Solitary waves in a binary nonlinear waveguide array

Based on the coupled-mode theory, the propagation of light pulses is studied analytically for a system of an infinite number of tunnel-coupled parallel equidistant waveguides of optically nonlinear materials; in the considered system, waveguides with a positive refractive index alternate with waveguides with a negative refractive index. Partial solutions to a system of nonlinear equations describing the evolution of these pulses are found in the case in which fields in adjacent waveguides differ only in the phase factor. For a solitary wave formed by coupled wave packets localized each in its own waveguide, these solutions describe the stationary propagation in a definite direction. It is shown that the coupling strength between waveguides has an effect on the propagation rate of the obtained stationary pulses.     

Analysis of the coupling of two non-parallel dielectric rod waveguides

In this paper the coupling between two closely spaced single mode dielectric rod waveguides is investigated when the corresponding propagation axes are not in the same plane. An approximate analysis is presented by assuming only first order interaction between the guided waves. For a given incident HE₁₁ mode (in one of the rod waveguides) the coupled wave amplitudes are computed in the other waveguide for both propagation directions. Numerical results are presented for several coupling geometries.     

Interactions of discrete solitons with structural defects

We investigated the interaction of discrete solitons with defect states fabricated in arrays of coupled waveguides. We achieved attractive and repulsive defects by decreasing and increasing, respectively, the spacing of one pair of waveguides in an otherwise uniform array. Linear and nonlinear propagation in the same samples show distinctly different properties. The role of the Peierls-Nabarro potential in the interaction of the soliton with the defect is discussed.     

Propagation and modulational instability of Rossby waves in stratified fluids

Perturbation analysis and scale expansion are used to derive the (2+1)-dimensional coupled nonlinear Schrödinger (CNLS) equations that can describe interactions of two Rossby waves propagating in stratified fluids. The (2+1)-dimensional equations can reflect and describe the wave propagation more intuitively and accurately. The properties of the two waves in the process of propagation can be analyzed by the solution obtained from the equations using the Hirota bilinear method, and the influence factors of modulational instability are analyzed. The results suggest that, when two Rossby waves with slightly different wave numbers propagate in the stratified fluids, the intensity of bright soliton decreases with the increases of dark soliton coefficients. In addition, the size of modulational instable area is related to the amplitude and wave number in y direction.     

Localized Optical Waves in Defocusing Regime of Negative-Index Materials

We study optical localized waves on a plane-wave background in negative-index materials governed by the defocusing nonlinear Schrodinger equation with self-steepening effect. Important characteristics of localized waves,such as the excitations, transitions, propagation stability, and mechanism, are revealed in detail. An intriguing sequential transition that involves the rogue wave, antidark-dark soliton pair, antidark soliton and antidark soliton pair can be triggered as the self-steepening effect attenuates. The corresponding phase diagram is established in the defocusing regime of negative-index materials. The propagation stability of the localized waves is confirmed numerically. In particular, our results illuminate the transition mechanism by establishing the exact correspondence between the transition and the modulation instability analysis.     

Localized waves in three-component coupled nonlinear Schrdinger equation

We study the generalized Darboux transformation to the three-component coupled nonlinear Schr ¨odinger equation.First-and second-order localized waves are obtained by this technique.In first-order localized wave,we get the interactional solutions between first-order rogue wave and one-dark,one-bright soliton respectively.Meanwhile,the interactional solutions between one-breather and first-order rogue wave are also given.In second-order localized wave,one-dark-one-bright soliton together with second-order rogue wave is presented in the first component,and two-bright soliton together with second-order rogue wave are gained respectively in the other two components.Besides,we observe second-order rogue wave together with one-breather in three components.Moreover,by increasing the absolute values of two free parameters,the nonlinear waves merge with each other distinctly.These results further reveal the interesting dynamic structures of localized waves in the three-component coupled system.     

Nonlinear band gap transmission in optical waveguide arrays

The effect of nonlinear transmission in coupled optical waveguide arrays is theoretically investigated and a realistic experimental setup is suggested. The beam is injected in a single boundary waveguide, linear refractive index of which (n(0)) is larger than refractive indexes (n) of other identical waveguides in the array. Particularly, the effect holds if omega(n(0)-n)/c>2Q, where Q is a linear coupling constant between array waveguides, omega is a carrier wave frequency, and c is a light velocity. Numerical experiments show that the energy transfers from the boundary waveguide to the waveguide array above a certain threshold intensity of the injected beam. This effect is due to the creation and the propagation of gap solitons in full analogy with a similar phenomenon in sine-Gordon lattice [Phys. Rev. Lett. 89, 134102 (2002)]].     

A waveguide amplifier based on a counterdirectional coupler

The propagation of continuous-wave radiation in tunnel-coupled waveguides, one of which is characterized by a negative refraction and linear losses while the other is made of an ordinary dielectric and represents a linear amplifier, is analyzed theoretically. We found that, in the case of linear waveguides, the losses can be compensated at certain values of the pump-wave amplitude depending on values of the gain and loss coefficients in the corresponding waveguides, resulting in the amplification of radiation at the output of the waveguide with the negative refraction. The Kerr nonlinearity of the amplifying waveguide prevents the compensation of losses due to the violation of the phase-matching condition between the coupled waves in a counterdirectional coupler.     

Talbot solitons

We propose a new type of scalar wave-mixing optical solitons, Talbot solitons. The soliton consists of sinusoidal and uniform components that are mutually coherent and jointly trapped in one direction. The intensity structure of the soliton oscillates in the propagation direction as a result of the linear Talbot effect and periodic nonlinear energy exchange between the components. Talbot solitons induce a 1D waveguide and a 2D photonic lattice within the waveguide that may be used for quasi-phase matching of frequency conversion and as a tunable waveguide filter.     

弯折波导杆的超声斜入射方法*

波导杆技术是一种有效的超声辅助检测方法,在提升高温关键承压设备安全运行方面具有重要作用。现有的波导换能器因直入式发射声波,常被用来在线监测壁厚的腐蚀进程,难以对指定方向的缺陷进行有效检测。为了解决这个难题,基于斯涅耳定理以及导波的频散特性提出了一种弯折结构的波导杆来实现超声斜入射。首先分析了弯折波导杆中水平剪切波的传播特性,探究了波导杆的厚度、弯折角度对杆中声波传播的影响规律;然后,进一步研究了弯折波导杆在半无限空间内的声束指向性;最后通过一对弯折波导杆在线检测结构内部缺陷的试验证明了波导超声斜入射的应用价值。研究结果为基于斜入射技术的波导超声在线监测提供了坚实的理论基础。     

Localized waves of the coupled cubic–quintic nonlinear Schrdinger equations in nonlinear optics

We investigate some novel localized waves on the plane wave background in the coupled cubic–quintic nonlinear Schr o¨dinger(CCQNLS) equations through the generalized Darboux transformation(DT). A special vector solution of the Lax pair of the CCQNLS system is elaborately constructed, based on the vector solution, various types of higherorder localized wave solutions of the CCQNLS system are constructed via the generalized DT. These abundant and novel localized waves constructed in the CCQNLS system include higher-order rogue waves, higher-order rogues interacting with multi-soliton or multi-breather separately. The first-and second-order semi-rational localized waves including several free parameters are mainly discussed:(i) the semi-rational solutions degenerate to the first-and second-order vector rogue wave solutions;(ii) hybrid solutions between a first-order rogue wave and a dark or bright soliton, a second-order rogue wave and two dark or bright solitons;(iii) hybrid solutions between a first-order rogue wave and a breather, a second-order rogue wave and two breathers. Some interesting and appealing dynamic properties of these types of localized waves are demonstrated, for example, these nonlinear waves merge with each other markedly by increasing the absolute value of α.These results further uncover some striking dynamic structures in the CCQNLS system.     

Controlling soliton refraction in optical lattices

We show in the framework of the 1D nonlinear Schr?dinger equation that the value of the refraction angle of a fundamental soliton beam passing through an optical lattice can be controlled by adjusting either the shape of an individual waveguide or the relative positions of the waveguides. In the case of the shallow refractive index modulation, we develop a general approach for the calculation of the refraction angle change. The shape of a single waveguide crucially affects the refraction direction due to the appearance of a structural form factor in the expression for the density of emitted waves. For a lattice of scatterers, wave-soliton interference inside the lattice leads to the appearance of an additional geometric form factor. As a result, the soliton refraction is more pronounced for the disordered lattices than for the periodic ones.     

Bright spatial solitons in controlled negative phase metamaterials

A fundamental discussion of linearly polarised bright spatial soliton beams that are localised in a planar waveguide is developed in a special way that leads to the introduction of nonlinear diffraction. It is emphasised, throughout, that this kind of diffraction dominates influences from non-paraxiality and typical quintic contributions to the nonlinearity. A major discussion is given that is based upon double-negative metamaterials and makes contact with previous literature. Both homogeneous and inhomogeneous diffraction-managed, planar waveguides are investigated with a view to examining the behaviour of narrow beam production and propagation. It is also shown that a Voigt configuration of an externally applied magnetic field can be used to create significant magnetooptic control over spatial soliton propagation in asymmetric waveguides. Both this type of control and diffraction-management lie at the heart of the numerical simulations given here. In all of these cases it is shown that nonlinear diffraction has a very important influence and will create an impact upon future applications.     

Application of the local mode theory to nonlinear waveguides

Local mode theory for two counterpropagating waves in nonlinear waveguides is formulated. This model allows us to describe the transverse effects as well as the counterpropagating waves interaction in optical waveguides. The results are applied to the analysis of the nonlinear Fabry-Perot waveguide resonator and are compared with the conventional coupled mode theory solution.     

Integrability Aspects and Soliton Solutions for a System Describing Ultrashort Pulse Propagation in an Inhomogeneous Multi-Component Medium

For the propagation of the ultrashort pulses in an inhomogeneousmulti-component nonlinear medium, a system of coupled equations isanalytically studied in this paper. Painlevé analysis shows thatthis system admits the Painlevé property under some constraints.By means of the Ablowitz-Kaup-Newell-Segur procedure, the Lax pairof this system is derived, and the Darboux transformation (DT) isconstructed with the help of the obtained Lax pair. With symboliccomputation, the soliton solutions are obtained by virtue of the DTalgorithm. Figures are plotted to illustrate the dynamical featuresof the soliton solutions. Characteristics of the solitonspropagating in an inhomogeneous multi-component nonlinear medium arediscussed: (i) Propagation of one soliton and two-peak soliton; (ii) Elastic interactions of the parabolic two solitons; (iii) Overlapphenomenon between two solitons; (iv) Collision of two head-onsolitons and two head-on two-peak solitons; (v) Two different typesof interactions of the three solitons; (vi) Decomposition phenomenonof one soliton into two solitons. The results might be useful in thestudy on the ultrashort-pulse propagation in the inhomogeneousmulti-component nonlinear media.     

Guided waves in elastic rectangular bars:A solution using partial plate mode decomposition

Similar to Auld's solution for Lamb waves,the wave modes in elastic rectangular bar are solved by partial wave decomposition method.The partial waves are composed of plate modes with the same wavenumber component in waveguide longitudinal direction,thus free boundary conditions on one pair of opposite surfaces are automatically satisfied.Based on completeness assumption and orthogonality of the plate modes,four independent eigenequations are eventually derived for dispersion curve and mode shape investigation.Numerical evaluation shows the calculated results are in consistent with the FEM results.It is then verified that the plate modes which obliquely bounced back and forth between the two opposite surfaces compose the guided modes traveling in the rectangular waveguides with certain wave numbers in transversely resonant cases.     

矩形截面固体波导中弹性导波模式的板波叠加解

参照板中兰姆波模式的子波叠加解求解了矩形截面固体波导中弹性导波的模式。其中子波设定为横向满足自由边界反射条件、纵向波数分量相同的各板波模式。假设声场的完备性,利用子波模式的正交性,结合矩形截面的几何对称性可以得到4组独立导波特征方程用于频散曲线以及导波模式计算,其计算结果与有限元法计算结果相符。研究以解析模型表明:矩形截面固体波导中的导波是其内部以一定纵向波数分量斜向传播的板波模式在两个自由侧面上经过反复反射与模式转化后,横向耦合谐振而形成的。      

Spatial optical solitons in inhomogeneous elliptic core saturating nonlinear fiber

We have investigated the propagation characteristics of spatial optical solitons in saturating nonlinear waveguide employing JWKB and paraxial ray approximation. We have obtained two second-order coupled nonlinear differential equations for transverse soliton widths of solitons. Threshold power for stable propagation of the beam has been calculated from these coupled equations. We have undertaken stability analysis, which predicts robustness of these solitons. Both guiding as well as antiguiding cases have been considered and shown that stable spatial soliton propagation is possible in both cases.     

Novel spatial solitons in light-induced photonic bandgap structures

The study of wave propagation in periodic systems is at the frontiers of physics, from fluids to condensed matter physics, and from photonic crystals to Bose-Einstein condensates. In optics, a typical example of periodic system is a closely-spaced waveguide array, in which collective behavior of wave propagation exhibits many intriguing phenomena that have no counterpart in homogeneous media. Even in a linear waveguide array, the diffraction property of a light beam changes due to evanescent coupling between nearby waveguide sites, leading to normal and anomalous discrete diffraction. In a nonlinear waveguide array, a balance between diffraction and self-action gives rise to novel localized states such as spatial “discrete solitons” in the semi-infinite (or total-internal-reflection) gap or spatial “gap solitons” in the Bragg reflection gaps. Recently, in a series of experiments, we have “fabricated” closely-spaced waveguide arrays (photonic lattices) by optical induction. Such photonic structures have attracted great interest due to their novel physics, link to photonic crystals, as well as potential applications in optical switching and navigation. In this review article, we present a brief overview on our experimental demonstrations of a number of novel spatial soliton phenomena in light-induced photonic bandgap structures, including self-trapping of fundamental discrete solitons and more sophisticated lattice gap solitons. Much of our work has direct impact on the study of similar discrete phenomena in systems beyond optics, including sound waves, water waves, and matter waves (Bose-Einstein condensates) propagating in periodic potentials.     

Waveguides induced by grey screening solitons

We investigate the properties of waveguides induced by one-dimensional grey screening solitons in biased photorefractive crystals. The results show that waveguides induced by grey screening solitons are always of single mode for all intensity ratios, i.e. the ratios between the peak intensity of the soliton and the dark irradiance. Our analysis indicates that the energy confined near the centre of the grey soliton and the propagation constant of the guided mode of the waveguide induced by the grey screening soliton increase monotonically with intensity ratio increasing. On the other hand, when the soliton greyness increases, the energy confined near the centre of the grey soliton and the propagation constant of the guided mode of the waveguide induced by the grey screening soliton decrease monotonically. Relevant examples are provided where photorefractive crystal is of the strontium barium niobate type.