Analysis of intrachannel nonlinear effects in highly dispersedoptical pulse transmission

We analyze intrachannel nonlinear effects in high-bit-rate transmission systems based on short optical pulses that are dispersion compensated. We perform an analytical study of a generic example with two pulses, in which case the nonlinearity shifts the pulses in time and results in the generation of leading and trailing pulse echoes. We show that in all the relevant range of parameters, the magnitude of the nonlinear impairments reduces monotonically with the reduction of pulse width and with the increase of the dispersion coefficient     

Analytical optimization of the net residual dispersion in SPM-limited dispersion-managed systems

Dispersion management is an effective technique to suppress the nonlinear impairment in fiber transmission systems, which includes tuning the amounts of precompensation, residual dispersion per span (RDPS), and net residual dispersion (NRD) of the systems. For self-phase modulation (SPM)-limited systems, optimizing the NRD is necessary because it can greatly improve the system performance. In this paper, an analytical method is presented to optimize NRD for SPM-limited dispersion-managed systems. The method is based on the correlation between the nonlinear impairment and the output pulse broadening of SPM-limited systems; therefore, dispersion-managed systems can be optimized through minimizing the output single-pulse broadening. A set of expressions is derived to calculate the output pulse broadening of the SPM-limited dispersion-managed system, from which the analytical result of optimal NRD is obtained. Furthermore, with the expressions of pulse broadening, how the nonlinear impairment depends on the amounts of precompensation and RDPS can be revealed conveniently.     

双曲正割脉冲在光纤中传输的非线性效应

高斯型脉冲在光纤中的传输已有解析解,而对于一些锁模激光器发射的双曲正割脉冲在光纤中的传输特性尚未有解析解。为了研究高功率双曲正割脉冲在单模光纤中的传输特性,文中借助于分步傅里叶方法分析了峰值功率5 000W的双曲正割脉冲在初始啁啾为1.7 rad/s,色散长度0.64 m,非线性长度1.53 m 时1 m 长的光纤中的脉冲演化过程。结果表明,其色散感应脉冲展宽的定性特征与高斯脉冲近似一致,但色散感应的频率啁啾沿脉冲不再是纯线性变化,若输入脉冲峰值功率过大,会引起频谱振荡。     

Dispersion compensation-free fiber laser mode-locked and stabilized by high-contrast saturable absorber mirror

We report here a compact diode-pumped fiber laser that represents a promising route to designing a portable and rugged picosecond light source. The laser presented in this paper is based on a high-contrast semiconductor saturable absorber mirror (SESAM) and targets reliable picosecond-range sources. The cavity is simple since no dispersion compensators are used, and the SESAM-based mode locking mechanism is robust and self-starting, resulting in low-maintenance turn-key operation. We investigated pulse formation in a short-length fiber cavity and found that nonlinear effects in a near-resonant SESAM in combination with large-cavity dispersion provide the predominant mechanism that causes pulse shaping. The role of a resonant high-contrast SESAM in preventing low-frequency Q-switching instability has been elucidated. The effect of the recovery time of the SESAM on the stretched pulse width and spectrum for resonant-type absorber mirrors was also studied.     

Evaluation of transmission characteristics of chirped DFB lasers indispersive optical fiber

Experimental and analytical results are presented for pulse distortion and receiver penalty associated with wavelength chirp of 1.5 μm distributed feedback (DFB) lasers in the presence of fiber dispersion. An approximate analytical model for dispersion penalty due to chirp is given and shown to provide reasonable agreement with the experimental results obtained for digital transmission at 1.7 Gb/s. The model captures the important features of chirp that lead to dispersion penalty, such as the maximum wavelength excursion, the chirping time, and the energy content at the leading edge of the pulse during chirp. The utility of the model is that the parameters used in it can be readily obtained from single experimental measurements. The limitations of the model are also discussed     

Spectrally Resolved Approach for Modeling Short Pulse Amplification in Er$^{3+}$-Doped Fibers

We study pulse propagation in Er³⁺-doped fiber amplifiers (EDFA) within the framework of a spectrally resolved pulse rate-propagation equations model. Our model accounts for the effects of gain dispersion, gain saturation, waveguide and chromatic dispersion, and amplified spontaneous emission. This model allows us to approximate the effects of nonlinear resonant dispersion on short pulse amplification in doped fibers, without reverting to the generalized nonlinear Schroedinger equation. Numerical results of the time-dependent power spectrum of the amplified pulse demonstrate subpicosecond pulse propagation in EDFAs     

Evolution behavior of chirped tan-hyperbolic pulse through single mode fiber in the simultaneous presence of fiber loss,dispersion and self-phase modulation

We present the results of tan-h pulse propagation through single mode fiber in dispersion dominant regime as well as in the simultaneous presence of fiber loss, group velocity dispersion and self-phase modulation. Both un-chirped/chirped cases have been considered. The pulse was propagated using split-step Fourier method based nonlinear Schrödinger equation. Results clearly show that in the absence of fiber nonlinearity, the pulse goes on broadening with the propagated distance. However, in the presence of the fiber nonlinearity, the pulse initially experiences compression and then undergoes broadening at a faster rate. As the value of sharpness parameter increases, the compression also increases. The results of compensation of group velocity dispersion using dispersion compensating fiber considering the setups of pre-, post- and the combination of pre- and post-compensations are also presented. These investigations provide a detailed study and deeper insight about how fiber responses to such type of optical pulses.     

RMS width of pulses in nonlinear dispersive fibers

An approximate analytical expression for the root means square (RMS) width of pulses propagating in nonlinear, dispersive fibers is derived. This result is useful for predicting how far a pulse can travel before it suffers significant distortion due to the combined influence of the nonlinearity of the refractive index and the dispersive properties of the fiber. This theory applies to pulses operating near the zero-dispersion wavelength where dispersion alone has a negligible influence, but where the combined influence of nonlinear self-phase modulation and dispersion can produce a significant effect     

阶跃光纤中相近频率传输区域的调制不稳定性

利用激光脉冲在光纤中传播时所遵守的相干非线性薛定谔耦合方程,研究了非线性双折射色散阶跃光纤(SWDF)中两相近频率的激光脉冲,其偏振方向相互正交且平行于光纤的双折射轴,且偏振方向沿2个双折射轴的分量强度相等时,在同为反常色散区和正常色散区所产生的调制不稳定性.结果表明,在反常非线性区和正常色散区都能产生调制不稳定性;在正常色散区存在不同的调制不稳定性功率区域,对应不同的功率区域导致增益谱表现出明显的不同,并且,当输入功率和波长差(或频率差)一定时,增益谱随传输距离变化保持形态不变.     

Experiment and analysis of two-photon absorption spectroscopy using a white-light continuum probe

We present an experimental technique along with the method of data analysis to give nondegenerate two-photon absorption (2PA) spectra. We use a femtosecond pump pulse and a white-light continuum (WLC) probe to rapidly generate the 2PA spectra of a variety of materials. In order to analyze data taken with this method, the spectral and temporal characteristics of the WLC must be known, along with the linear dispersion of the sample. This allows determination of the temporal walk-off of the pump and probe pulses as a function of frequency caused by group-velocity mismatch. Data correction can then be performed to obtain the nonlinear losses. We derive an analytical formula for the normalized nonlinear transmittance that is valid under quite general experimental parameters. We verify this on ZnS and use it for the determination of 2PA spectra of some organic compounds in solution. We also compare some of the data on organics with two-photon fluorescence data and find good agreement.     

光纤布拉格光栅非线性孤子的特性分析

以非线性耦合模理论为基础，用数值计算的方法分析了光纤光栅非线性孤子的特性。结果表明，在较弱光脉冲输入时，脉冲被展宽幅度降低；在强光脉冲输入时，脉冲的幅度，速度和脉宽保持不变，孤子形成；当更强光脉冲输入时，脉冲被压缩同时产生随距离而变的线性啁啾。当波长位于负色散区的弱脉冲和位于正常色散区的强泵浦脉冲共同传输时，输入弱脉冲被压缩。     

超高斯型色散渐减光纤中脉冲的传输特性分析

为了研究超高斯脉冲在具有不同陡峭程度的超高斯型色散渐减光纤中的传输特性，采用了非线性薛定谔方程和分步傅里叶变换的方法，数值模拟了超高斯脉冲在超高斯型色散渐减光纤中的演化规律。在反常色散区考虑色散和非线性效应的情况下，对超高斯脉冲的阐述特性进行了时域和频域上的理论分析与实验验证。结果表明，陡峭程度m=4时, 超高斯型色散渐减光纤的传输特性最好。此研究对超高斯型色散渐减光纤中脉冲的传输特性分析是有帮助的。     

Cr4+:YAG激光器增益介质的非线性效应对振荡脉冲的影响

Cr4+:YAG晶体具有独特的增益特性和非线性特性，从Cr4+:YAG激光器的传播方程出发讨论了晶体的非线性效应对激光脉冲的影响，由于激光晶体的非线性效应Cr4+∶YAG激光器可以在不存在其他锁模器件情形下自锁模，并使激光脉冲出现频率啁啾，在激光器腔内进行色散补偿并使色散与非线性效应达到平衡时腔内可形成孤子脉冲，成为一种孤子源。     

负折射介质中高阶非线性效应所致啁啾的研究

利用分步傅里叶法对负折射介质中的广义非线性薛定谔方程进行数值模拟,进而分别得到自相位调制、赝五阶非线性、自陡峭、二阶非线性色散所致啁啾及各项非线性所致总啁啾的演变图.从啁啾上分析了负折射介质中各项非线性效应在脉冲传输时的作用,结果表明,负折射介质中,自陡系数取值的正负可控使脉冲中心位置可向前后沿偏移;在正常色散区,赝五阶非线性系数为负时加速脉冲的展宽,二阶非线性色散项系数取正时使脉冲展宽,取负时使脉冲变窄.     

啁啾型周期性调制晶体中感应非线性群速度色散的研究

提出了一种研究啁啾型周期极性铌酸锂晶体 (CPPLN)中非线性群速度色散的简单方法。发现不仅谐波可以获得色散 ,而且在一定条件下基频光也可以在CPPLN中获得色散。讨论了CPPLN的色散特性 ,并与传统色散元件进行了比较。     

单脉冲锁模光纤激光器输出特性的数值研究

为了研究不同腔内净色散下单脉冲被动锁模光纤激光器的输出特性,采用以非线性薛定谔方程为数学模型和分步傅里叶的方法,对激光脉冲在腔内的演化进行了理论分析。获得了在保持单脉冲稳定输出时激光器一些参量与腔内净色散的变化关系,并针对净色散为正的情况,对输出脉冲进行了腔外解啁啾压缩,压缩比达到10倍以上,分析了压缩所需的负色散值以及压缩后脉宽的情况。结果表明,小信号增益系数最大值与净腔色散大体上成正比关系,且当小信号增益系数达到最大值时,输出脉冲的脉宽以及相应的时间带宽积呈现逐渐增加的趋势,3dB带宽则呈现出先增加后减少的趋势。该研究结果为优化被动锁模光纤激光器提供了参考。     

Ultrashort-Pulse High-Power Yb3+-Doped Fiber Amplifiers

Ultrashort optical pulse propagation in high-power Yb³⁺-doped fiber amplifiers (YDFA) is studied using a spectrally resolved nonlinear power equation for the coupled pulse components. The Yb³⁺ ions transitions are modeled using a rate equation. Examples for high-power YDFAs with normal dispersion show good qualitative agreement with experimental results. We analyze the effects of the incident pulse wavelength, pulse peak power, Yb³⁺ concentration, pump filling factor, fiber length, pumping configuration, pump power and nonlinear index, on the intensity distribution of short amplified pulses. We also demonstrate the spectral compression of an initially negative-chirped pulse.     

高双折射光纤中矢量调制不稳定性

利用光脉冲在光纤中传播时所遵守的相干非线性薛定谔耦合方程,研究了偏振方向沿两个双折射轴的分量强度相等时,在反常色散区和正常色散区所产生的调制不稳定性.结果表明在反常色散区和正常色散区,对应不同的功率区域输入脉冲有不同的增益谱,并且当双折射性质变化时导致增益谱表现出明显的不同.     

Stretched-pulse optical fiber communications

We compare numerically long-distance propagation of two types of nonlinear pulses: a stretched pulse in a fiber with alternating normal and anomalous dispersion and a soliton in a fiber with uniformly anomalous dispersion. Numerical evaluation of timing jitter and Q factor reveals that stretched pulses can be propagated over longer distances than solitons with the same (averaged) fiber dispersion in the presence of weak fixed-frequency filtering. We also examine pulse-to-pulse interactions between stretched pulses and the influence of fluctuations of the fiber dispersion.     

Nonlinear property analysis of long-period fiber gratings usingdiscretized coupled-mode theory

We present generalized mathematical expressions for coupled-mode equations for nonlinear pulse propagation in fiber gratings using discretized coupled-mode theory and quantitatively analyze the nonlinear properties of long-period fiber gratings, considering multimode coupling between the core mode and several cladding modes. The calculations yield nonlinear responses for the case of long-period fiber gratings, including pulse shaping and all-optical switching in the self- and cross-phase modulation regimes. In addition, we briefly discuss the group delay properties of long-period fiber gratings and present several numerical examples of nonlinear pulse compression, which is related to strong dispersion and soliton-like behavior in fiber gratings