-gold collisions of the Relativistic Heavy Ion Collider a perfect fluid of strongly interacting quark gluon plasma (sQGP) is created. The time evolution of this fluid can be described by hydrodynamical models. After an expansion, hadrons are created during the freeze-out period. Their distribution reveals information about the final state. To investigate the time evolution one needs to analyze penetrating probes: e.g. direct photon observations. In this paper we analyze a 1+3 dimensional solution of relativistic hydrodynamics. We calculate momentum distribution, azimuthal asymmetry and momentum correlations of direct photons. Based on earlier fits to hadronic spectra, we compare photon calculations to measurements to determine the equations of state and the initial temperature of sQGP. We find that the initial temperature in the center of the fireball is 507±12 MeV, while for the sound speed we get c _s =0.36±0.02. We also estimate a systematic error of these results. We find that the measured azimuthal asymmetry is also compatible with this model. We also predict a photon source that is significantly larger in the out direction than in the side direction.     

Travelling wave solutions for (<Emphasis Type="Italic">N</Emphasis> + 1)-dimensional nonlinear evolution equations

In this paper, we implement the exp-function method to obtain the exact travelling wave solutions of (N + 1)-dimensional nonlinear evolution equations. Four models, the (N + 1)-dimensional generalized Boussinesq equation, (N + 1)-dimensional sine-cosine-Gordon equation, (N + 1)-double sinh-Gordon equation and (N + 1)-sinhcosinh-Gordon equation, are used as vehicles to conduct the analysis. New travelling wave solutions are derived.     

On dual Schur domain decomposition method for linear first-order transient problems

This paper addresses some numerical and theoretical aspects of dual Schur domain decomposition methods for linear first-order transient partial differential equations. The spatially discrete system of equations resulting from a dual Schur domain decomposition method can be expressed as a system of differential-algebraic equations (DAEs). In this work, we consider the trapezoidal family of schemes for integrating the ordinary differential equations (ODEs) for each subdomain and present four different coupling methods, corresponding to different algebraic constraints, for enforcing kinematic continuity on the interface between the subdomains. Unlike the continuous formulation, the discretized formulation of the transient problem is unable to enforce simultaneously the continuity of both the primary variable and its rate along the subdomain interface (except for the backward Euler method).Method 1 (d-continuity) is based on the conventional approach using continuity of the primary variable and we show that this method is unstable for a lot of commonly used time integrators including the mid-point rule. To alleviate this difficulty, we propose a new Method 2 (modified d-continuity) and prove its stability for coupling all time integrators in the trapezoidal family (except the forward Euler). Method 3 (v-continuity) is based on enforcing the continuity of the time derivative of the primary variable. However, this constraint introduces a drift in the primary variable on the interface. We present Method 4 (Baumgarte stabilized) which uses Baumgarte stabilization to limit this drift and we derive bounds for the stabilization parameter to ensure stability. Our stability analysis is based on the “energy” method, and one of the main contributions of this paper is the extension of the energy method (which was previously introduced in the context of numerical methods for ODEs) to assess the stability of numerical formulations for index-2 differential-algebraic equations (DAEs). Finally, we present numerical examples to corroborate our theoretical predictions.     

Chern-Simons solitons,Toda theories and the chiral model

The two-dimensional self-dual Chern-Simons equations are equivalent to the conditions for static, zero-energy solutions of the (2+1)-dimensional gauged nonlinear Schrödinger equation with Chern-Simons matter-gauge dynamics. In this paper we classify all finite chargeSU(N) solutions by first transforming the self-dual Chern-Simons equations into the two-dimensional chiral model (or harmonic map) equations, and then using the Uhlenbeck-Wood classification of harmonic maps into the unitary groups. This construction also leads to a new relationship between theSU(N) Toda andSU(N) chiral model solutions.This work is supported in part by funds provided by the U.S. Department of Energy (D.O.E.) under contract #DE-AC02-76ER03069, and NSF grant #87-08447     

Existence of Solutions to the Bethe Ansatz Equations for the 1D Hubbard Model: Finite Lattice and Thermodynamic Limit

In this work, we present a proof of the existence of real and ordered solutions to the generalized Bethe Ansatz equations for the one dimensional Hubbard model on a finite lattice, with periodic boundary conditions. The existence of a continuous set of solutions extending from any U>0 to U=∞ is also shown. We use this continuity property, combined with the proof that the norm of the wavefunction obtained with the generalized Bethe Ansatz is not zero, to prove that the solution gives us the ground state of the finite system, as assumed by Lieb and Wu. Lastly, for the absolute ground state at half-filling, we show that the solution converges to a distribution in the thermodynamic limit. This limit distribution satisfies the integral equations that led to the Lieb-Wu solution of the 1D Hubbard model.     

QUANTUM EQUATIONS FOR MASSLESS PARTICLES OF ANY SPIN

By decomposing the mass squared operator for zero mass particles of spin s we obtain one-particle quantum equations for any spin on which 2s–1 subsidiary conditions are imposed. The derived equations are consistent with the two component neutrino equation and the Maxwell equations. Subsidiary conditions for the spins 1, , and 2 are presented.