- 标题
- 摘要
- 关键词
- 实验方案
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Lax pair, Darboux-dressing transformation and localized waves of the coupled mixed derivative nonlinear Schr??dinger equation in a birefringent optical fiber
摘要： Under investigation in this paper is a coupled mixed derivative nonlinear Schr¨odinger equation, which can describe the pulse propagation in the femtosecond or picosecond regime of a birefringent optical fiber. Based on a Lax pair, we provide a Darboux transformation, and obtain the breather wave solutions. Then, a novel vector rogue wave solution is constructed by using Darboux-dressing transformation and asymptotic expansion. Those solutions exhibit some elastic and collision behaviors between a localized wave and a bright-dark soliton. Our works can be of importance in the theoretical experiments of the rogue wave generation mechanism and propagation trajectory.
关键词： Localized waves,Darboux-dressing transformation,The coupled mixed derivative nonlinear Schr¨odinger equation
更新于2025-09-23 15:21:01
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Optical bright and dark soliton solutions for coupled nonlinear Schr??dinger (CNLS) equations by the variational iteration method
摘要： This paper studies optical bright and dark soliton solutions for coupled nonlinear Schr¨odinger (CNLS) equations in the anomalous and dispersive regimes. We operate the variational iteration method (VIM) to derive a set of diverse types of bright and dark optical soliton solutions. The VIM gives the solution in a rapidly convergent series without any need for physical restrictions or changing the nonlinearity issue. The presented analysis shows the pertinent features of the VIM method in handling nonlinear evolution equations.
关键词： optical solitons,variational iteration method.,Coupled nonlinear Schr¨odinger equation
更新于2025-09-23 15:21:01
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Nonlinear surface waves propagating along the composite waveguide consisting of self-focusing slab between defocusing media separated by interfaces with nonlinear response
摘要： The model of the composite symmetric waveguide consisting of self-focusing slab between defocusing nonlinear media separated by interfaces characterized by own nonlinearity response is proposed. Two new types of nonlinear surface waves propagating along it with anti-phase amplitude oscillations at interface planes are found. The frequencies of the nonlinear surface waves existing near the interfaces with the nonlinear response only are calculated analytically. The conditions of the surface wave existence are found. The frequencies and localization distances of the surface waves in dependence on nonlinearity waveguide parameters, slab width and interface characteristics are analyzed.
关键词： interface,nonlinear Schr€odinger equation,surface wave,Layered structure,waveguide
更新于2025-09-23 15:19:57
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Numerical approaches for solving the nonlinear Schr??dinger equation in the nonlinear fiber optics formalism
摘要： This work presents a novel numerical stability analysis of a collection of pseudo-spectral methods, also known as split-step methods, for solving pulse propagation modelled by the nonlinear Schr¨odinger equation in the nonlinear ?ber optics formalism. In order to guarantee the convergence of di?erent pulse propagation dynamics, the numerical solutions of the pseudo-spectral methods (split-step Fourier method, symmetric split-step Fourier method, fourth order Runge-Kutta in the interaction picture method, and an optimization of split-step Fourier schemes for pulse propagation over long distances) are tested by the validation of the conservation laws that govern this system. The presented numerical results are an illustrative guide to consider in the selection of an appropriate numerical method in future investigations of a wide variety of propagation problems that involve the interplay of the linear and nonlinear contribution in the nonlinear Schr¨odinger equation, in order to reproduce accurately a speci?c phenomenology using this formalism.
关键词： nonlinear ?ber optics,Nonlinear Schr¨odinger equation,split-step methods,optical ?ber,optical pulse propagation
更新于2025-09-19 17:13:59
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Dark two-soliton solutions for nonlinear Schr?dinger equations in inhomogeneous optical fibers
摘要： In this paper, the variable coefficient nonlinear Schr¨odinger equation is investigated analytically. With the bilinear method, the bilinear forms and analytic soliton solutions are obtained. Based on the obtained analytic solutions, the effect of free parameters on the control of soliton transmission is studied. Influences of second-order and third-order dispersion coefficients on dark solitons are discussed. Results in this paper would be of great significance in the generation of dark solitons.
关键词： Bilinear method,Nonlinear Schr¨odinger equation,Partial differential equation,Solitons
更新于2025-09-16 10:30:52
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Dynamics of higher-order localized waves for a coupled nonlinear Schr?dinger equation
摘要： In this paper, dynamics of higher-order localized waves for a coupled nonlinear Schr¨odinger equation are investigated. Based on the generalized Darboux transformation, the first- to the third-order interactional localized wave solutions are derived through algebraic iteration. Specially, the new form of seed solutions is supposed, which is related to the normalized distance and retarded time. Many novel dynamic structures are demonstrated in the localized waves, particularly the third-order localized ones, where rogue waves coexist with dark-bright solitons and breathers in the three-dimensional plots. Furthermore, the classification of the Nth-order localized waves is given in the form of a table. In addition, an interesting phenomenon is observed that the order of rogue waves and the number of dark-bright solitons and breathers are consistent with the order of localized waves. These appealing results will be helpful to enrich the studies of localized waves for the coupled system.
关键词： Coupled nonlinear Schr¨odinger equation,Localized waves,Generalized Darboux transformation
更新于2025-09-16 10:30:52
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[IEEE 2019 Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC) - Munich, Germany (2019.6.23-2019.6.27)] 2019 Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC) - Topological Control of Optical Nonlinear Waves
摘要： Controlling nonlinear optical processes is a signi?cant challenge in photonics. Shock waves, rogue waves, and solitons are widespread, from optics to hydrodynamics. Intense research is dedicated to advanced techniques for tailoring extreme waves and ?nding the conditions to induce transitions from one kind of wave to another. We develop a new strategy to supervise, modify or tune a laser beam in third-order nonlinear materials, when light propagation is ruled by the nonlinear Schr¨odinger equation (NLSE). We denote our approach topological control (TC). TC is based on the one-to-one correspondence between the number of wave packet oscillating phases and the genus of toroidal surfaces associated with the NLSE solutions by the Riemann theta function [1]. For a box-shaped wave in a focusing Kerr medium, TC allows to control transitions from dispersive shock waves (DSWs), to rogue waves (RWs) and soliton gases (SGs). We prove that our method is experimentally realizable in a photorefractive crystal [2]. Speci?cally, we use the parametric time-dependence of photorefractive nonlinearity to shape the asymptotic wave pro?le. We tailor time-dependent propagation coef?cients, as nonlinearity and dispersion, to explore each region in the state-diagram [Fig. 1(a)] and observe all the phases in the nonlinear wave evolution [Fig. 1(b)]. This new technique casts light on focusing DSWs and RW generation, and can be extended to many other nonlinear phenomena, from classical to quantum ones.
关键词： photorefractive crystal,nonlinear Schr¨odinger equation,topological control,nonlinear optical processes,shock waves,rogue waves,solitons
更新于2025-09-11 14:15:04
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[IEEE 2019 Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC) - Munich, Germany (2019.6.23-2019.6.27)] 2019 Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC) - Spatial Akhmediev Breathers in Slab Waveguides
摘要： The analytical breather-solutions of the Nonlinear Schr¨odinger Equation (NLS) have been intensively studied and veri?ed experimentally in the time-space system of optical pulse propagation in ?bers. In space-space systems, i.e. in optical beam propagation breathers in ultra-fast nonlinear media have not been observed due to the breather’s in?nite background and a resulting extremely large power. In a lithium niobate slab waveguide with two second-harmonic (SH) resonances the resulting quasi-cubic cascaded quadratic nonlinearity provided together with the intrinsic cubic susceptibility enough nonlinearity for breather excitation at experimentally reachable powers. We could characterize the ?rst ultra-fast spatial-spatial optical breathers in a 5-cm-long titanium in diffused lithium niobate slab waveguide at power levels down to tens of kW. The guided fundamental wave (FW) TM0 ?lm mode at l=1.32mm is phase-matched for type-I SH generation to TE0 and TE1 SH modes at temperatures near 295 and 344C. With temperature tuning the phase-mismatch and the two effective cascaded nonlinearities were adjusted. For breather observation, we aimed for a large phase-mismatch with low SH levels such that the cascaded nonlinearity is quasi-cubic and the propagation is well approximated by the NLS and its breather solutions. A frequency-doubled Nd:YAG-pumped OPA with CW-seeding delivered 5-ps long pulses with up to 200kW peak power in the waveguide. With a cylindrical telescope the beam was transformed into a very wide elliptical beam to approximate the breather background. The beam was end-?re coupled into the FW TM0 mode. A variable few% of the beam were separated and coupled with a tilt and good overlap to the main beam into the waveguide to produce a spatial modulation of the input with adjustable period and modulation depth. A beam width of 1.5mm was large enough in the compromise between available beam power and in?nite beam width. A beam with a transverse modulation with periods between 130 to 300mm approximates a constant background with modulation well enough to trigger modulation instability that develops eventually into the breather. The FW and the SH output of the waveguide were imaged into cameras. By changing the power the breather moves along the waveguide and the whole breather can be sampled at the waveguide end during a power scan. Each sample is normalized to its total power. An example is shown in Fig.1. Fig.1(left) Measured breather, scanned at the waveguide output dependent on power. (right) Simulation of the measurement. The in?uence of deviations from ideal theory and real world conditions like ?nite beam width, damping, non-uniform phase-mismatch, pulsed input, and cascading instead of an exact cubic nonlinearity was investigated in simulations describing the experiment very well (see example in Fig.1). The new platform is very versatile. A wide parameter space of different nonlinearity, varying transverse breather period and input modulation depth was investigated. Higher-order breathers were observed (see the grow-ing maxima between the main peaks in Fig.1). The drastic temperature-dependent reduction of the power level for breather formation due to cascading was observed. The expected speci?c details of quadratic breathers like a SH following the FW was documented. The spatial breather spectra showed the expected triangular shape.
关键词： modulation instability,lithium niobate slab waveguide,Nonlinear Schr¨odinger Equation,cascaded quadratic nonlinearity,optical breathers
更新于2025-09-11 14:15:04
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The Effect of Gain and Strong Dissipative Structures on Nonlinear Schr?dinger Equations in Optical Fiber
摘要： We consider the initial value problem for the nonlinear Schr¨odinger equation satisfying the strong dissipative condition I?? < 0 and |I??| > ((?? ? 1)/2√??)|R??| in one space dimension. Our purpose in this paper is to study how the gain coefficient ??(??) and strong dissipative nonlinearity ??|V|???1V affect solutions to the nonlinear Schr¨odinger equation for large initial data. We prove global existence of solutions and present some time decay estimates of solutions for large initial data.
关键词： nonlinear Schr¨odinger equation,global existence,gain coefficient,strong dissipative condition,time decay estimates
更新于2025-09-11 14:15:04
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Construction of dispersive optical solutions of the resonant nonlinear Schr?dinger equation using two different methods
摘要： The resonant nonlinear Schr¨odinger equation is studied in this work with the aid of two methods, namely the exponential rational function method and the modified exponential function method. This equation is used to describe the propagation of optical pulses in nonlinear optical fibers. Being concise and straightforward, these methods are used to build new exact analytical solutions of the model. The solutions obtained are not yet reported in the literature. The methods proposed can be extended to other types of nonlinear evolution equations in mathematical physics.
关键词： modified exponential function method,new exact analytical solutions,exponential rational function method,Resonant nonlinear Schr¨odinger equation
更新于2025-09-11 14:15:04