Dispersion-Managed Optical Solitons with Higher-Order Nonlinearity

In this paper we have investigated the propagation characteristics of optical solitons in dispersion managed optical communication systems taking into account of the effect of quintic nonlinearity. Using variational formalism, several ordinary differential equations have been established for pulse parameters. These equations have been solved numerically to investigate the propagation characteristics. It has been noticed that stable periodic pulse propagation is possible over long distance. Numerical simulation has been undertaken to show that parabolic nonlinearity reduces collision distance between neighbouring pulses of the same channel.     

用变分法研究高阶色散和五阶非线性对高斯脉冲在光纤中传输特性的影响

从修正的非线性薛定谔方程出发,采用变分法,导出了在高阶色散和五阶非线性共同作用情况下高斯型脉冲参量随传输距离的演化方程组;求出了振幅与脉宽、频率与啁啾、脉宽与啁啾之间的三个重要约束关系;并进一步得出了脉宽随传输距离演化的解析解和脉冲中心位置随传输距离的演化规律;描绘了高阶色散和五阶非线性下,脉宽随传输距离演化的图形.结果表明:光纤中的高阶色散和五阶非线性都会影响高斯型脉冲各个参量的演化,但脉宽和振幅间的绝热关系并未改变.高阶色散使高斯型脉冲的脉宽展宽,五阶非线性使高斯型脉冲的脉宽压缩,它们对脉宽或初始啁啾的影响可以在一定程度上抵消,从而有可能使脉冲近似实现保形传输.     

五阶非线性作用下光纤中类明孤子运动方程的变分研究

当考虑到五阶非线性对光脉冲传输的影响时, 光纤中类明孤子的传输服从含五阶非线性修正项的非线性Schrdinger方程。利用何氏半反推法建立该类明孤子运动方程的变分形式, 然后应用何氏变分法导出该方程基态孤子解的双曲正割表达式。同时, 受何氏指数函数方法的启发, 建立了一种新的高斯表达式。一方面, 基于得到的显式表达式相关学者可进一步研究五阶非线性对光脉冲传输的影响。另一方面, 该求解过程也进一步显示了用何氏变分法求解数学物理中非线性发展方程的简洁有效性。     

Femtosecond Pulse Propagation in Optical Fibers Under Higher Order Effects: A Collective Variable Approach

Employing collective variable approach, femtosecond pulse propagation has been investigated in optical fibers using the higher order nonlinear Schrödinger equation. In order to view the pulse dynamics along the propagation distance, variation of different pulse parameters, called collective variables, such as pulse amplitude, width, chirp, pulse center and frequency has been investigated by numerically solving the set of ordinary equations obtained from collective variable approach.     

色散和非线性效应对高斯脉冲综合影响的理论分析

从光孤子传输所满足的非线性薛定谔方程出发,采用单独分析和综合分析对比,分析了影响高斯脉冲传输的色散、非线性等因素,结果表明：二阶色散参量只会影响脉冲的幅值,对脉冲形状影响不大,而输入脉冲的啁啾则是使脉冲发生形变的主要原因|在啁啾、三阶色散和五阶非线性的共同作用下,它们对脉冲都会产生较大的影响,且存在相互影响和制约作用,在某一临界值,对脉冲存在着较高的压缩增益效应和“整形”作用.从理论上提出了改善高斯光脉冲在光纤中传输特性的解决方案,这对光纤孤子通信的实践过程具有一定的理论借鉴意义.     

Chirped optical pulse propagation in saturating nonlinear media

Using a variational method, we have investigated the propagation characteristics of a chirped optical pulse in anomalously dispersive media possessing saturating nonlinearity. For the special case of uniform loss less media, the dynamics of the temporal width of the pulse is shown to be equivalent to an oscillator of unit mass which is executing its motion under some effective potential well. The potential is examined and four different types of behavior of the pulse width are noticed. The role of saturation parameter and the initial chirp in determining the propagation characteristics have been examined. It is found that, both high value of chirp and saturation are detrimental to stable pulse propagation. Particularly, the effect of chirp becomes severe with the increase in the value of saturation. We have shown that incorporation of saturation in the nonlinearity leads to the existence of bistable soliton. For the case of a lossy medium, net broadening of width takes place over many cycles of oscillation. The net broadening decreases with the increase in the value of saturation.     

五阶非线性光纤中连续谱相位扰动下的光传输与脉冲串产生

根据包含五阶非线性的扩展非线性薛定谔方程,数值研究了高斯型连续谱相位扰动而不是传统单色扰动下基于调制不稳定性的高重复率脉冲串产生.结果表明:脉冲串也能像传统情形那样形成,但却呈现出不同的特性.如脉冲数目有限,且各脉冲的高度、强度及间距不等.脉冲数目随传输距离增加而增加.而五阶非线性能使脉冲宽度和间距变小因而有利于高重复率脉冲串产生,负五阶非线性则相反.对脉冲串形成过程中演变啁啾的数值计算表明,啁啾及其随距离的变化都是高度非单调的,五阶非线性将改变啁啾的范围和量值.     

Analysis of femtosecond optical pulse propagation in one-dimensional nonlinear photonic crystals using finite-difference time-domain method

In this paper, we have used the finite-difference time-domain (FDTD) method to analyze the optical pulse propagation in a nonlinear, one-dimensional photonic crystal (1DPC). Hyperbolic secant pulses with various carrier wavelengths are utilized in this study. In a nonlinear regime, a 1DPC introduces a photonic band-gap whose central wavelength and width depend on the input pulse intensity. In the present work, three different cases are considered. These correspond to the carrier wavelengths of the incident pulses being out of, near to, and partially in the band-gap. For each case, the effect of nonlinearity on pulse propagation is investigated. Also, we have analyzed the two-frequency regime, in which each of the two pulses has a different carrier frequency (wavelength). This kind of study can be done directly with FDTD without any further computational burden but it is somewhat complicated using nonlinear coupled-mode equations (NLCME) and nonlinear Schrödinger equation (NLSE), which require separate treatments for each carrier wavelength.     

Effect of laser beam induced nonlinearity on the performance of crystalline lens

This paper presents the performance of the human crystalline lens having gradient index (GRIN) structure in the presence of a moderate power laser pulse. Nonlinear dynamical equations have been set-up governing the laser pulse propagation in the lens by taking into account the nonlinearity introduced by the laser pulse. Semi-analytical results have been obtained by using the paraxial ray approximation when GRIN and nonlinearity effects are simultaneously present. Performance of the lens has been analyzed in two explicit cases. In the first case, only the GRIN structure is considered while in the second case the nonlinearity and the GRIN both are considered. A moderate power laser pulse can be used for self-focusing in the crystalline lens when GRIN effects alone are not sufficient to focus the laser pulse in the crystalline lens.     

原子的共振激发—速率方程与半经典理论的比较

本文由半经典理论推得了原子电离率随脉冲空间传输出现周期性起伏这一新的相干作用结果,这点与速率方程的预计相差甚远.文中定量说明了利用速率方程对同位素分离过程进行分析时产生的系统误差,为实验分析工作提供了依据.     

Ultraslow solitons due to large quintic nonlinearity in coupled quantum well structures driven by two control laser beams

In this paper, we have shown the existence of large amounts of quintic nonlinearity in asymmetric three-coupled quantum wells, which arise due to a probe pulse and two controlling laser beams. The possibilities of generation and propagation of ultraslow bright optical solitons in these systems have been examined in situations of both Kerr and quintic nonlinearities. We have also demonstrated numerically that these solitons are stable. The modulation instability of a continuous or quasi-continuous wave probe beam has been also investigated and the role of quintic nonlinearity in suppressing this instability has been addressed.     

Nonlinearity management and diffraction management for the stabilization of two-dimensional spatial solitons

The nonlinear Schrödinger equation which governs the dynamics of two-dimensional spatial solitons in Kerr media with periodically varying diffraction and nonlinearity has been analyzed in this paper using variational approach and numerical studies. Analytical expressions for soliton parameters have been derived using variational analysis. Variational equations and partial differential equation have been simulated numerically. Analytical and numerical studies have shown that nonlinearity management and diffraction management stabilize the pulse against decay or collapse providing undisturbed propagation even for larger energies of the incident beam.     

Higher-order effects on self-similar parabolic pulse in the microstructured fibre amplifier

By considering higher-order effects, the properties of self-similar parabolic pulses propagating in the microstructured fibre amplifier with a normal group-velocity dispersion have been investigated. The numerical results indicate that the higher-order effects can badly distort self-similar parabolic pulse shape and optical spectrum, and at the same time the peak shift and oscillation appear, while the pulse still reveals highly linear chirp but grows into asymmetry. The influence of different higher-order effects on self-similar parabolic pulse propagation has been analysed. It shows that the self-steepening plays a more important role. We can manipulate the geometrical parameters of the microstructured fibre amplifier to gain a suitable dispersion and nonlinearity coefficient which will keep high-quality self-similar parabolic pulse propagation. These results are significant for the further study of self-similar parabolic pulse propagation.     

纵向非均匀介质波导中超短光脉冲演化方程

本文利用约化摄动方法,从非线性介质中的原始Maxwell方程出发,首次导出了纵向非均匀介质波导中超短光脉冲演化方程,给出了描述飞秒光脉冲波包演化方程的两种等价表达式。     

Propagation characteristics of nonlinear optical fibers with complex refractive index. A transmission line model approach

The transmission line model has been modified in order to evaluate nonlinear waves guided by optical fibers with complex refractive index. It is proven that the proposed model is able to tackle fibers with losses or gain, under the presence of arbitrary nonlinearity. The method is applied for the calculation of weakly guided lossy nonlinear optical fibers considering various configurations and Kerr nonlinearity. Power depended propagation characteristics have been calculated and plotted for the fundamental mode and the potential use of the method in optical fiber amplifiers with index nonlinearity is also discussed.     

Three-dimensional FDTD method for optical pulse propagation analysis in microstructured optical fibers

We propose a three-dimensional (3D) finite-difference time-domain (FDTD) method to analyze the pulse propagation characteristics in microstructured optical fibers (MOFs). The computation domain size is greatly reduced by adopting the technique of moving problem space. The propagating pulse is virtually held in the buffer cell of the problem space as simulation continues. This method is capable to investigate the temporal evolution of the propagating pulse. Spectral information can be obtained by Fourier analysis. As an example, the influence of the kerr nonlinearity on the optical pulse propagation in a Lorentz dispersive MOF is demonstrated. The model is also used to simulate the nonlinear interactions between the pump spectral broadening and third harmonic generations in a highly nonlinear fused silica nanowire with good agreement with the generalized nonlinear envelop equation (GNEE) model.     

A heuristic method to simulate the pulse propagation in nonlinear fiber bragg gratings

In this paper we simulated the pulse propagation and the switching effects in nonlinear fiber Bragg gratings using a combination of Fourier series analysis technique and Jacobi iterative method. The effects of nonlinearity and dispersion on the pulse propagation have been studied extensively. An all optical self switch was designed by this simulation. This switch is operated based on the input power.     

An improved nonlinear optical pulse propagation equation

A new equation for self-focusing of extremely focused short-duration intense pulses is derived using a method that treats diffraction and dispersion to all orders with nonlinearity present, and self-consistently determines the nonlinear derivative terms present in the propagation equation. It generalizes both the previous formulation of linear optical pulse propagation to the nonlinear regime, and the cw nonlinear regime propagation to the pulsed regime by including temporal characteristics of the pulse. We apply the new equation and propagate a tightly focused picosecond pulse in silica and explicitly show the effects of spatial-derivative nonlinear coupling terms.     

Dynamics of ultimately short pulses in partially absorbing media

Propagation of broad-band ultimately short light pulses in a partially absorbing medium is analyzed in the framework of the three-level model. Nonlinear wave equations are obtained describing propagation of light pulses in media with quadratic (all three transitions are allowed) or cubic (one of the transitions is forbidden) nonlinearity in the range of optical transparency or with the sine-Gordon-type nonlinearity in the region of absorption. Using the averaged variational principle, the approximate solutions of equations in the form of unipolar soliton-like signals are found and conditions of their transverse stability are determined. A stable propagation of a broad-band pulse is shown to be possible under conditions when monochromatic signals exhibit self-focusing.     

Interaction of an ultrashort optical pulse with the impurity subsystem of a hydrogen-containing ferroelectric

The dynamics of an ultrashort optical pulse in impurity-containing ferroelectrics with hydrogen bonds has been considered in terms of microscopic pseudospin formalism, which uses the approximation of unidirectional propagation without limitations on the pulse power. The effective equations for the electric field amplitude and ferroelectric polarization have been obtained and numerically solved. Quasi-soliton propagation modes of ultrashort optical pulses are revealed, and their dependences on the microscopic Hamiltonian parameters are analyzed.