Recovery of the solitons using a lattice Boltzmann model

We formulate a lattice Boltzmann model which simulates Korteweg-de Vries equation by using a method of higher moments of lattice Boltzmann equation. Using a series of lattice Boltzmann equations in different time scales and the conservation law in time scale to, we obtain equilibrium distribution function. The numerical examples show that the method can be used to simulate soliton.

A family of interesting exact solutions of the sine-Gordon equation

By using AKNS [Phys. Rev. Lett. 31 (1973) 125] system and introducing the wave function, a family of interesting exact solutions of the sine-Gordon equation are constructed. These solutions seem to be some soliton, kink, and anti-kink ones respectively for the different choice of the spectrum, whereas due to the interaction between two traveling-waves they have some properties different from usual soliton, kink, and anti-kink solutions.

Bismuth-doped fiber integrated ring laser mode-locked with a nanotube-based saturable absorber

We demonstrate passive mode-locking of a bismuth-doped fiber laser using a singlewall nanotube-based saturable absorber. Stable operation in the all-normal dispersion and average soliton regime is obtained, with an all-fiber integrated format. © 2010 Optical Society of America.

Noise and stability in giant-chirp oscillators mode-locked with a nanotube-based saturable absorber

We compare experimental results showing stable dissipative-soliton solutions exist in mode-locked lasers with ultra-large normal dispersion (as large as 21.5 ps2), with both the analytic framework provided by Haus' master-equation and full numerical simulations. © 2010 Optical Society of America.

The effect of the surface tension on non-propagating solitary waves

In this paper, the effect of the surface tension is considered carefully in the study of non-propagating solitary waves. The parameter plane of the surface tension and the fluid depth is divided into three regions; in two of them a breather soliton can be produced. In literature the parameters of breather solitons are all in one of the parameter regions. The new region reported here has been confirmed by our experiments. In the third region, the theoretical solution is a kink soliton, but a kind of the non-propagating solitary wave similar to the breather soliton was found in our experiments besides the kink soliton.

Analysis and optimization of stress wave propagation in two-dimensional granular crystals with defects

Granular crystals are compact periodic assemblies of elastic particles in Hertzian contact whose dynamic response can be tuned from strongly nonlinear to linear by the addition of a static precompression force. This unique feature allows for a wide range of studies that include the investigation of new fundamental nonlinear phenomena in discrete systems such as solitary waves, shock waves, discrete breathers and other defect modes. In the absence of precompression, a particularly interesting property of these systems is their ability to support the formation and propagation of spatially localized soliton-like waves with highly tunable properties. The wealth of parameters one can modify (particle size, geometry and material properties, periodicity of the crystal, presence of a static force, type of excitation, etc.) makes them ideal candidates for the design of new materials for practical applications. This thesis describes several ways to optimally control and tailor the propagation of stress waves in granular crystals through the use of heterogeneities (interstitial defect particles and material heterogeneities) in otherwise perfectly ordered systems. We focus on uncompressed two-dimensional granular crystals with interstitial spherical intruders and composite hexagonal packings and study their dynamic response using a combination of experimental, numerical and analytical techniques. We first investigate the interaction of defect particles with a solitary wave and utilize this fundamental knowledge in the optimal design of novel composite wave guides, shock or vibration absorbers obtained using gradient-based optimization methods.

Few-cycle relativistic solitons in plasmas

A set of exact one-dimensional solutions to coupled nonlinear equations describing the propagation of a relativistic ultrashort circularly polarized laser pulse in a cold collisionless and bounded plasma where electrons have an initial velocity in the laser propagating direction is presented. The solutions investigated here are in the form of quickly moving envelop solitons at a propagation velocity comparable to the light speed. The features of solitons in both underdense and overdense plasmas with electrons having different given initial velocities in the laser propagating direction are described. It is found that the amplitude of solitons is larger and soliton width shorter in plasmas where electrons have a larger initial velocity. In overdense plasmas, soliton duration is shorter, the amplitude higher than that in underdense plasmas where electrons have the same initial velocity.

Enhanced dispersive wave generation by using chirped pulses in a microstructured fiber

A theoretical investigation on the nonlinear pulse propagation and dispersive wave generation in the anomalous dispersion region of a microstructured fiber is presented. By simulating the dispersive wave generation under different conditions. it is found that the generation mechanism of the dispersive wave is mainly due to the pulse trapping across the zero-dispersion wavelength. By varying the initial pulse chirp, the output spectrum can be broadened and the intensity of the dispersive wave can be obviously enhanced. In particular, there exists an optimal positive chirp which maximizes the intensity of the dispersive wave. This effect can be explained by the energy transfer from the Raman soliton to the dispersive wave due to the effect of the pulse trapping and the effect of the higher-order dispersion. From the phase aspect, the explanation of this effect is also included. (C) 2004 Elsevier B.V. All rights reserved.

Nonlinear copropagation of two optical pulses of different frequencies in photonic crystal fibers

A theoretical investigation of the nonlinear copropagation of two optical pulses of different frequencies in a photonic crystal fiber is presented. Different phenomena are observed depending on whether the wavelength of the signal pulse is located in the normal or the anomalous dispersion region. In particular, it is found that the phenomenon of pulse trapping occurs when the signal wavelength is located in the normal dispersion region while the pump wavelength is located in the anomalous dispersion region. The signal pulse suffers cross-phase modulation by the Raman shifted soliton pulse and it is trapped and copropagates with the Raman soliton pulse along the fiber. As the input peak power of the pump pulse is increased, the red-shift of the Raman soliton is considerably enhanced with the simultaneous further blue-shift of the trapped pulse to satisfy the condition of group velocity matching.

Standing ultrashort relativistic solitons in overdense plasmas

By using a one-dimensional self-consistent relativistic fluid model, an investigation is made numerically on relativistic electromagnetic solitons with a high intensity in cold overdense plasmas with an electrons' initial velocity opposite to the laser propagating direction. Two types of standing solitons with zero group velocity are found at the given electrons' initial velocities. One is single-humped with a weakly relativistic intensity; the another is multi-humped with a strong relativistic amplitude. The properties of these two types of solitons are presented in detail.

Carrier-envelope phase dependence of few-cycle ultrashort laser pulse propagation in a polar molecule medium

We theoretically investigate carrier-envelope phase dependence of few-cycle ultrashort laser pulse propagation in a polar molecule medium. Our results show that a soliton pulse can be generated during the two-photon resonant propagation of few-cycle pulse in the polar molecule medium. Moreover, the main features of the soliton pulse, such as pulse duration and intensity, depend crucially on the carrier-envelope phase of the incident pulse, which could be utilized to determine the carrier-envelope phase of a few-cycle ultrashort laser pulse from a mode-locked oscillator.

XPM-induced pulse compression in birefringent dispersion decreasing fiber

The pulse compression induced by cross-phase modulation in birefringent dispersion decreasing fiber is discussed theoretically by solving the coupled Schrodinger equations which include the contribution of the high-order non-linear effects, and third-order dispersion. In particular, it is found that a high quality compressed signal pulse can be obtained by a pump pulse of low intense through the technique. The dependence of optimum compression on the non-linear factor N, time delay tau(d) and the dispersive ratio f is also discussed in detail. (c) 2005 Elsevier B.V. All rights reserved.

Optical generaton of millimeter-wave pulses using a fiber Bragg grating in a fiber-optics system

A scheme is proposed to transform an optical pulse into a millimeter-wave frequency modulation pulse by using a weak fiber Bragg grating (FBG) in a fiber-optics system. The Fourier transformation method is used to obtain the required spectrum response function of the FBG for the Gaussian pulse, soliton pulse, and Lorenz shape pulse. On the condition of the first-order Born approximation of the weak fiber grating, the relation of the refractive index distribution and the spectrum response function of the FBG satisfies the Fourier transformation, and the corresponding refractive index distribution forms are obtained for single-frequency modulation and linear-frequency modulation millimeter-wave pulse generation. The performances of the designed fiber gratings are also studied by a numerical simulation method for a supershort pulse transmission. (c) 2007 Optical Society of America.

色散管理孤子传输特性分析

色散管理孤子光波系统的色散图周期由具有正负色散值的两段光纤组成，并且在系统中周期性放置集中放大器及滤波器装置。采用变分法获得了描述此种系统性能的常微分方程组，并利用这组方程数值研究了各种参量对孤子传输性能的影响。研究结果表明，虽然从整体趋势上看，当要求色散管理孤子有较好的稳定性时，应适当降低系统的色散管理强度，但在一定条件下，调整光纤放大器的位置以及正负色散光纤的色散差值，可同时获得相对较大的色散管理强度和好的孤子稳定性；总体来讲，集总放大器的位置会对孤子传输的稳定性、色散管理孤子的能量增强因子、脉冲最佳

初始啁啾对光纤中传播的飞秒光孤子的影响

采用分步傅里叶变换作为数值模拟的方法，以二阶飞秒光孤子和基态飞秒光孤子为例，讨论了初始啁啾对光纤中传播的飞秒光孤子的时域特征和频谱结构的影响，概括出如下的结论：初始啁啾通过影响飞秒光孤子谱线的红移，而对飞秒光孤子由拉曼效应引发的脉冲延迟产生较大影响，正的初始啁啾使脉冲延迟加剧，负的初始啁啾使脉冲延迟减小。