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.     

Optimal design of dispersion management for a soliton wavelength-division-multiplexed system

We obtain analytical formulas for minimizing chirp and timing jitter that lead to optimal designs for a soliton-wavelength-division-multiplexed system with dispersion management and lumped amplifiers. The method used here is the guiding-center theory, from which we obtain a stationary pulse shape (guiding-center soliton) that has enhanced power and an increased time-bandwidth product compared with those of a soliton alone.     

Supermode-noise-free eighth-order femtosecond soliton from a backward dark-optical-comb-injection mode-locked semiconductor optical amplifier fiber laser

A backward dark-optical-comb-injection mode-locked semiconductor optical amplifier fiber laser (SOAFL) with a femtosecond pulse width and an ultrahigh supermode-noise suppressing ratio (SMSR) is primarily demonstrated. The mode-locked SOAFL pulse with a spectral linewidth of 0.45 nm is shortened from 15 to 8.6 ps under chirp compensation in a 420 m long dispersion-compensated fiber, corresponding to a time-bandwidth product of 0.48. The eighth-order soliton is obtained by the nonlinearly soliton's compression of the chirp-compensated SOAFL pulse in a 112 m long single-mode fiber at an input peak power of 51 W, providing the pulse width, the linewidth, and the nearly transform-limited time-bandwidth product are <200 fs, 13.8 nm, and 0.34, respectively. The phase noise and integrated timing jitter at an offset frequency below 1 MHz are -105 dBc/Hz and 0.8 ps, respectively. An ultrahigh pulse-compression ratio of 43 and a SMSR of 87 dB for the eighth-order SOAFL soliton are reported.     

Effects of initial frequency chirp on the linear propagation characteristics of the exponential optical pulse

In this paper, the linear propagation characteristics of the exponential optical pulse with initial linear and nonlinear frequency chirp are numerically studied in a single mode fibre for \be₂<0. It can be found that the temporal full width at half maximum and time-bandwidth product of exponential pulse monotonically increase with the increase of propagation distance and decrease with the increase of linear chirp C for C<0.5, go through an initial decreasing stage near \zeta=1, then increase with the increase of propagation distance and linear chirp C for C\geq0.5. The broadening of pulses with negative chirp is faster than that with positive chirp. The exponential pulse with linear chirp gradually evolves into a near-Gaussian pulse. The effect of nonlinear chirp on waveform of the pulse is much greater than that of linear chirp. The temporal waveform breaking of exponential pulse with nonlinear chirp is first observed in linear propagation. Furthermore, the expressions of the spectral width and time-bandwidth product of the exponential optical pulse with the frequency chirp are given by use of the numerical analysis method.     

光脉冲在标准单模光纤中演化形成孤子的实验研究

利用二次谐波频率分辨光学门脉冲分析仪从实验上分析研究了具有啁啾的10 GHz光脉冲在不同输入功率下演化形成孤子的规律和特点。实验发现:输入脉冲在光纤中传输3.5个色散长度时,其时间宽度、频率啁啾和时间带宽积都随着输入功率的增加而减小。当输入功率大于一阶孤子功率的理论值时,光脉冲能够演化形成孤子;脉冲在随后传输过程中其宽度基本保持不变,波形、频率啁啾和时间带宽积仍随着传输距离的变化而变化;输入功率越高,形成的一阶孤子脉冲的宽度越窄。当输入功率小于一阶孤子功率的理论值时,输出脉冲的时间宽度随着传输距离的增加而增加,频率啁啾随着传输距离的增加而减小,光脉冲不能演化形成孤子。     

Enhanced pulse compression induced by the interaction between the third—order dispersion and the cross—phase modulation in birefringent fibres

In this paper,we report on the enhanced pulse compression due to the interaction between the positive third-order dispersion (TOD) and the nonlinear effect (cross-phase modulation effect) in birefringent fibres.Polarization soliton compression along the slow axis can be enhanced in a birefringent fibre with positive third-order dispersion,while the polarization soliton compression along the fast axis can be enhanced in the fibre with negative third-order dispersion.Moreover,there is an optimal third-order dispersion parameter for obtaining the optimal pulse compression.Redshifted initial chirp is helpful to the pulse compression,while blueshifted chirp is detrimental to the pulse compression.There is also an optimal chirp parameter to reach maximum pulse compression.The optimal pulse compression for TOD parameters under different N-order solitons is also found.     

Influence of Nonlinear Gain Saturation on the Time-Bandwidth Product of Optical Pulse from a Gain-Switched Semiconductor Laser

It is found numerically that the time-bandwidth product (TBP) of optical pulse from a gain-switched semiconductor laser operating under a sufficient gain saturation condition increases monotonously with increasing modulation amplitude. This enhancement of the TBP becomes remarkable for longer-wavelength semiconductor lasers (1.3, 1.55 μm) having large value of the gain compression factor ε (∼ 10⁻²³ m³), making the pulse chirp estimation using the TBP difficult.     

压缩平稳重调脉冲的色散渐减光纤的设计

文章根据平稳重调脉冲(SRP)在梳状光纤(CPF)结构中的压缩原理,对色散渐减光纤(DDF)的色散特性进行设计,结果发现该色散渐减光纤的色散特性呈线性递减.对于平稳重调脉冲其压缩比与功率比等于光纤始末两端二阶色散系数的比值.当色散渐减光纤的斜率足够小时,无啁啾基阶孤子可以近似为平稳重调脉冲,当色散渐减光纤的色散斜率较大时,无啁啾基阶孤子不能近似为平稳重调脉冲.当基阶孤子带有与光纤色散斜率成正比的线性啁啾时,脉冲的压缩比与功率比更接近于光纤始末两端二阶色散系数的比值.说明带有线性啁啾的基阶孤子比不带啁啾的基阶孤子更接近于平稳重调脉冲. 关键词： 平稳重调脉冲(SRP) 梳状光纤(CPF) 色散渐减光纤(DDF) 色散递减表达式     

Compression of harmonic pulses by using material dispersion

We utilize the dispersion property of an X-ray filter material for the generation of a single sub-50-as pulse from high-order harmonics. The attosecond pulse, formed by selecting the spectral range of high-order harmonic radiation, contains an intrinsic chirp corresponding to the quadratic phase variation during a half cycle of a laser pulse. We show that this chirp can be compensated by using the negative group-delay dispersion of a thin X-ray filter, compressing the attosecond pulse down to sub-50-as. PACS 42.65.Re; 42.50.Hz; 42.65.Ky     

高斯脉冲在半导体光放大器中传输的解析表征

采用解析方法,在考虑材料损耗和色散的情况下,详细研究了无啁啾高斯脉冲和啁啾高斯脉冲在半导体光放大器中传输的物理过程,分析了强度增益、脉冲宽度和频率啁啾与线宽增强因子、色散系数、小信号增益特征参数及初始啁啾之间的关系。结果表明:当输入变换极限的高斯脉冲时,色散会引起增益压缩,脉冲展宽和频率啁啾;同样情况下,线宽增强因子越大,脉宽加宽越明显,输出脉冲啁啾越大,且随着线宽增强因子的增大,输出脉冲啁啾极大值向特征参数值较小的一边移动。当输入啁啾高斯脉冲时,初始脉冲啁啾越大,增益压缩越明显,啁啾系数为正时,脉冲单纯展宽,输出啁啾随特征参数的增大而逐渐减小,啁啾系数为负时,初始啁啾与群速度色散导致的啁啾相互竞争,致使脉冲先被压缩后被展宽;脉冲最窄处对应的特征参数随线宽增强因子的增大而先增大后减小,输出啁啾随特征参数的增大而经历振荡后趋于平稳。     

级联单模光纤中初始啁啾对高阶孤子脉冲压缩的影响

采用两段级联单模光纤对高阶孤子脉冲进行压缩。两段光纤具有不同的反常色散值,当高阶孤子脉冲在第一段光纤中获得最大程度压缩时,通过转换色散值不同的光纤,使压缩脉冲继续以高阶孤子的形式在第二段光纤中再次被压缩。每段光纤的长度都进行了优化,使得脉冲在每段光纤中都获得最大程度的压缩。基于非线性薛定谔方程,数值研究了初始啁啾对高阶孤子脉冲压缩的影响。研究结果表明,初始啁啾对高阶孤子脉冲的压缩有重要影响。与无初始啁啾时的情形相比,正的初始啁啾能增强每段光纤中脉冲的压缩效果,降低压缩脉冲的基座能量,而负初始啁啾的影响则相反。随着初始啁啾参量Cp的增大,脉冲在每段光纤中的压缩因子均增加,而基座能量、最优光纤长度均减小。     

负啁啾脉冲在正负色散光纤中传输特性研究

对负啁啾脉冲在正常色散光纤中传输特性进行了数值分析和实验研究，数值分析与实验结果基本一致。数值分析和实验证明正常色散光纤不仅能压窄负啁啾的脉宽而且能压窄频谱，采用正常色散光纤消啁啾后用色散位移光纤为传输媒质成功地进行了一阶和高阶孤子传输。     

受激喇曼散射对自相似脉冲产生的影响

研究了在受激喇曼散射与三阶色散共同作用下,自相似脉冲在具有正常色散的色散渐减光纤中的演化情况.结果表明:在同一个传输距离上,当考虑受激喇曼散射与三阶色散的共同影响时,脉冲中心的不对称特性相对好转;产生中心漂移与边缘振荡较只有三阶色散作用时要减弱,啁啾仍然具有很强的线性特性,但是线性范围减小,导致频谱的窄化以及对接下来自相似脉冲的压缩产生了不利影响;而且光纤长度的延长并没有起到展宽啁啾线性范围的效果,反而导致严重的啁啾非线性;因此对脉冲进行压缩后,压缩脉冲质量较不考虑受激喇曼散射时要差.     

四阶色散对飞秒高斯脉冲传输的影响

推导了考虑二、三、四阶色散的高斯脉冲传输方程;利用计算机数值模拟的方法,研究了四阶色散(FOD)对飞秒高斯脉冲在单模光纤中传输特性的影响.模拟结果显示：只有在入射脉冲宽度窄到飞秒量级时,即对应传输速率很高的情况下,FOD对脉冲的影响才明显;FOD导致脉冲形状发生了畸变,畸变特点不同于二、三阶色散;随着初始脉宽逐渐减小,FOD所致的飞秒高斯脉冲畸变经历了一个脉冲仅仅展宽,到展宽脉冲的两翼出现“底座”,到展宽脉冲的两翼出现具有微小振荡“底座”的变化过程.     

初始啁啾补偿光纤色散效应的适用范围

以啁啾高斯脉冲在单模光纤中的传输为例,分别就线性初始啁啾对光纤二阶和三阶色散的补偿进行了系统的理论分析和数值计算,结果表明：线性初始啁啾对光纤的二阶色散（线性色散）有一定的补偿作用,但不能有效地用于三阶色散的补偿.     

Optimizing input and output chirps up to the third-order for sub-nanojoule,ultra-short pulse compression in small core area PCF

Compression of sub-nanojoule laser pulses using a commercially available photonic crystal fiber (PCF) with zero dispersion wavelength of 860 nm is discussed. A twofold pulse compression starting from 24 fs transform limited seed pulses around 800 nm is experimentally demonstrated as a verification of our simulations. Theory shows that by the optimization of input and output chirp parameters up to the third order, high quality, 5.7 fs pulses can be generated from a cost efficient experimental setup. Further calculations show that 1 ps pulses with central wavelength of 800 nm can be compressed down to 50 fs in the normal dispersion regime of the fiber with proper dispersion compensation. Calculations also show that dispersion flattened fibers can improve both the quality and the duration of compressed pulses. PACS 42.65.Re     

Femtosecond Transform-Limited Pulse Generation by Compensating for the Linear Chirp of SPM Spectra in Dispersion Shifted Fibers

A simple technique of pulse compression, based on the linear chirp compensation of self-phase modulation (SPM) spectra in dispersion shifted fibers, is demonstrated. The optimization procedure is carried out, for a short span of a single-mode fiber, using a parabolic law, which describes the behavior of the squared output pulse width versus the pump peak power in the case of Gaussian pulses. The experimental results give a minimum pulse duration of 233 fs, which is in good agreement with the model. Shorter and coherent pulses, down to 90 fs, have been obtained by inserting an interference filter at the optical output.     

Study of femtosecond soliton dynamics in photonic crystal fiber using the moment method

We investigate the dynamics of femtosecond solitons in photonic crystal fibers (PCFs) by including high-order dispersion terms until to sixth-order in the generalized nonlinear Schrödinger equation, in addition to the nonlinear effects of the self phase modulation, self steepening and Raman scattering. We calculate theoretically the pulse parameters using the moment method. In the case of the fundamental soliton, our computed equations are coupled and difficult to solve analytically. However, we use the finite difference method to calculate numerically pulse parameters using an initially hyperbolic secant pulse at 1550-nm with different peak powers along 10m-PCF. Our numerical results show that the nonlinear regimes allow obtaining pulse compressions and initial pulse amplitudes. Furthermore, we remark a pulse broadening, and weak shifts of the peak power positions and frequencies in the critical and dispersive regimes. The use of an initial chirp provides a better pulse compressions and especially for low input powers. Also, the initial positive chirp reduces the optimal compression position lengths, while the negative one increases them. Therefore, we conclude that our theoretical calculations and numerical simulation results show that the moment method associated with the finite differences method is effective for the study of femtosecond pulse dynamics in PCFs.     

Distortion of parabolic pulse due to higher-order effects in a dispersion-decreasing fiber

Considering Third-order Dispersion (TOD) and Stimulated Raman Scattering effect (SRS) simultaneously, the properties of the self-similar parabolic pulse evolution in a dispersion-decreasing optical fiber with normal group-velocity dispersion are firstly investigated in our paper. Our results show that parabolic pulses are distorted and the characteristic of exactly self-similarity will be lost due to the High-order effects. When only the TOD is taken into account, the chirp still reveals highly linear but glows into asymmetric which causes the waveform appearing optical wave breaking. When only considering SRS, the pulse still reveals highly linear chirp only linearity range narrow down, resulting in delaying the self-similar evolution. When considering SRS and TOD simultaneously, parabolic pulses are distorted less and the characteristic of exactly self-similarity will be better due to SRS effect than only considering TOD effect. The highly linear chirp in optical pulse still allows for efficient and high-quality pulse compression by use of dispersion compensation technique.     

Direct generation of 128-fs Gaussian pulses from a compensation-free fiber laser using dual mode-locking mechanisms

We have experimentally demonstrated the direct generation of 128-fs pulses in an all-anomalous-dispersion all-fiber mode-locked laser. The laser is free of dispersion compensation in the cavity based on standard single mode fiber (SMF). The time-bandwidth product is 0.536. The laser is achieved by using two mode-lockers, one is nonlinear polarization rotation (NPR), and the other is nonlinear amplifying loop mirror. The coexistence of dual mode-locking mechanisms can decrease the cavity length to 12-m, and also results in producing high-quality pulses with a Gaussian shape both on the pulse profile and spectrum, but without Kelly sidebands.