具有高阶色散项的交叉相位调制不稳定性分析

以包含了三、四阶色散项的耦合非线性薛定谔方程为基础,重点研究了三、四阶色散对交叉相位调制不稳定性的影响。结果表明：三阶色散对调制不稳定性不起作用;当满足一定条件时,由于四阶色散的影响,不仅在光纤的反常色散区,而且在光纤的正常色散区,交叉相位所致的调制不稳定性均发生在两个频谱区。当光纤各参量及两束入射光波功率一定时,光纤反常色散区第一区域的增益谱要比正常色散区第一区域的增益谱宽;同时,反常色散区第二区域的增益谱比正常色散区第二区域的增益谱更靠近零点;进一步对比反、正常色散区的这两个频谱区,发现两个频谱区的范围有确定的对应关系。     

Modulational Instability of Spinor Condensates in an Optical Lattice

We obtain analytically the static states and corresponding collective-excitation spectra of a quasi-onedimensional spin-1 condensate modulated by a long-wavelength optical lattice in the weak lattice limit. It is demonstrated that both ferromagnetic and antiferromagnetic condensates may exhibit dynamical instability, which agree with the results with numerical simulation. In the homogeneous limit, our results reduce to the previous results for homogeneous spinor condensates, i.e., dynamical instability can occur only for ferromagnetic interaction and an antiferromagnetic condensate is always dynamically stable.     

Statistical Approach of Modulational Instability in the Class of Derivative Nonlinear Schrödinger Equations

The modulational instability (MI) in the class of NLS equations is discussed using a statistical approach (SAMI). A kinetic equation for the two-point correlation function is studied in a linear approximation, and an integral stability equation is found. The modulational instability is associated with a positive imaginary part of the frequency. The integral equation is solved for different types of initial distributions (δ-function, Lorentzian) and the results are compared with those obtained using a deterministic approach (DAMI). The differences between MI of the normal NLS equation and derivative NLS equations is emphasized. PACS: 05.45.     

准二维光学系统的调制不稳定性分析

本文利用时间相关的变分法对准二维的非线性薛定谔方程平面波的调制不稳定性进行了研究。在拉格朗日变分的框架下推导出相与振幅的演化方程,进而对线性化扰动方程的解进行了数值模拟,直观地展示了平面波的调制不稳定性。最后通过对能量方程有效势的分析,严格地得到了平面波解调制不稳定的判断准则。     

零色散附近的交叉相位调制不稳定性分析

以三、四阶色散项的耦合非线性薛定谔方程为基础,考虑光纤损耗及高阶色散,研究了双光束在零色散附近的交叉相位调制不稳定性.理论上导出描述交叉相位调制不稳定性的色散方程,并进行数值模拟计算.结果表明：由于四阶色散的影响,在光纤的正常、反常色散区,交叉相位调制不稳定性均发生在两个频谱区.如光脉冲工作在最小群速度色散附近时,四阶色散对光纤的交叉相位调制不稳定性将起决定性作用,可使增益谱出现一个新的峰值.光纤损耗使增益的谱宽变窄.对给定的传输距离,随着光纤向零色散附近靠近,两个频谱区谱宽增加直到相互重叠.数值分析了两光波有差别时的交叉相位调制不稳定性.     

Magneto‐Modulational Instability in Relativistic Plasmas

The behavior of magnetic fields generated by high frequency transverse plasmons in relativistic plasmas can be described by a set of nonlinear coupling equations, which has considered the nonlinear wave–wave, wave– particle interactions and the relativistic effects of electrons. Modulational instability of the spontaneous magnetic fields is investigated on the basis of the nonlinear coupling equations. Analytical and numerical results indicate the self‐generated magnetic fields are modulationally unstable and will be localized in a narrow region. The characteristic scale and maximum growth rate of the magnetic fields depend on the average Lorentz factor of electrons and the energy density of transverse plasmons. The relativistic effects of electrons will enhance the self‐focusing of magnetic fields (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modulational Instability of Ion-Acoustic Waves in a Warm Plasma with a Relativistic Electron Beam

The modulational instability of ion-acoustic wave in a collisionless, unmagnetized plasma consisting ofwarm ions, hot isothermal electrons, and relativistic electron beam is studied. A modified nonlinear Schrodinger equationincluding one additional term that comes from the effect of relativistic electron beam is derived. It is found that theinclusion of a relativistic electron beam would modify the modulational instability of the wave packet and could notadmit any stationary soliton waves.     

Stationary States and Modulational Instability of Coupled Two-Component Bose-Einstein Condensates in a Ring Trap

We investigate modulational instability (MI) of a coupled two-component Bose-Einstein condensates in a rotating ring trap. The excitation spectrum and the MI condition of the system are presented analytically. We find that the coupling between the two components strongly modifies the MI condition, and the MI condition is phase-dependent. Furthermore, we discuss the effect of MI on both density excitation and spin excitation. If the inter- and intra-component interaction strengths are all equal, the MI causes density excitation but not spin excitation, and if the inter- and intra-component interaction strengths are different, the MI causes both density excitation and spin excitation. Our results provide a promising approach for controlling the stability and excitation of a rotating two-component Bose-Einstein condensates by modulating its coupling strength and interaction strength.     

包含高阶色散的色散缓变光纤中交叉相位调制不稳定性分析

从包含高阶色散的广义非线性薛定谔方程出发,得到了色散缓变光纤中交叉相位调制不稳定增益谱,研究了增益谱随入射功率及光纤纵向色散参量的变化关系.结果表明：由于四阶色散的影响,在色散缓变光纤的正、反常色散区,交叉相位调制不稳定均发生在两个频谱区.反常色散区两频谱区宽度均比正常色散区宽,且反常色散区第二频谱区更靠近零点,说明色散缓变光纤中交叉相位调制不稳定更容易发生在反常色散区.增益谱宽都随两入射光波功率比值的增加而增大.色散缓变光纤中交叉相位调制不稳定增益谱宽比常规光纤的宽,且随着光纤纵向色散参量μ的增大色散缓变光纤中交叉相位调制不稳定越来越明显.     

Modulational instability for a self-attractive two-component Bose--Einstein condensate

By means of the multiple-scale expansion method, the coupled nonlinear Schr?dinger equations without an explicit external potential are obtained in two-dimensional geometry for a self-attractive Bose-Einstein condensate composed of different hyperfine states. The modulational instability of two-component condensate is investigated by using a simple technique. Based on the discussion about two typical cases, the explicit expression of the growth rate for a purely growing modulational instability and the optimum stable conditions are given and analysed analytically. The results show that the modulational instability of this two-dimensional system is quite different from that in a one-dimensional system.     

Modulational instability of ion—acoustic waves in a warm plasma

Using the standard reductive perturbation technique,a nonlinear Schroedinger equation is derived to study the modulational instability of finite-amplitude ion-acoustic waves in a non-magnetized warm plasma.It is found that the inclusion of ion temperature in the equation modifies the nature of the ion-acoustic wave stability and the soliton stuctures.The effects of ion plasma temperature on the modulational stability and ion-acoustic wave properties are inestigated in detail.     

变分法研究二维光晶格中玻色-爱因斯坦凝聚的调制不稳定性

利用含时变分法研究了二维光晶格中准二维玻色-爱因斯坦凝聚中的调制不稳定性. 在平均场近似下, 由准二维Gross-Pitaevskii方程出发, 利用变分法给出了调制波振幅和相位所满足的时间演化方程, 通过求解时间演化方程和能量分析法给出了发生调制不稳定性的条件, 决定于平面波振幅, 晶格强度, 调制波的波矢量和原子之间的两体相互作用.     

Modulational instability of incoherently coupled beams in azobenzene-containing polymer with photoisomerization nonlinearity

The modulational instability of two incoherently coupled beams in azobenzene-containing polymer with photoisomerization nonlinearity is investigated analytically and numerically. Our results show that as a precursor to spatial optical soliton formation, modulational instability can be adjusted and controlled by the wavelength combinations of the signal and background beams. We also discuss the dependences of strength of modulational instability on intensities of two signal beams and background beam. These findings make it possible to predict the formation of incoherently coupled soliton pairs in azobenzene-containing polymer.     

光晶格中双组分玻色-爱因斯坦凝聚系统的调制不稳定性

利用线性稳定分析的方法,在不满足原子流相等的条件下,对光晶格中双组分玻色-爱因斯坦凝聚原子(BEC)系统的调制不稳定性区域与不同BEC组分的波长和不同的调制波长,以及两组分BEC间相互作用大小之间的关系进行了研究.结果显示,光晶格中双组分BEC系统的调制稳定性的区域在不满足原子流相等的条件下,随不同的波长,不同的调制和相互作用之间的大小会出现了较大的变化.相应结果可为实际应用中如何操控双组分BEC提供有用的信息.     

Modulational instability of a weakly relativistic ion acoustic wave in a warm plasma with nonthermal electrons

An investigation has been made of modulational instability of a nonlinear ion acoustic wave in a weakly relativistic warm unmagnetized nonthermal plasma whose constituents are an inertial ion fluid and nonthermally distributed electrons. Up to the second order of the perturbation theory, a nonlinear Schr?dinger type (NST) equation for the complex amplitude of the perturbed ion density is obtained. The coefficients of this equation show that the relativistic effect, the finite ion temperature and the nonthermal electrons modify the condition of the modulational stability. The association between the small-wavenumber limit of the NST equation and the oscillatory solution of the Korteweg－de Varies equation, obtained by a reductive perturbation theory, is satisfied.     

光晶格中双组分偶极玻色-爱因斯坦凝聚体的调制不稳定性

利用线性稳定性分析的方法,对光晶格中双组分偶极玻色-爱因斯坦凝聚体(Bose-Einstein condensates,简称BECs)的调制不稳定性进行了研究.得到了光晶格中双组分偶极BECs原子系统调制不稳定性区域的分布与在位相互作用和由偶极-偶极相互作用所导致的格点间BECs相互作用之间的关系.结果显示,格点间BECs的相互作用对光晶格中双组分偶极BECs的调制不稳定性有较大的影响,这可为实际应用中如何操控双组分偶极BECs提供有用的信息. 关键词： 光晶格 双组分玻色-爱因斯坦凝聚体 调制不稳定性 偶极-偶极相互作用     

Modulational instability of dust-ion-acoustic waves in pair-ion plasma having non-thermal non-extensive electrons

The modulational instability (MI) criteria of dust-ion-acoustic (DIA) waves (DIAWs) have been investigated in a four-component pair-ion plasma having inertial pair ions, inertialess non-thermal non-extensive electrons, and immobile negatively charged massive dust grains. A nonlinear Schrödinger equation (NLSE) is derived by using reductive perturbation method. The nonlinear and dispersive coefficients of the NLSE can predict the modulationally stable and unstable parametric regimes of DIAWs and associated first and second-order DIA rogue waves (DIARWs). The MI growth rate and the configuration of the DIARWs are examined, and it is found that the MI growth rate increases (decreases) with increasing the number density of the negatively charged dust grains in the presence (absence) of the negative ions. It is also observed that the amplitude and width of the DIARWs increase (decrease) with the negative (positive) ion mass. The implications of the results to laboratory and space plasmas are briefly discussed.     

五阶非线性下零色散附近的调制不稳定性

在同时考虑光纤损耗、高阶色散以及高阶非线性情况下,从广义非线性薛定谔方程出发,研究了零色散附近的调制不稳定性,分析了四阶色散和五阶非线性对增益谱的影响.结果表明：当光脉冲工作在零色散附近时,四阶色散对调制不稳定性起决定作用,它使反常色散区的增益谱变宽.在光纤正常色散区,正（负）五阶非线性使增益谱的谱宽和峰值增大（减小）;但在反常色散区,五阶非线性仅改变增益谱的峰值,几乎不影响谱宽.     

Exciton-phonon interaction in Y2O3 and Sc2O3 thin films

An investigation is made of the fundamental absorption edge of Y₂O₃ thin films. Based on its temperature dependence the exciton-phonon interaction is studied, which makes it possible to interpret the absorption edge as the absorption of self-localized excitons. A number of parameters of the energy spectrum of the investigated films are determined. I. Franko State University, 50, Dragomanov St., L'vov, 290005, Ukraine. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 66, No. 1, pp. 132–134, January–February, 1999.     

Instability of Interacting Ghost Dark Energy Model in an Anisotropic Universe

A new dark energy model called “ghost dark energy” was recently suggested to explain the observed accelerating expansion of the universe. This model originates from the Veneziano ghost of QCD. The dark energy density is proportional to Hubble parameter, ρ _Λ = α H, where α is a constant of order \({\Lambda }^{3}_{QCD}\) and Λ _{Q C D} ～ 100M e V is QCD mass scale. In this paper, we investigate about the stability of generalized QCD ghost dark energy model against perturbations in the anisotropic background. At first, the ghost dark energy model of the universe with spatial BI model with/without the interaction between dark matter and dark energy is discussed. In particular, the equation of state and the deceleration parameters and a differential equation governing the evolution of this dark energy model are obtained. Then, we use the squared sound speed \({v_{s}^{2}}\) the sign of which determines the stability of the model. We explore the stability of this model in the presence/absence of interaction between dark energy and dark matter in both flat and non-isotropic geometry. In conclusion, we find evidence that the ghost dark energy might can not lead to a stable universe favored by observations at the present time in BI universe.