Propagation of Electromagnetic Pulses in an Inhomogeneous Scattering Absorbing Medium. Invariant Temporal Properties

We present analytical solutions of the Ishimaru parabolic equation for the coherence function of electromagnetic field. The equation describes the temporal properties of the pulse at the output of an inhomogeneous dissipative scattering medium. An explicit expression for the Green's function of the problem is found. It is shown that the temporal part of the Green's function has an invariant Laguerre form. Numerical results describing the shapes of the studied temporal pulses at the output of the pass interval of the medium are also given. Time scales characterizing the shapes of the Laguerre output pulses are proposed and the influence of the parameters of the medium on the properties of the resulting pulses is analyzed.     

Stability criterion for dissipative soliton solutions of the one-, two-, and three-dimensional complex cubic-quintic Ginzburg-Landau equations

The generation and nonlinear dynamics of multidimensional optical dissipative solitonic pulses are examined. The variational method is extended to complex dissipative systems, in order to obtain steady state solutions of the (D + 1)-dimensional complex cubic-quintic Ginzburg-Landau equation (D = 1, 2, 3). A stability criterion is established fixing a domain of dissipative parameters for stable steady state solutions. Following numerical simulations, evolution of any input pulse from this domain leads to stable dissipative solitons.     

基于耗散孤子种子的啁啾脉冲光纤放大系统输出特性

以不同滤波器带宽下获得的全正色散光纤激光器耗散孤子作为啁啾脉冲放大(CPA)系统的种子脉冲, 研究了光栅对和光纤展宽器CPA系统输出脉冲的可压缩性. 结果表明, 对于大能量耗散孤子种子脉冲, 当CPA系统采用正色散光纤展宽器时, 光纤群速色散与自相位调制之间的相互作用不仅可抑制耗散孤子脉冲光谱调制的影响, 还可使脉冲在光纤展宽器中自相似演化, 从而可提高CPA输出脉冲的可压缩性. 通过优化光纤展宽器长度, 对于耗散孤子种子源, 采用光纤展宽器的CPA系统输出脉冲可压缩性与主脉冲所占脉冲总能量之比均优于采用光栅对展宽器时的情况.     

Stratified quantization approach to dissipative quantum systems: Derivation of the Hamiltonian and kinetic equations for reduced density matrices

A technique for describing dissipative quantum systems that utilizes a fundamental Hamiltonian, which is composed of intrinsic operators of the system, is presented. The specific system considered is a capacitor (or free particle) that is coupled to a resistor (or dissipative medium). The microscopic mechanisms that lead to dissipation are represented by the standard Hamiltonian. Now dissipation is really a collective phenomenon of entities that comprise a macroscopic or mesoscopic object. Hence operators that describe the collective features of the dissipative medium are utilized to construct the Hamiltonian that represents the coupled resistor and capacitor. Quantization of the spatial gauge function is introduced. The magnetic energy part of the coupled Hamiltonian is written in terms of that quantized gauge function and the current density of the dissipative medium. A detailed derivation of the kinetic equation that represents the capacitor or free particle is presented. The partial spectral densities and functions related to spectral densities, which enter the kinetic equations as coefficients of commutators, are evaluated. Explicit expressions for the nonMarkoffian contribution in terms of products of spectral densities and related functions are given. The influence of all two-time correlation functions are considered. Also stated is a remainder term that is a product of partial spectral densities and which is due to higher order terms in the correlation density matrix. The Markoffian part of the kinetic equation is compared with the Master equation that is obtained using the standard generator in the axiomatic approach. A detailed derivation of the Master equation that represents the dissipative medium is also presented. The dynamical equation for the resistor depends on the spatial wavevector, and the influence of the free particle on the diagonal elements (in wavevector space) is stated.     

The influence of viscous heating and wall thermal conditions on the thermal ignition of a poiseuille/couette reactive flow

This paper investigates the stationary thermal stability of an exothermic reactive viscous non-Newtonian fluid between two parallel walls in the plane Poiseuille and generalized Couette flow configurations for two different thermal conditions. Assuming the system is adiabatic with negligible reactant consumption, the closed-form solution obtained from the momentum equation was inserted into the energy equation due to the dissipative effect of viscosity. The resulting energy equation was analyzed for criticality using a variational technique. The influence of the viscous heating parameter (Γ), wall dynamical (Λ) and the thermal conditions of the walls on the thermal ignition parameters were examined.     

多脉冲激光辐照下介质损伤理论研究

针对纳秒脉冲和飞秒脉冲不同的损伤机制,分别建立了两种多脉冲激光损伤模型。脉宽小于10 ps时,损伤是由于等离子体形成造成介质发生烧蚀所致,对此建立了基于电子密度演化方程的介质击穿模型;脉宽大于100 ps时,损伤是由于热沉积造成介质发生熔融所致,对此建立了基于傅里叶热传导方程的介质热损伤模型。通过计算两种模型下激光参数和材料参数对多脉冲损伤的影响,发现由于损伤机理不同,不同参数对单脉冲损伤阈值和多脉冲损伤阈值的影响趋势不完全一致,敏感程度也不同。通过计算得到了与实验结果一致的多脉冲损伤阈值与脉冲数间关系,使定量预估多脉冲损伤阈值和元件使用寿命成为可能。     

Spontaneous soliton production by an optical pulse with a nonlinear shift of the carrier frequency

The perturbed nonlinear Schrödinger equation model is used to investigate the decay of a strong optical pulse in an absorbing medium with consideration of the nonlinear frequency shift of the pulse. The regularities of the spontaneous soliton production process are investigated numerically. It is established that with the use of the nonlinear frequency shift effect, not only can dissipative losses be compensated in waveguides, but the retarded signal can also be amplified.     

全正色散多波长被动锁模耗散孤子掺镱光纤激光器

报道了一种带有周期性双折射光纤滤波器的全正色散多波长被动锁模耗散孤子掺镱光纤激光器. 通过数值模拟发现加入滤波器后激光器能输出多波长耗散孤子脉冲, 调节滤波器带宽大小可以得到不同波长个数和波长间隔的多波长锁模耗散孤子脉冲. 在激光器产生的四波长和五波长耗散孤子脉冲中观察到了耗散孤子分子, 并且通过调节滤波器参数和饱和功率可以改变多波长脉冲中耗散孤子分子的个数和波长. 这是在被动锁模光纤激光器中首次实现包含有耗散孤子分子的多波长脉冲. 另外还在实验上实现了全正色散双波长被动锁模耗散孤子的产生. 关键词： 全正色散 耗散孤子 多波长脉冲 孤子分子     

A STOCHASTIC OPTIMAL SEMI-ACTIVE CONTROL STRATEGY FOR ER/MR DAMPERS

A stochastic optimal semi-active control strategy for randomly excited systems using electrorheological/magnetorheological (ER/MR) dampers is proposed. A system excited by random loading and controlled by using ER/MR dampers is modelled as a controlled, stochastically excited and dissipated Hamiltonian system with n degrees of freedom. The control forces produced by ER/MR dampers are split into a passive part and an active part. The passive control force is further split into a conservative part and a dissipative part, which are combined with the conservative force and dissipative force of the uncontrolled system, respectively, to form a new Hamiltonian and an overall passive dissipative force. The stochastic averaging method for quasi-Hamiltonian systems is applied to the modified system to obtain partially completed averaged Itô stochastic differential equations. Then, the stochastic dynamical programming principle is applied to the partially averaged Itô equations to establish a dynamical programming equation. The optimal control law is obtained from minimizing the dynamical programming equation subject to the constraints of ER/MR damping forces, and the fully completed averaged Itô equations are obtained from the partially completed averaged Itô equations by replacing the control forces with the optimal control forces and by averaging the terms involving the control forces. Finally, the response of semi-actively controlled system is obtained from solving the final dynamical programming equation and the Fokker-Planck-Kolmogorov equation associated with the fully completed averaged Itô equations of the system. Two examples are given to illustrate the application and effectiveness of the proposed stochastic optimal semi-active control strategy.     

Dissipative soliton in an amplifier with a Bragg grating

A dissipative soliton in an amplifier with a Bragg grating is numerically investigated by direct simulation of Maxwell-Bloch equations. The result of the simulation indicates that a solitary wave can exist in such a medium. However, the pulse shape of the dissipative soliton is asymmetrical because of the gain saturation effect. This gain saturation effect results from the high power of the ultrashort dissipative soliton. The influence of amplifier gain on the solitary wave is also investigated.     

On the quantization of dissipative systems

A recent paper of Dekker on the quantization of dissipative systems is examined in some detail. It is argued that one can construct a large number of classical equivalent Hamiltonians for damped systems. These can be formally quantized according to Dirac's method, and the resulting equations are mathematically consistent, but yield different eigenfunctions for the same classical system. However, this procedure should be rejected on physical grounds. That is in quantum mechanics, unlike classical dynamics, the definition of the time derivative of a dynamical variable is unique, and is given by the commutator of the proper Hamiltonian (or the energy operator) and that variable. If the proper Hamiltonian is used for the quantization of a damped system, then the quantal equations are inconsistent for the cases where the rate of energy dissipation depends on the velocity of the particle. As an alternative approach to the quantal theory of dissipative phenomena, a generalization of the Hamilton-Jacobi formalism is considered, where the equation for the principle functionS, depends not only on the space and time derivatives ofS, but onS itself. This leads to a new class of damped systems in classical mechanics. The original Schrödinger method of quantization via the Hamilton-Jacobi equation has been applied to this class of dissipative systems, with the result that the wave equation in this case is a solution of a non-linear Schrödinger-Langevin equation. This formulation has no analogue in the Hamiltonian approach, since in the latter, the resulting wave equation is always linear.Supported in part by a grant from the National Research Council of Canada.     

Dissipative Nonlinear Schrödinger Equation with External Forcing in Rotational Stratified Fluids and Its Solution

The dissipative nonlinear Schrödinger equation with a forcing item is derived by using of multiple scales analysis and perturbation method as a mathematical model of describing envelope solitary Rossby waves with dissipation effect and external forcing in rotational stratified fluids. By analyzing the evolution of amplitude of envelope solitary Rossby waves, it is found that the shear of basic flow, Brunt-Vaisala frequency and β effect are important factors in forming the envelope solitary Rossby waves. By employing Jacobi elliptic function expansion method and Hirota's direct method, the analytic solutions of dissipative nonlinear Schrödinger equation and forced nonlinear Schrödinger equation are derived, respectively. With the help of these solutions, the effects of dissipation and external forcing on the evolution of envelope solitary Rossby wave are also discussed in detail. The results show that dissipation causes slowly decrease of amplitude of envelope solitary Rossby waves and slowly increase of width, while it has no effect on the propagation speed and different types of external forcing can excite the same envelope solitary Rossby waves. It is notable that dissipation and different types of external forcing have certain influence on the carrier frequency of envelope solitary Rossby waves.     

Dynamics of traveling pulses in heterogeneous media

One of the fundamental issues of pulse dynamics in dissipative systems is clarifying how the heterogeneity in the media influences the propagating manner. Heterogeneity is the most important and ubiquitous type of external perturbation. We focus on a class of one-dimensional traveling pulses, the associated parameters of which are close to drift and/or saddle-node bifurcations. The advantage in studying the dynamics in such a class is twofold: First, it gives us a perfect microcosm for the variety of outputs in a general setting when pulses encounter heterogeneities. Second, it allows us to reduce the original partial differential equation dynamics to a tractable finite-dimensional system. Such pulses are sensitive when they run into heterogeneities and show rich responses such as annihilation, pinning, splitting, rebound, as well as penetration. The reduced ordinary differential equations (ODEs) explain all these dynamics and the underlying bifurcational structure controlling the transitions among different dynamic regimes. It turns out that there are hidden ordered patterns associated with the critical points of ODEs that play a pivotal role in understanding the responses of the pulse; in fact, the depinning of pulses can be explained in terms of global bifurcations among those critical points. We focus mainly on a bump and periodic types of heterogeneity, however our approach is also applicable to general cases. It should be noted that there appears to be spatio-temporal chaos for a periodic type of heterogeneity when its period becomes comparable with the size of the pulse.     

Computer simulation of passive mode-locking of dye lasers with consideration of coherent light-matter interaction

A numerical model of passive mode-locking of dye lasers is presented, which allows the calculation of the steady state pulse parameters without any limitation to pulse energy and duration. The solutions are compared with previous analytical results based on a rate equation treatment (i.e. without considering the phase memory). The pulse evolution and the influence of cavity dumping on the steady state are discussed.     

Dispersion managed dissipative solitons with higher order nonlinearity and frequency-selective feedback

We present the generation and interaction dynamics of dispersion managed soliton in a dissipative cubic-quintic nonlinear optical fiber coupled with frequency-selective feedback. Analytically, perturbative variational method is used to obtain evolution equations for different soliton parameters that are subsequently solved to study the propagation characteristics of the dispersion managed dissipative solitons (DMDS). The DMDSs show breather like characteristics and are found to be robust against certain level of initial noise. Both the standard Gaussian and more generic super-Gaussian pulse profile are shown to yield stable DMDS. Interaction of two DMDSs of same phase may lead to a bound state. By varying the temporal separation and phase difference between the DMDSs the bound state can be switched between low to high speed regime.     

Self-action of ultrasonic pulses in a marble rod

The nonlinear effects due to the self-action of finite-amplitude ultrasonic pulses (limitation of both amplitude and carrier phase delay) propagating in a marble rod are studied experimentally and theoretically. On the basis of the measured amplitude dependences, a nonlinear equation of state is proposed for the propagation medium. With the use of this equation, the experimental results are analytically described and the nonlinear parameters of marble are determined. It is shown that the dissipative and reactive high-frequency nonlinearities of marble are caused by different mechanisms.     

Charmonium suppression in the presence of dissipative forces in a strongly-coupled quark–gluon plasma

We study the survival of charmonium states in a strongly-coupled quark–gluon plasma in the presence of dissipative forces. We consider first-order dissipative corrections to the plasma equation of motion in the Bjorken boost-invariant expansion with a strongly-coupled equation of state for QGP and study the survival of these states with the dissociation temperatures obtained by correcting the full Cornell potential not its Coulomb part alone with a dielectric function encoding the effects of deconfined medium. We further explore the sensitivity of prompt and sequential suppression of these states to the shear viscosity-to-entropy density ratio, η/s from perturbative QCD and AdS/CFT predictions. Our results show nice agreement with the recent experimental results at RHIC.     

Variation of wave action: Modulations of the phase shift for strongly nonlinear dispersive waves with weak dissipation

Strongly nonlinear dispersive waves described by a general Klein—Gordon equation with slowly varying coefficients and a dissipative perturbation are analyzed using the method of multiple scales. We use the exact equation of wave action. The spatial and temporal slow modulations of the phase shift are shown to be governed by a new equation, which results from linearization of the wave action, its flux, and its dissipation due to perturbations of the slow parameters: frequency and wave number (vector). This result extends to nonlinear partial differential equations, the quite recent work by the authors on nonlinear oscillations governed by ordinary differential equations.     

高非线性光纤产生自相似抛物线脉冲的特性研究

基于脉冲在光纤中传输所满足的非线性薛定谔方程,采用数值计算的方法对脉冲在高非线性光纤中演化成自相似抛物线脉冲的传输特性进行了研究。结果表明,脉冲在不同初始能量和啁啾参量的情况下,高非线性光纤产生自相似抛物线脉冲,且随着归一化长度的增大,脉冲的自相似指数从0.0796减小到0.0720。进一步的研究表明:啁啾高斯脉冲在光纤传输过程中,脉冲逐渐展宽,同时正啁啾越大,其自相似演化结果越差;参数N=8的正负啁啾脉冲分别演化成平顶自相似抛物线脉冲以及三角形脉冲。