Propagation dynamics of dipole breathing wave in lossy nonlocal nonlinear media

In the framework of nonlinear wave optics,we report the evolution process of a dipole breathing wave in lossy nonlocal nonlinear media based on the nonlocal nonlinear Schr?dinger equation.The analytical expression of the dipole breathing wave in such a nonlinear system is obtained by using the variational method.Taking advantage of the analytical expression,we analyze the influences of various physical parameters on the breathing wave propagation,including the propagation loss and the input power on the beam width,the beam intensity,and the wavefront curvature.Also,the corresponding analytical solutions are obtained.The validity of the analysis results is verified by numerical simulation.This study provides some new insights for investigating beam propagation in lossy nonlinear media.     

Random-phase surface-wave solitons in nonlocal nonlinear media

We demonstrate, theoretically and experimentally, incoherent surface solitons in a noninstantaneous nonlocal nonlinear media. These incoherent surface waves are located at the interface between a nonlinear medium with long-range nonlocality and a linear dielectric medium (air).     

Elliptic incoherent accessible solitons in strongly nonlocal media

We study the propagation of elliptic incoherent accessible solitons in strongly nonlocal media with noninstantaneous Kerr nonlinearity. For this soliton to exist, the coherence properties of the incoherent beam should be anisotropic. The total power of the incident beam should also equal to a critical value which depend on the beam width as well as the coherence properties. When initial parameters of the beam do not satisfy the existence conditions, the elliptic incoherent accessible solitons will undergo linear harmonic oscillation in different states. Corresponding properties are studied in detail.     

强时间非局域系统中自相位调制诱导的“脉冲镜像”啁啾

非局域非线性是目前非线性光学乃至非线性科学研究领域的热点. 本文研究了时间非局域系统中的脉冲啁啾特性, 发现了一个非常有趣的现象：当系统的时间非局域程度很强时, 由自相位调制引起的非线性啁啾可以近似成为脉冲强度的“镜像”, 并且, 这种特性与脉冲包络的具体形式无关. 利用这种特性, 分析了脉冲在强时间非局域系统中传输的时间演化过程.     

Elliptic incoherent solitons in strongly nonlocal media with anisotropic Kerr nonlinearity

The propagation of elliptic incoherent beam in strongly nonlocal media with noninstantaneous anisotropic Kerr nonlinearity is systematically investigated. Using the mutual coherence function approach, we obtain the existence curve of such solitons and an interesting outcome: correlation characteristics of the elliptic incoherent solitons can be anisotropic as well as isotropic. When the existence conditions of solitons are not satisfied, the elliptic incoherent beam will undergo periodic oscillation. Nonstationary evolution behaviors of the elliptic beam are shown in detail by numerical calculation. It is also obtained that the oscillation periods of the beam in x and y direction are different and the elliptic beam will become circular at some propagation distance under special conditions.     

The nonlinear Schrödinger equation and the propagation of weakly nonlinear waves in optical fibers and on the water surface

The dynamics of waves in weakly nonlinear dispersive media can be described by the nonlinear Schrödinger equation (NLSE). An important feature of the equation is that it can be derived in a number of different physical contexts; therefore, analogies between different fields, such as for example fiber optics, water waves, plasma waves and Bose–Einstein condensates, can be established. Here, we investigate the similarities between wave propagation in optical Kerr media and water waves. In particular, we discuss the modulation instability (MI) in both media. In analogy to the water wave problem, we derive for Kerr-media the Benjamin–Feir index, i.e. a nondimensional parameter related to the probability of formation of rogue waves in incoherent wave trains.     

时空非相干光孤子的传播和相干特性

研究了时空非相干椭圆形高斯光束在饱和对数型非线性介质中的自陷行为,得到了孤子的形成条件并分析了其相干特性,讨论了光束自陷的变化形式,发现光束的初态和材料非线性对其有决定性的影响, 并进一步获得了光束半径和光束相干半径的解析表达式,发现光束的相干特性不但会随传播距离产生周期性的变化,且随组份频率的增大而减弱.     

Incoherent solitons in strongly nonlocal media: The coherent density theory

We study the properties of one dimension incoherent accessible solitons in strongly nonlocal media with noninstantaneous Kerr nonlinearity. Following the coherent density theory, we obtain an exact solution of such incoherent solitons. The spatial width of the incoherent solitons is related to the incoherent angular power spectrum θ₀ as well as the incident power. The evolution properties of the intensity profile and the coherence characteristics are also discussed in detail when the solitons undergo periodic harmonic oscillation.     

Modulation instability of incoherent beams in noninstantaneous nonlinear media

We show that modulation instability can exist with partially spatially incoherent light beams in a noninstantaneous nonlinear environment. For such incoherent modulation instability to occur, the value of the nonlinearity has to exceed a threshold imposed by the degree of spatial coherence.     

Wave characteristics of single-walled fluid-conveying carbon nanotubes subjected to multi-physical fields

Wave propagation in single-walled carbon nanotubes (SWCNTs) conveying fluids and placed in multi-physical fields (including magnetic and temperature fields) is studied in this paper. The nanotubes are modelled as Timoshenko beams. Based on the nonlocal beam theory, the governing equations of motion are derived using Hamilton's principle, and then solved by Galerkin approach, leading to two second-order ordinary differential equations (ODEs). Numerical simulations are carried out to verify the analytical model proposed in the present study, and determine the influences of the nonlocal parameter, the fluid velocity and flow density, the temperature and magnetic field flux change, and the surrounding elastic medium on the wave behaviour of SWCNTs. The results show that the nonlocal parameter has a considerable influence on dynamic behaviour of the nanotube and the fluid flow inside it. The results also show that the magnetic and temperature fields play an important role on the wave propagation characteristics of SWCNTs.     

Waveguides formed by incoherent dark solitons

We demonstrate experimentally optical guidance of coherent light beams, using incoherent light. Such guidance is made possible by generation of partially spatially incoherent self-trapped dark beams (dark incoherent solitons) in a noninstantaneous nonlinear medium. In the one-dimensional case, the incoherent solitons induce single and Y-junction planar waveguides, whereas in the two-dimensional case, they form circular waveguides. These experiments introduce the possibility of controlling high-power laser beams with low-power incoherent light sources such as LED's or lightbulbs.     

Interaction of Nonlocal Incoherent White-Light Solitons

The propagation and interaction of nonlocal incoherent white-light solitons in strongly nonlocal kerr media is investigated. Numerical simulations show that the interaction properties of nonlocal incoherent white-light solitons are different from the case in local media. The interactions of nonlocal incoherent white-light solitons are always attractive independent of their relative phase, while the other parameters such as the extent of nonlocality and the input power have a great impact on the soliton interactions. Pertinent numerical examples are presented to show their propagation and interaction behaviour further.     

Propagations of Fresnel diffraction accelerating beam in Schrödinger equation with nonlocal nonlinearity

Accelerating beams have been the subject of extensive research in the last few decades because of their self-acceleration and diffraction-free propagation over several Rayleigh lengths. Here, we investigate the propagation dynamics of a Fresnel diffraction beam using the nonlocal nonlinear Schrödinger equation (NNLSE). When a nonlocal nonlinearity is introduced into the linear Schrödinger equation without invoking an external potential, the evolution behaviors of incident Fresnel diffraction beams are modulated regularly, and certain novel phenomena are observed. We show through numerical calculations, under varying degrees of nonlocality, that nonlocality significantly affects the evolution of Fresnel diffraction beams. Further, we briefly discuss the two-dimensional case as the equivalent of the product of two one-dimensional cases. At a critical point, the Airy-like intensity profile oscillates between the first and third quadrants, and the process repeats during propagation to yield an unusual oscillation. Our results are expected to contribute to the understanding of NNLSE and nonlinear optics.     

Gerdjikov-Ivanov方程的精确解

研究在量子场理论、弱非线性色散水波、非线性光学等领域中出现的Gerdjikov-Ivanov方程.对Gerdjikov-Ivanov方程的研究会导出具有高次非线性项的非线性数学物理方程.选取Liénard方程作为辅助常微分方程,借助于它并根据齐次平衡原则,求解了Gerdjikov-Ivanov方程,得到了该方程的包络孤立波解和包络正弦波解. 关键词： 齐次平衡原则 F展开法 Gerdjikov-Ivanov方程 包络孤立波解     

Incoherent spatial optical solitons in photorefractive crystals

In this paper we have presented a theoretical investigation on the propagation properties of incoherent solitons in photorefractive media which is characterized by noninstantaneous saturating nonlinearity. Using mutual coherence function approach, we have obtained the equation of existence curve for such solitons. We have discussed the coherence characteristics of these solitons. We have found that solitons with a particular radius can possess two different critical powers. The dynamical evolution of these solitons has been discussed in detail by both analytical and numerical simulation.     

Transmission of images through highly nonlinear media by gradient-index lenses formed by incoherent solitons

We experimentally demonstrate image transmission through a noninstantaneous self-focusing medium. A partially spatially incoherent soliton is used to form a multimode waveguide in a photorefractive crystal, and the modes of that waveguide are used to transmit an incoherent image through this nonlinear medium.     

Nonlinear bandgap properties in a nonlocal piezoelectric phononic crystal nanobeam

Applying nonlocal elasticity theory, von Kármán type nonlinear strain-displacement relation and plane wave expansion (PWE) method to Euler-Bernoulli beam, the calculation method of band structure of a nonlinear nonlocal piezoelectric phononic crystal (PC) nanobeam is proposed and formulized. In order to investigate the properties of wave propagating in the nanobeam in detail, band gaps of first four orders are picked, and the corresponding influence rules of electro-mechanical coupling fields, nonlocal effect and geometric parameters on band gaps are studied. During the researches, external electrical voltage and axial force are chosen as the influencing parameters related to electro-mechanical coupling fields. Scale coefficient is chosen as the influencing parameter corresponding to nonlocal effect. Length ratio between materials PZT-4 and epoxy and height-width ratio are chosen as the influencing parameters of geometric parameters. Moreover, all the influence rules are compared to those in linear nanobeam. The results are expected to be of help for the design of micro and nano devices based on piezoelectric periodic nanobeam.