Modulational Instability in a Pair of Non-identical Coupled Nonlinear Electrical Transmission Lines

In this work, we investigate the dynamics of modulated waves non-identical coupled nonlinear transmission lines. Traditional methods for avoiding mode mixing in identical coupled nonlinear electrical lines consist of adding the same number of linear inductors in each branch. Adding linear inductors in a single line leads to asymmetric coupled nonlinear electrical transmission lines which propagate the signal and the mode mixing. On one hand, the difference between the two lines induced the fission for only one mode of propagation. This fission is influenced by the amplitude of the signal and the amount of the input energy as well; it also narrows the width of the input pulse soliton, leading to a possible increasing of the bit rate. On the other hand, the dissymmetry of the two lines converts the network into a good amplifier for the ω_ mode which corresponds to the regime admitting low frequencies.     

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。     

Effects of Line Parameters on Soliton-Like Propagation in Nonlinear Transmission Lines: Application to the Optimization of Frequency Triplers

In this paper, soliton propagation in nonlinear transmission lines (NLTLs) periodically loaded with heterostructure barrier varactors is studied. From the lumped element equivalent circuit of the line we have analyzed the influence of transmission line parameters (i.e, per-section inductance and capacitance) on soliton propagation characteristics. It is shown that by increasing these parameters, a faster separation of input signals into solitons is achieved. From the point of view of NLTL harmonic generation, this gives additional flexibility to optimize multiplier performance by appropriate circuit design. These conclusions are supported from the analysis of a frequency tripler, where device losses are included.     

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.     

光时分复用准线性传输系统的非线性相互作用

研究了高速色散控制准线性传输系统中的信道内交叉相位调制和信道内四波混频等非线性相互作用,分析了信道内交叉相位调制导致定时抖动和信道内四波混频导致振幅抖动随距离和色散分布强度变化的规律,然后运用快速傅里叶变换法分析了信道内交叉相位调制导致的2^5-1的伪随机码流的定时抖动和振幅抖动及寄生脉冲的产生．证实了理论分析。最后通过数值模拟实现了色散分布强度为127的强色散控制系统中准线性脉冲序列1600km的稳定传输,结论对用标准单模光纤实现高速传输具有重要意义。     

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.     

Nonlinear Topological Effects in Optical Coupled Hexagonal Lattice

Topological physics in optical lattices have attracted much attention in recent years. The nonlinear effects on such optical systems remain well-explored and a large amount of progress has been achieved. In this paper, under the mean-field approximation for a nonlinearly optical coupled boson–hexagonal lattice system, we calculate the nonlinear Dirac cone and discuss its dependence on the parameters of the system. Due to the special structure of the cone, the Berry phase (two-dimensional Zak phase) acquired around these Dirac cones is quantized, and the critical value can be modulated by interactions between different lattices sites. We numerically calculate the overall Aharonov-Bohm (AB) phase and find that it is also quantized, which provides a possible topological number by which we can characterize the quantum phases. Furthermore, we find that topological phase transition occurs when the band gap closes at the nonlinear Dirac points. This is different from linear systems, in which the transition happens when the band gap closes and reopens at the Dirac points.     

Nonlinear Saturation Amplitude in Classical Planar Richtmyer–Meshkov Instability

The classical planar Richtmyer–Meshkov instability(RMI) at a fluid interface supported by a constant pressure is investigated by a formal perturbation expansion up to the third order,and then according to definition of nonlinear saturation amplitude(NSA) in Rayleigh–Taylor instability(RTI),the NSA in planar RMI is obtained explicitly.It is found that the NSA in planar RMI is affected by the initial perturbation wavelength and the initial amplitude of the interface,while the effect of the initial amplitude of the interface on the NSA is less than that of the initial perturbation wavelength.Without marginal influence of the initial amplitude,the NSA increases linearly with wavelength.The NSA normalized by the wavelength in planar RMI is about 0.11,larger than that corresponding to RTI.     

Modulational Instability of Dust Ion Acoustic Waves in a Collisional Dusty Plasma

The modulational instability of dust ion acoustic waves in a dust plasma with ion-dust collision effects is studied. Using the perturbation method, a modified nonlinear Schrodinger equation contains a damping term that comes from the effect of the ion-dust collision is derived. It is found that the inclusion of the ion-dust collision would modify the modulational instability of the wave packet and could not admit any stationary envelope solitary waves.     

Optimization of Nonlinear Transmission Lines for Harmonic Generation: The Role of the Capacitance-Voltage Characteristic and the Area Effect

In this paper, nonlinear transmission lines (NLTLs) periodically loaded with symmetric voltage dependent capacitances are investigated by means of computer simulation. Specifically, we have studied the role that the C-V characteristic plays on the performance of NLTLs as frequency multipliers. The main conclusion of the work is that the area under the C(V) curve is a key parameter for the optimization of conversion efficiency. This result is interpreted on the basis of soliton like propagation in NLTLs.     

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.     

Modulational Instability of Dust Ion Acoustic Waves in a Collisional Dusty Plasma

The modulational instability of dust ion accoustic waves in a dust plasma with ion-dust collision effects is studied.Using the perturbation method,a modified nonlinear Schroedinger equation contains a damping term that comes from the effect of the ion-dust collision is derived.It is found that the inclusion of the ion-dust collision would modify the modulational instability of the wave packet and could not admit any stationary envelope solitary waves.     

Modulational Instability and Energy Localization in a Chain of Interacting Frenkel Excitons

The modulational instability in one-dimensional molecule chain of interacting Frenkel excitons is investigated. The formation of localized modes via modulational instability is predicted and the previous numerical and analytical results are explained. The Peierls-Nabarro (PN) potential barrier for the localized modes is also discussed.     

非线性孪相干态的光子统计性质

利用f振子的湮没算符和产生算符的逆算符的性质，得到了SU(1，1)李代数的两个双模非厄密实现，在此基础上引入了两种非线性孪相干态，并讨论了它们的光子统计性质和相位特性。     

Generalized Darboux Transformations,Rogue Waves,and Modulation Instability for the Coherently Coupled Nonlinear Schrödinger Equations in Nonlinear Optics

Nonlinear optics plays a central role in the advancement of optical science and laser‐based technologies. The second‐order rogue‐wave solutions and modulation instability for the coherently coupled nonlinear Schrödinger equations with the positive coherent coupling in nonlinear optics are reported in this paper. Generalized Darboux transformations for such coupled equations are derived, with which the second‐order rational solutions for the purpose of modelling the rogue waves are obtained. With respect to the slowly‐varying complex amplitudes of two interacting optical modes, it is observed that 1) number of valleys of the second‐order rogue waves increases and peak value of the second‐order rogue wave decreases first and then increases; 2) single‐hump second‐order rogue wave turns into the double‐hump second‐order rogue wave; 3) single‐hump bright second‐order rogue wave turns into the dark second‐order rogue wave and finally becomes the three‐hump bright second‐order rogue wave. Meanwhile, baseband modulation instability through the linear stability analysis is seen.     

A Solvable Model in Two—Dimensional Gravity Coupled to a Nonlinear Matter Field

The two-dimensional gravity model with a coupling constant k=4 and a vanishing cosmological constant coupled to a nonlinear matter field is investigated.We found that the classical equations of motion are exactly solvable and the static solutions of the induced metric and scalar curvature can be obtained analytically.These soulutions may be used to describe the naked singularity at the origin.     

掺锗硅基高非线性光纤超连续光源研究

利用非线性偏振旋转锁模掺铒光纤激光器和1100m长的掺锗硅基高非线性光纤制作了超连续光源,获得了从1150～1750nm的超宽带输出光谱,其中1150～1350nm波段光谱起伏小于3dB,1600～1700nm波段平坦度优于1dB,并有很好的向长波延展空间。光谱展宽的机理为孤子分裂与受激拉曼散射,而四波混频使光谱进一步展宽。     

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.