初始啁啾对脉冲频谱演变的影响

本文从理论上分析了色散和非线性对脉冲频谱的影响 ,采用数值方法求解了非线性薛定谔方程的频域解。模拟了初始啁啾对不同形状脉冲频谱的作用。研究结果表明 :初始啁啾对频谱的影响随脉冲形状而变化。对高斯型脉冲 ,正的初始啁啾导致频谱严重展宽 ,负初始啁啾对频谱影响较小。超高斯型脉冲的频谱出现了旁瓣 ,这会引起能量的损失 ;而初始啁啾对其频谱的影响并不大。孤子型脉冲的频谱受初始啁啾的影响较大 ,尤其是高阶孤子。因此 ,为了保证脉冲稳定传输 ,必须消除初始啁啾。     

Bloch方程的解析解及其在水峰抑制和特形脉冲设计中的应用

用Laplace变换方法求出了Bloch方程在各种不同物理条件下的解析解,这些解析解物理图象清楚,便于分析,克服了数值解中的困难.解析解和相应的结论已用于水峰抑制和特形脉冲的设计.对于水峰抑制,本文指出抑制效果是有极限的,并给出了抑制效果的极限以及最佳抑制时间的近似计算公式.在特形脉冲的模拟过程中,我们发现只有同时考虑全部四类解析解,才能得到正确的模拟结果,另外,模拟还表明,要在保持激励频谱形状不变的条件下,得到不同倾倒角的脉冲必须改变激励脉冲的形状,相应实验的结果与我们给出的上述结论完全吻合。     

具有几个光振荡周期长度的飞秒激光脉冲在线性色散介质中的传输

给出了描写具有几个光振荡周期长度的飞秒激光脉冲在线性色散介质中传输方程的解。对脉冲的传输特性进行了数值摸拟 ,分别考察了来源于电子和晶格的正常和反常群速色散对脉冲展宽和脉冲形状畸变的影响。     

超短脉冲复宗量辛格高斯光束

利用理论解析推导的方法，在傍轴近似条件下，给出了一组新的超短脉冲光束的解析解，称为超短脉冲复宗量辛格高斯光束.此脉冲光束解的每个频率分量都是复宗量高斯光束，时间脉冲的形状为辛格函数.对这种超短脉冲光束及其在自由空间中的传输过程进行了较为细致的研究，讨论了超短脉冲复宗量辛格高斯光束的轴上光强、光强的横向分布、脉冲极性反转、脉冲延迟等性质. 关键词： 脉冲光束 缓变包络近似 脉冲传输     

哈肯激光方程自脉冲解的稳定性分析

本文详细地研究了哈肯激光方程的自脉冲不稳定性,得出了自脉冲解的解析表达式,并对其进行了稳定性分析。结果表明,无论是对于第三类激光系统还是对于第四类激光系统,哈肯激光方程的自脉冲解都是不稳定的。     

Ladder型三能级介质中传播的少周期激光脉冲的空间分布

利用由时域有限差分法和预估校正法求得全波Maxwell-Bloch方程的数值解,研究少周期超短激光脉冲在Ladder型三能级原子介质中传播时脉冲及介质粒子布居的空间分布.结果表明,脉冲及介质粒子布居的空间分布规律随脉冲面积的改变而发生明显的变化.当脉冲面积较小时,脉冲形状不规则,振荡次数较多;当脉冲面积较大时,脉冲形状变得较为规则,振荡次数明显减少.随着脉冲面积的增大,脉冲振幅和传播速度逐渐增大,各能级粒子布居振荡次数增多,不同时刻的脉冲和粒子布居空间分布的变化明显减小.粒子布居的空间分布与脉冲的空间分布密切相关.     

控制脉冲形状对太赫兹光非对称解复用器开关特性的影响

在考虑了太赫兹光非对称解复用器 (TOAD)中半导体光放大器 (SOA)的增益饱和与恢复效应的基础上 ,深入研究了超高斯控制脉冲对半导体光放大器的动态增益响应及太赫兹光非对称解复用器开关特性的影响 ,并与高斯控制脉冲的情形进行了比较。结果表明 :相对于高斯控制脉冲而言 ,超高斯控制脉冲使半导体光放大器的增益转折区减小 ,显著影响太赫兹光非对称解复用器的开关窗口形状 ,当信号光相对于控制光时延一定 ,或环时间非对称性及信号光相对于控制光的全部时延一定时 ,超高斯控制脉冲都将使太赫兹光非对称解复用器的最大开关比降低     

控制脉冲形状对太赫我非对称解复用器开关特性的影响

在考虑了太赫兹光非对称解复用器（TOAD）中半导体光放大器（SOA）的增益饱和与恢复效应的基础上，深入研究了超高斯控制脉冲对半导体光放大器的动态增益响应及太赫兹光非对称解复用器开关特性的影响，并与高斯控制脉冲的情形进行了比较。结果表明：相对于高斯控制脉冲而言，超高斯控制脉冲使半导体光放大器的增益转折区减小，显著影响太赫兹光非对称解复用器的开关窗口形状，当信号光相对于控制光时延一定，或环时间非对称性及信号光相对于控制光的全部时延一定时，超高斯控制脉冲都将使太赫兹光非对称解复用器的最大开关比降低。     

激光放大器的稳定脉冲

本文求得了激光放大器速率方程的小信号解析解,分析了获得稳定脉冲的条件以及泵浦对脉冲放大变形的影响.     

皮秒类提升脉冲串的产生与传输

通过函数和变量变换给出变系数非线性薛定谔方程的一个新的精确解,它可以用来描述非均匀光纤中的调制不稳定过程.基于这个精确解我们给出一类新的类提升脉冲串,并讨论该脉冲串的传输特性.结果表明,当类提升脉冲串能量大于某一阈值时类提升脉冲串可以稳定传输.同时我们还比较指数控制系统和理想系统中类提升脉冲串的传输,结果表明选择合适的控制系统可以抑制脉冲间的相互作用,这对增加光通信的传输比特率是非常有益的.     

Quantum description of a dye laser threshold region

The renormalized Fokker-Planck equation for a dye laser is derived from the Liouvillevon Neuman equation and its stationary solution, as well as the numerically calculated line shapes and the noise spectra for the quantum threshold region are given. The calculations were performed for values of the laser parameters which enable to compare the semiclassical bistable solutions with the threshold and those without the threshold. A difference in the behavior of the line shapes in the threshold region for both cases are discussed.     

Product measures and dynamics for solid-on-solid interfaces

A two-species asymmetric exclusion process is considered with general transition rates subject only to the constraint of charge conservation. Conditions for the existence of a stationary product measure are found in both the cases of odd-even parallel dynamics and continuous-time dynamics. The results are then applied to a one-dimensional restricted solid-on-solid model, considered as a model of driven interfacial growth, showing a nontrivial dependence of the stationary measure on the external driving field. The dependence of the growth velocity on the slope of the interface is given and interface shapes in finite volume with opposite boundary conditions are investigated numerically     

Free vibration analysis of the completely free rectangular plate by the method of superposition

While the subject of free vibration analysis of the completely free rectangular plate has a history which goes back nearly two centuries it remains a fact that most theoretical solutions to this classical problem are considered to be at best approximate in nature. This is because of the difficulties which have been encountered in trying to obtain solutions which satisfy the free edge conditions as well as the governing differential equation. In a new approach to this problem, by using the method of superposition, it is shown that solutions which satisfy identically the differential equation and which satisfy the boundary conditions with any desired degree of accuracy are obtained. Eigenvalues of four digit accuracy are provided for a wide range of plate aspect ratios and modal shapes. Exact delineation is made between the three families of modes which are characteristic of this plate vibration problem. Accurate modal shapes are provided for the response of completely free square plates.     

Stationary perfect fluid solutions with differential rotation

In the framework of a class of metrics allowing for a timelike and a spacelike symmetries, usually referred to as stationary and axisymmetric gravitational fields, coupled to differentially rotating perfect fluids, the existing exact solutions to the corresponding Einstein equations are analyzed from the point of view of the fulfillment of the energy conditions and the existence of an axis of rotation. The main conclusion is that none of the reported exact solutions fulfills all these physical requirements, and at most, they can be thought of as stationary cyclic symmetric cosmological spacetimes.     

Modulational instability and envelope solutions of nonlinear dispersive wave equations

The nonlinear Schrödinger equation describing the evolution of the plane wave solutions of the Hirota equation and of the Boussinesq equation are obtained. The conditions for modulational instability and the localised stationary solutions are derived.     

Self-organization of two-dimensional waves in an active dispersive-dissipative nonlinear medium

We consider the pattern-formation dynamics of a two-dimensional (2D) nonlinear evolution equation that includes the effects of instability, dissipation, and dispersion. We construct 2D stationary solitary pulse solutions of this equation, and we develop a coherent structures theory that describes the weak interaction of these pulses. We show that in the strongly dispersive case, 2D pulses organize themselves into V shapes. Our theoretical findings are in good agreement with time-dependent computations of the fully nonlinear system.     

Reflections of Nonstationary Signals in Media with Intense Fluctuations of Irregularities

With the help of the invariant embedding method, we obtain an equation for the kernel of the backscattering operator and find numerically its solutions corresponding to the response of the medium to an incident delta-impulse. The statistical characteristics of reflections of such impulses are determined in the case of intense fluctuations of irregularities given the logarithmic derivative of the medium impedance is a continuous stationary centered Gaussian process with the unit variance and a finite correlation radius. We study the temporal evolution of the statistical distribution of reflected signals. Examples of reflections for various shapes of incident impulses are discussed.     

Free vibration of a circular plate elastically restrained along some radial segments

An analysis is presented for the free vibration of a circular plate restrained against deflection along radial segments. With the reaction forces acting on the segments regarded as unknown harmonic loads, the stationary response of the plate to these loads is expressed by the use of the Green function. The force distributions along the segments are expanded into Fourier series with unknown coefficients, and the homogeneous equations for the coefficients are derived by restraint conditions on the supports. The natural frequencies and the mode shapes of the plate are determined by calculating the eigenvalues and eigenvectors of the equations. The method is applied to circular plates supported along several radial segments located at equal angular intervals, the natural frequencies and the mode shapes of the plates are calculated numerically and the effect of the supports is discussed.     

Vortex structures with complex points singularities in two-dimensional Euler equations. New exact solutions

In this work we present a new class of exact stationary solutions for two-dimensional (2D) Euler equations. Unlike already known solutions, the new ones contain complex singularities. We consider point singularities which have a vector field index greater than 1 as complex. For example, the dipole singularity is complex because its index is equal to 2. We present in explicit form a large class of exact localized stationary solutions for 2D Euler equations with a singularity whose index is equal to 3. The solutions obtained are expressed in terms of elementary functions. These solutions represent a complex singularity point surrounded by a vortex satellite structure. We also discuss the motion equation of singularities and conditions for singularity point stationarity which provide the stationarity of the complex vortex configuration.