基于优化微扰技术的高速多跨距非线性光纤通信系统研究
|
摘要
在高速多跨距非线性光纤通信系统中,光纤色散和非线性效应对通信质量的影响日益严重,已成为限制光纤通信系统向更高容量发展的主要因素。因而在现有设备的基础上对系统进行有效的色散和非线性效应补偿,提高信道容量已成为当前光纤通信领域一个主要的研究方向。本文提出了基于加权微扰技术的数字反向传输,分别在波分复用(WDM)系统和偏振波分复用(PDM-WDM)系统中对光纤色散和非线性进行了同步补偿,显著地提高了补偿精度,降低了所需计算量；提出利用分段微扰技术对含非线性噪声的多跨距光纤通信系统的信道容量进行了解析计算,获得了不同传输速率及不同非线性系数下信道容量随输入功率变化的曲线；在短计算步长下提出了简化微扰技术,有效地降低了所需计算量；在多跨距光纤传输中提出了低阶改进微扰技术,为非线性效应的分析及补偿提供了更为精确的半解析模型。本文主要的创新研究内容及重要结论如下：
提出了加权微扰技术(APT),不仅使传统的微扰理论适用于数字反向传输,而且引入了加权非迭代概念首次得到了一个反向传输后的非迭代递归解析输出信号表达式,大大降低所需运算量的同时提高了传统微扰技术的精确度,并且可以对WDM系统中信道间的色散走离失真及色散和非线性效应之间的相互作用进行补偿。理论研究及数值仿真结果表明,相对传统数字反向传输,基于加权微扰技术的数字反向传输在每信道每抽样点上能减少6Nspan个乘法计算数量。并且当输入功率大于-2dBm,能降低对重采样速率的需求,同时拥有更高的补偿精度。在计算步长等于跨距长度,输入功率为3dBm时能有效地提高2.4dB系统Q值。
基于加权微扰技术,推导出了偏振复用-波分复用(PDM-WDM)系统中反向耦合Manakov方程组的半解析解,通过递归运算获得了此系统中多跨距光纤传输链路的输出信号半解析表达式。得到PDM-WDM系统中基于加权微扰技术的数字反向传输原理图,并对所需的计算量进行了理论分析,研究结果表明加权微扰技术在每信道每抽样点上能减少17Nspaan个乘法计算数量。由数值仿真结果对比可知,在输入功率等于2dBm,非线性系数为3.5(W·km)-1时,基于加权微扰技术的数字反向传输系统Q值比传统数字反向传输系统Q值提高了46%。当系统信道数为24,输入功率为-1dBm时,系统Q值有3.5dB的提高。高非线性系数、高输入功率和多信道下加权微扰技术拥有更好的补偿效果。
提出利用分段微扰技术对含乘性噪声的多跨距非线性光纤通信系统的信道容量进行解析计算。获得了关于输入输出的条件概率转移密度函数的半解析表达式。在同时考虑光纤损耗、色散、Kerr非线性效应及ASE噪声的情况下,解析推导出了信道容量的表达式。计算分析了系统各参数对信道容量产生的影响,结果表明信道容量不会随着输入功率的提高而单调增大,而是在达到一个峰值点后随着输入功率的继续增大而减小；光纤非线性效应对信道容量的影响严重,在高输入功率和长距离传输下会加速信道容量的衰减；在输入功率小于9mW的情况下,通过提高系统传输速率(>40Gbit/s),可以获得更大的信道容量峰值,但是在高输入功率条件下这种效果将明显减弱。
为减少传统微扰方法的计算量,在小计算步长下提出了简化微扰技术。理论推导和数值仿真计算得到当计算步长小于30km时,简化微扰技术能保持较高计算精度的同时有效降低运算量,可取代传统微扰方法来使用。在多跨距非线性光纤传输链路中提出了低阶改进微扰技术,理论分析表明低阶改进微扰技术在只取一阶微扰解的情况下能有效补偿高阶微扰项舍弃所带来的计算误差,提高计算精度。数值仿真结果表明低阶改进微扰技术在输入功率为8mW,传输距离为120km时,提高2.1dB计算精度,并且随着传输距离和输入功率的继续增大计算精度提高更为显著。
综合上述研究结果可知,本文提出四种优化微扰技术为高速多跨距非线性光纤系统性能的优化及信道容量的解析计算提供了更为精确有效的计算模型,对进一步提高系统传输速率、扩大通信容量的相关研究具有重要的理论和应用价值。
In high-speed multispan nonlinear optical fiber systems, nonconstructive effects of fiber nonlinearity and dispersion can significantly degrade signal quality, which limits the transmission capacity. Therfore, mitigating or compensating these impairments to increase information capacity becomes a crucial research component for optical communication. In this dissertation, a weighted perturbation technique is proposed for digital backward propagation (DBP) to compensate fiber nonlinearity and dispersion jointly in both wavelength-division multiplexing (WDM) and polarization-division multiplexed WDM (PDM-WDM) systems, which can acquire a more accurate compensation result and reduce computational complexity effectively. A piecewise perturbation technique is developed to examine the information capacity of the multispan optical fiber communication system with multiplicative noise as a nonlinear channel. The relationship between the nonlinear channel capacity and input signal power with various Kerr nonlinear coefficients and bit rates is analysed rigorously. With the purpose of reducing computational load, a simplified perturbation technique is presented when step size is short. Furthermore, a modified low-order perturbation technique is derived in multispan optical fiber transmission systems. Based on it, a more accurate semi-analytical solution of nonlinear Schrodinger equation (NLSE) can be obtained.
A weighted perturbation technique is proposed and basing on this technique, an improved digital backward propagation (IDBP) is investigated to compensate Kerr effects and dispersion jointly in WDM systems. In this weighted perturbation technique, a non-iterative weighted concept is presented to replace the iterative in the analytical recursion expression, which can dramatically simplify the complexity and improve accuracy compared to the traditional perturbation technique (TPT). Furthermore, an analytical recursion expression of the output after backward propagation is obtained initially, which the inter-channel walk-off effect and the combined nonlinear distortion cased by Kerr nonlinearity and dispersion can be consisted in. The research indicates that about6Nspan more multiplications per sample per channel will be required for conventional DBP (CDBP) than IDBP. When launch power is higher than-2dBm, IDBP allows a lower oversampling rate and is more accurate than CDBP for nonlinearity compensation, especially about2.4dB benefits than CDBP at3dBm with one step size per span.
With the application of weighted perturbation technique in PDM-WDM systems, a semi-analytical solution of coupled Manakov equations can be obtained. Moreover, an analytical recursion expression of the output after backward propagation is derived. Based on this, the improved digital backward propagation (IDBP) is extended into PDM-WDM systems. A rigorous analysis of the computational cost is carried out and numerical simulations are performed in the corresponding transmission system with various parameters. The results indicate that about17Nspan more multiplications per sample per channel will be required for CDBP than IDBP in PDM-WDM systems. Comparison with CDBP, there will be46percent improvement of Q-factor for IDBP at2dBm with high Kerr nonlinear coefficient and3.5dB benefits at-1dBm with24channels.
A piecewise perturbation technique is developed to examine the information capacity of the multispan optical fiber communication system with multiplicative noise as a nonlinear channel and a semianalytic expression of the conditional PDF is obtained initially. What is more, the information capacity is deduced analytically when chromatic dispersion, Kerr nonlinearity, fiber losses, and ASE noise play the importance role simultaneously. The researches indicate that there will be no help to improve the channel capacity by improving input signal power. For a higher speed transmission system, the channel capacity appears to be a larger peak value, then follows it with weakening quickly with the input power increasing, which means a larger value of the channel capacity can be obtained for a high bit rate (>40Gbit/s) transmission channel at the input power levels such that Pin,<9mW.
A simplified perturbation technique is put forward to reduce computational load when step size is shorter than30km, which can replace TPT for numerical simulation. Additionally, in order to compensate the deviation from ignoring the high-order perturbation solution, a modified low-order perturbation technique is derived in multispan optical fiber transmission systems. The results of numerical simulations carried out show that this technique provides about2.1dB benefits than TPT at8mW with120km transmission distance and performs even better with larger transmission distance and launch power.
The overall results of this dissertation illustrate that the four proposed perturbation techniques can provide more accurate results to improve the performance of high-speed multispan nonlinear optical fiber systems and calculate it information capacity analytically. This related study has significant theorical and practical value for increasing the system capacity and transmission rate.
提出了加权微扰技术(APT),不仅使传统的微扰理论适用于数字反向传输,而且引入了加权非迭代概念首次得到了一个反向传输后的非迭代递归解析输出信号表达式,大大降低所需运算量的同时提高了传统微扰技术的精确度,并且可以对WDM系统中信道间的色散走离失真及色散和非线性效应之间的相互作用进行补偿。理论研究及数值仿真结果表明,相对传统数字反向传输,基于加权微扰技术的数字反向传输在每信道每抽样点上能减少6Nspan个乘法计算数量。并且当输入功率大于-2dBm,能降低对重采样速率的需求,同时拥有更高的补偿精度。在计算步长等于跨距长度,输入功率为3dBm时能有效地提高2.4dB系统Q值。
基于加权微扰技术,推导出了偏振复用-波分复用(PDM-WDM)系统中反向耦合Manakov方程组的半解析解,通过递归运算获得了此系统中多跨距光纤传输链路的输出信号半解析表达式。得到PDM-WDM系统中基于加权微扰技术的数字反向传输原理图,并对所需的计算量进行了理论分析,研究结果表明加权微扰技术在每信道每抽样点上能减少17Nspaan个乘法计算数量。由数值仿真结果对比可知,在输入功率等于2dBm,非线性系数为3.5(W·km)-1时,基于加权微扰技术的数字反向传输系统Q值比传统数字反向传输系统Q值提高了46%。当系统信道数为24,输入功率为-1dBm时,系统Q值有3.5dB的提高。高非线性系数、高输入功率和多信道下加权微扰技术拥有更好的补偿效果。
提出利用分段微扰技术对含乘性噪声的多跨距非线性光纤通信系统的信道容量进行解析计算。获得了关于输入输出的条件概率转移密度函数的半解析表达式。在同时考虑光纤损耗、色散、Kerr非线性效应及ASE噪声的情况下,解析推导出了信道容量的表达式。计算分析了系统各参数对信道容量产生的影响,结果表明信道容量不会随着输入功率的提高而单调增大,而是在达到一个峰值点后随着输入功率的继续增大而减小；光纤非线性效应对信道容量的影响严重,在高输入功率和长距离传输下会加速信道容量的衰减；在输入功率小于9mW的情况下,通过提高系统传输速率(>40Gbit/s),可以获得更大的信道容量峰值,但是在高输入功率条件下这种效果将明显减弱。
为减少传统微扰方法的计算量,在小计算步长下提出了简化微扰技术。理论推导和数值仿真计算得到当计算步长小于30km时,简化微扰技术能保持较高计算精度的同时有效降低运算量,可取代传统微扰方法来使用。在多跨距非线性光纤传输链路中提出了低阶改进微扰技术,理论分析表明低阶改进微扰技术在只取一阶微扰解的情况下能有效补偿高阶微扰项舍弃所带来的计算误差,提高计算精度。数值仿真结果表明低阶改进微扰技术在输入功率为8mW,传输距离为120km时,提高2.1dB计算精度,并且随着传输距离和输入功率的继续增大计算精度提高更为显著。
综合上述研究结果可知,本文提出四种优化微扰技术为高速多跨距非线性光纤系统性能的优化及信道容量的解析计算提供了更为精确有效的计算模型,对进一步提高系统传输速率、扩大通信容量的相关研究具有重要的理论和应用价值。
In high-speed multispan nonlinear optical fiber systems, nonconstructive effects of fiber nonlinearity and dispersion can significantly degrade signal quality, which limits the transmission capacity. Therfore, mitigating or compensating these impairments to increase information capacity becomes a crucial research component for optical communication. In this dissertation, a weighted perturbation technique is proposed for digital backward propagation (DBP) to compensate fiber nonlinearity and dispersion jointly in both wavelength-division multiplexing (WDM) and polarization-division multiplexed WDM (PDM-WDM) systems, which can acquire a more accurate compensation result and reduce computational complexity effectively. A piecewise perturbation technique is developed to examine the information capacity of the multispan optical fiber communication system with multiplicative noise as a nonlinear channel. The relationship between the nonlinear channel capacity and input signal power with various Kerr nonlinear coefficients and bit rates is analysed rigorously. With the purpose of reducing computational load, a simplified perturbation technique is presented when step size is short. Furthermore, a modified low-order perturbation technique is derived in multispan optical fiber transmission systems. Based on it, a more accurate semi-analytical solution of nonlinear Schrodinger equation (NLSE) can be obtained.
A weighted perturbation technique is proposed and basing on this technique, an improved digital backward propagation (IDBP) is investigated to compensate Kerr effects and dispersion jointly in WDM systems. In this weighted perturbation technique, a non-iterative weighted concept is presented to replace the iterative in the analytical recursion expression, which can dramatically simplify the complexity and improve accuracy compared to the traditional perturbation technique (TPT). Furthermore, an analytical recursion expression of the output after backward propagation is obtained initially, which the inter-channel walk-off effect and the combined nonlinear distortion cased by Kerr nonlinearity and dispersion can be consisted in. The research indicates that about6Nspan more multiplications per sample per channel will be required for conventional DBP (CDBP) than IDBP. When launch power is higher than-2dBm, IDBP allows a lower oversampling rate and is more accurate than CDBP for nonlinearity compensation, especially about2.4dB benefits than CDBP at3dBm with one step size per span.
With the application of weighted perturbation technique in PDM-WDM systems, a semi-analytical solution of coupled Manakov equations can be obtained. Moreover, an analytical recursion expression of the output after backward propagation is derived. Based on this, the improved digital backward propagation (IDBP) is extended into PDM-WDM systems. A rigorous analysis of the computational cost is carried out and numerical simulations are performed in the corresponding transmission system with various parameters. The results indicate that about17Nspan more multiplications per sample per channel will be required for CDBP than IDBP in PDM-WDM systems. Comparison with CDBP, there will be46percent improvement of Q-factor for IDBP at2dBm with high Kerr nonlinear coefficient and3.5dB benefits at-1dBm with24channels.
A piecewise perturbation technique is developed to examine the information capacity of the multispan optical fiber communication system with multiplicative noise as a nonlinear channel and a semianalytic expression of the conditional PDF is obtained initially. What is more, the information capacity is deduced analytically when chromatic dispersion, Kerr nonlinearity, fiber losses, and ASE noise play the importance role simultaneously. The researches indicate that there will be no help to improve the channel capacity by improving input signal power. For a higher speed transmission system, the channel capacity appears to be a larger peak value, then follows it with weakening quickly with the input power increasing, which means a larger value of the channel capacity can be obtained for a high bit rate (>40Gbit/s) transmission channel at the input power levels such that Pin,<9mW.
A simplified perturbation technique is put forward to reduce computational load when step size is shorter than30km, which can replace TPT for numerical simulation. Additionally, in order to compensate the deviation from ignoring the high-order perturbation solution, a modified low-order perturbation technique is derived in multispan optical fiber transmission systems. The results of numerical simulations carried out show that this technique provides about2.1dB benefits than TPT at8mW with120km transmission distance and performs even better with larger transmission distance and launch power.
The overall results of this dissertation illustrate that the four proposed perturbation techniques can provide more accurate results to improve the performance of high-speed multispan nonlinear optical fiber systems and calculate it information capacity analytically. This related study has significant theorical and practical value for increasing the system capacity and transmission rate.
引文
[1]Maiman TH. Stimulated optical radiation in ruby[J]. Nature,1960,187:493-494.
[2]K. C. Kao and G. A. Hockham. Dielectric-fiber surface waveguides for optical frequencies[J]. Proc.IEE,1966,113(7):1151-1158.
[3]C. Randy Giles, Emmanuel Desurvire. Modeling Erbium-Doped Fiber Amplifiers[J]. IEEE Journal of lightwave technology,1991,9(2):271-283.
[4]Jay Sharping, Yoshitomo Okawachi, Alexander Gaeta. Wide bandwidth slow light using a Raman fiber amplifier[J]. Optics Express,2005,16(16):6092-6098.
[5]Hideki Ishio, Junichiro Minowa, Kiyoshi Nosu. Review and status of wavelength-division-multiplexing technology and its application[J]. Journal of lightwave technology,1984,LT-2(4):448-462
[6]C. A. Brackett. Dense wavelength division multiplexing networks:principles and applications[J]. Journal on selected areas in communications,1990,8(6):948-964
[7]A. R. Chraplyvy. Limitations on lightwave communications imposed by optical-fber nonlinearities[J]. J. Lightw. Technol.,1990,8(10):1548-1557.
[8]N. S. Bergano. Wavelength division multiplexing in long-haul transoceanic transmission systems[J]. J. Lightw. Technol.,2005,23(12):4125-4139.
[9]M. Jinno, T. Sakamoto, J. Kani, S. Aisawa, K. Oda, M. Fukui, H. Ono, K. Oguchi. First demonstration of 1580 nm wavelength band WDM transmission for doubling usable bandwidth and suppressing FWM in DSF[J]. Electronics Letters,1997,33(10):882-883.
[10]K. O. Hill, F. Bilodeau, B. Malo, T. Kitagawa, S. Theriault, D. C. Johnson, J. Albert, K. Takiguchi. Chirped in-fber Bragg gratings for compensation of optical-fiber dispersion[J]. Opt. Lett.,1994,19:1314-1316.
[11]C. K. Madsen, G. Lenz. Optical all-pass filters for phase response design with applications for dispersion compensation[J]. Photonics Technology Letters,1998,10(7):994-996.
[12]A. Yariv, D. Fekete, D. M. Pepper. Compensation for channel dispersion by nonlinear optical phase conjugation[J]. Opt. Lett.,1979,4:52-54.
[13]S. Watanabe, T. Naito, T. Chikama. Compensation of chromatic dispersion in a single-mode fiber by optical phase conjugation[J]. Photonics Technology Letters,1993,5(1):92-95.
[14]C. D. Poole, J. M. Wiesenfeld, D. J. Digiovanni, A. M. Vengsarkar. Optical fiber-based dispersion compensation using higher order modes near cutoff[J]. J. Lightw. Technol.,1994, 12(10):1746-1758.
[15]Quang Le N. T., Torben Veng, Lars Gruner-Nielsen. New dispersion compensating module for compensation of dispersion and dispersion slope of non-zero dispersion fibres in the C-band[C]. OFC2000, paper TuH5-1.
[16]K. Mukasa, H. Moridaira, T. Yagi, K. Kokura. New type of dispersion management transmission line with MDFSD for long-haul 40 Gb/s transmission[C]. OFC2002, paper THGG2.
[17]Xiaoqiong Qi, Xiaoping Zhang, Haiqing Wei, David V. Plant. Linearity of nonlinear perturbations in fiber-optic transmission lines and its applications to nonlinear compensations[J]. J. Opt. Soc. Am. B.,2006,23(10):2032-2039.
[18]H. Wei and D. V. Plant. Fundamental equations of nonlinear fiber optics in optical modeling and performance predictions[C]. Proc. SPIE5178,2003:255-266.
[19]B. Xu, M. Brandt-Pearce. Analysis of noise amplification by a CW pump signal due to fiber nonlinearity[J]. Photonics Technology Letters,2004,16(4):1062-1064.
[20]J. P. Gordon, L. F. Mollenauer. Phase noise in photonic communications-systems using linear-amplifiers[J]. Optics Letters,1990,15(23):1351-1353.
[21]F. Zhang, C. A. Bunge, K. Petermann. Analysis of nonlinear phase noise in single-channel retum-to-zero differential phase-shift keying transmission systems[J]. Optics Letters,2006, 31(8):1038-1040.
[22]C. C. Wei, J. Chen. Convergence of phase fluctuation induced by intrachannel four-wave mixing in differential phase-shift keying transmission systems via phase fluctuation averaging[J]. Optics Lettes,2007,32(10):1217-1219.
[23]Xiao Qiong Qi, Xiaoping Zhang, Qun Feng Shao. Reduction of parametric amplified noise on nonlinear fiber channels by use of wiener filtering[J]. J. Lightw. Technol.,2008, 26(18):3210-3215.
[24]漆晓琼,邵群峰,张晓萍。基于沃尔泰拉理论的集总光纤非线性噪声补偿[J]。中国激光,2007,34(11)：1527-1532.
[25]Dong Yang, Shiva Kumar. Realization of optical OFDM using time lenses and its comparison with optical OFDM using FFT[J]. Opt. Express,2009,17:17214-17226.
[26]S. Kumar, D. Yang. Optical implementation of orthogonal frequency-division multiplexing using time lenses[J]. Opt. Lett.,2008,33(17):2002-2004.
[27]M. S. Afiad, Dirk van den Borne, Sander Lars Jansen, Torsten Wuth, Maxim Kuschnerov, Guido Grosso, Antonio Napoli, Huug de Waardt. A comparison of electrical and optical dispersion compensation for 111-Gb/s POLMUX-RZ-DQPSK[J]. J. Lightw. Technol.,2009, 27(16):3590-3598.
[28]K. Roberts, L. Chuandong, L. Strawczynski, M. O. Sullivan, I. Hardcastle. Electronic precompensation of optical nonlinearity[J]. IEEE Photon. Technol. Lett.,2006, 18(2):403-405.
[29]X. Li, X. Chen, G. Goldfarb, E. Mateo, I. Kim, F. Yaman, G. Li. Electronic post-compensation of WDM transmission impairments using coherent detection and digital signal processing[J]. Opt. Express,2008,16(2):880-888.
[30]G. Goldfarb, M. G. Taylor, G. Li. Experimental demonstration of fiber impairment compensation using the split-step finite-impulse-response filtering method[J]. IEEE Photon. Technol. Lett.,2008,20(22):1887-1889.
[31]E. Mateo, L. Zhu, G. Li. Impact of XPM and FWM on the digital implementation of impairment compensation for WDM transmission using backward propagation[J]. Opt. Express,2008,16(20):16124-16137.
[32]R.-J. Essiambre, P. J. Winzer, X. Q. Wang, W. Lee, C. A. White, E. C. Burrows. Electronic predistortion and fiber nonlinearity[J]. IEEE Photon. Technol. Lett.,2006,18:1804-1806.
[33]V. E. Zakharrov, A. B. Shabat. A scheme for intergrating the nonlinear equations of mathematical physics by the method of the inverse scattering problem[J]. Functional Analysis and its Applications,1974,8(3):226-235.
[34]J. A. C. Weidenman, B. M. Herbst. Split-step methods for the solution of the nonlinear schrodinger equation[J]. SIAM J. Numer. Anal,1986,23(3):485-507.
[35]Akira Hasegawa, Frederick Tappert. Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. I. Anomalous dispersion[J]. Applied Physics Letters,1973, 23(3):142-144.
[36]V. S. Shchesnovich, E. V. Doktorov. Perturbation theory for the modified nonlinear Schrodinger solitons[J]. Physica D,1999,129:115-129.
[37]Y. Kodama, S. Wabnitz. Analytical theory of guiding center nonreturn to zero and return to zero signal transmission in normally dispersive nonlinear optical fibers[J]. Opt. Lett.1995, 20:2291-2293.
[38]K. V. Peddannragari, Maite Brandt-Pearce. Volterra series approach for fiber optic communication system designs[J]. J. Lightw. Technol.,1998,16(11):2046-2055.
[39]Jacklyn D. Reis, A. L. Teixeira. Unveiling nonlinear effects in dense coherent optical WDM systems with volterra series[J]. Optics Express,2010,8660-8670.
[40]Armando Vannucci, Paolo Serna, Alberto Bononi. The RP method:a new tool for the iterative solution of the nonlinear Schrodinger equation[J]. J. Lightw. Technol.,2002, 20(7):1102-1112.
[41]Jong-Hyung Lee. Analysis and characterization of fiber nonlinearities with detecministic and stochastic signal sources[D]. Virginia Polytechnic Institute and State University,2000.
[42]Govind P. Agrawall. Nonlinear Fiber Optics (third edition)[M]. Beijing:World Publishing Corporation,2005.
[43]A. K. Atieh, P. Myslinski, J. Chrostowski, P. Galko. Measuring the Raman time constant (T_R) for soliton pulses in standard single-mode fiber[J]. J. Lightw. Technol.,1999, 17(2):216
[44]D. Zwillinger. Handbook of differential equations[M]. Boston Academic,1989:528-531.
[45]Finlay M. Knox, Wladek Forysiak, Nicholas J. Doran.10-Gbt/s soliton communication systems over standard fiber at 1.55 um and the use of dipersion compensation[J]. J. Lightw. Technol.,1995,13(10):1955-1962.
[46]Nicholas J. Smith, Nicholas J. Doran, Wladek Forysiak, Finlay M. Knox. Soliton transmission using periodic dispersion compensation[J]. J. Lightw. Technol.,1997, 15(10):1808-1822.
[47]A. R. Chrapyvy. Limitations on lightwave communications imposed by optical-fiber nonlinearities[J]. J. Lightw. Technol.,1990,8(10):1548-1557.
[48]Seb J. Savory, Giancarlo Gavioli, Robert I. Killey, Polina Bayvel. Electronic compensation of chromatic dispersion using a digital coherent receiver [J]. Optics express,2007, 15(5):2120-2126.
[49]Mike Sieben, Jan Conradi, David E. Dodds. Optical single sideband transmission at 10 Gb/s using only electrical dispersion compensation[J]. J. Lightw. Technol.,1999, 17(10):1742-1749.
[50]G. Charlet, N. Maaref, J. Renaudier, H. Mardoyan, P. Tran, S. Bigo. Transmission of 40 Gb/s QPSK with coherent detection over ultra-long distance improved by nonlinearity mitigation[C]. In Proc. Eur. Conf. Opt. Commun., Cannes France,2006.
[51]K. Roberts, L. Chuandong, L. Strawczynski, M. O'Sullivan, I. Hardcastle. Electronic precompensation of optical nonlinearity[J]. IEEE Photon. Technol. Lett.,2006,18:403-405.
[52]K. Kikuchi. Electronic post-compensation for nonlinear phase fluctuations in a 1000-km 20-Gbit/s optical quadrature phase-shift keying transmission system using the digital coherent receiver[J]. Opt. Express,2008,16:889-896.
[53]L. B. Y. Du, A. J. Lowery. Fiber nonlinearity precompensation for long-haul links using direct-detection optical OFDM[J]. Opt. Express,2008,16:6209-6215.
[54]E. Yamazaki, F. Inuzuka, K. Yonenaga, A. Takada, M. Koga. Compensation of interchannel crosstalk induced by optical fiber nonlinearity in carrier phase-locked WDM system[J]. IEEE Photon. Technol. Lett.,2007,19:9-11.
[55]C. Kurtzke. Suppression of fiber nonlinearities by appropriate dispersion management[J]. IEEE Photo. Technol. Lett.,1993,5(10):1250-1252.
[56]C. Behrens, R. I. Killy, S. J. Savory, P. Bayvel. Reducing the impact of intrachannel nonlinearities by pulse-width optimization in multi-level phase-shift-keyed transmission[C]. In Proc. EOCO,2009, pp.1-2.
[57]O. Kuzucu, Y. Okawachi, R. Salem, M. A. Foster, A. C. Tumer-Foster, M. Lipson, A. L. Gaeta, Spectral phase conjugation via temporal imaging[J]. Opt. Express,2009, 17(22):20605-20614.
[58]Y. Han, G. Li. Coherent optical communication using polarization multiple-input-multiple-output[J]. Opt. Express,2005,13(19):7527-7534.
[59]T. Pfau, S. Hoffmann, O. Adamczyk, R. Peveling, V. Herath, M. Porrmann, R. Noe. Coherent optical communication:towards realtime systems at 40 Gb/s and beyond[J]. Opt. Express,2008,16(2):866-872.
[60]L. B. Du and A. J. Lowery. Improved single channel backpropagation for intra-channel fiber nonlinearity compensation in long-haul optical communication systems[J].Optics Express, 2010,18:17075-17088.
[61]R. Waegemans, S. Herbst, L. Holbein, P. Watts, P. Bayvel, C. Furst and R. I. Killey.10.7 Gb/s electronic predistortion transmitter using commercial FPGAs and D/A converters implementing real-time DSP for chromatic dispension and SPM compensation[J]. Optics Express,2009,17:8630-8640.
[62]S. J. Savory. Digital filters for coherent optical receivers[J]. Optics Express,2008, 16:804-817.
[63]R. Asif, C. Y. Lin and B. Schmauss. Digital backward propagation:A Technique to Compensate Fiber Dispersion and Nonlinear Impairments. Digital Signal Processing[M], InTech-Book Publisher,2011.
[64]Mahdi Malekiha, Dong Yang, Shiva Kumar. Comparison of optical back propagation schemes for fiber-optic communications[J]. Optical Fiber Technology,2013,19:4-9.
[65]E. F. Mateo, G. Li. Compensation of interchannel nonlinearities using enhanced coupled equations for digital backward propagation[J]. Applied Optics,2009,48:6-10.
[66]X. Li, X. Chen, G. Goldfarb, E. Mateo, I. Kim, F. Yaman and G. Li. Electronic post-compensation of WDM transmission impairments using coherent detection and digital signal processing[J]. Optics Express,2008,16:880-888.
[67]E. Ip. Nonlinear compensation using backpropagation for polarization-multiplexed Transmission[J]. Journal of Lightwave Technology,2010,28:939-951.
[68]R. Asif, C. Y. Lin, M. Holtmannspoetter and B. Schmauss. Optimized digital backward propagation for phase modulated signals in mixed-optical fiber transmission link[J]. Optics Express,2010,18:22796-22807.
[69]S. J. Savory, G. Gavioli, E. Torrengo and P. Poggiolini. Impact of interchannel nonlinearities on a split-step intrachannel nonlinear equalizer[J]. IEEE Photonics Technology Letters,2010, 22:673-675.
[70]E. Ip and J. M. Kahn. Compensation of dispersion and nonlinear impairments using digital backpropagation[J]. J. Lightw. Technol.,2008,26:3416-3425.
[71]D. Rafique, A. Ellis. Impact of signal-ASE four-wave mixing on the effectiveness of digital back-propagation in 112 Gb/s PM-QPSK systems[J]. Optics Express,2011,19:3449-3454.
[72]E. F. Mateo, F. Yaman and G. Li. Efficient compensation of inter-channel nonlinear effects via digital backward propagation in WDM optical transmission[J]. Optics Express,2010, 18:15144-15154.
[73]D. Rafique, M. Mussolin, M. Forzati, J. Martensson, M. N. Chugtai and A. D. Ellis. Compensation of intra-channel nonlinear fibre impairments using simplified digital back-propagation algorithm[J]. Optics Express,2011,19:9453-9460.
[74]W. Yan, Z. Tao, L. Dou, L. Li, S. Oda, T. Tanimura, T. Hoshida and J. C. Rasmussen. Low complexity digital perturbation back-propagation[C]. In Proc. ECOC,2011.
[75]L. Zhu and G. Li. Nonlinearity compensation using dispersion-folded digital backward propagation[J]. Optics Express,2012,20(13):14362-14370.
[76]Hoon Kim, Alan H. Gnauck. Experimental investigation of the performance limitation of DPSK systems due to nonlinear phase noise[J]. IEEE Photo. Technol. Lett.,2003, 15(2):320-322.
[77]J. P. Gordon, L. F. Mollenauer. Phase noise in photonic communications systems using linear amplifiers[J]. Optics Letters,1990,15(33):1351-1353.
[78]C. Pare, A. Villeneuve, P.-A. Belanger. Compensating for dispersion and the nonlinear Kerr effect without phase conjugation[J]. Optics Letters,1996,21(7):459-461.
[79]B. Schmauss, R. Asif and C-Y. Lin. Recent advances in digital backward propagation algorithm for coherent transmission systems with higher order modulation formats[C]. In Proc. SPIE.2012.
[80]L. Lin, Z. Tao, L. Dou, W. Yan, S. Oda, T. Tanimura, T. Hoshida and J. Rasmussen. Implementation efficient non-linear equalizer based on correlated digital back-propagation[C]. In Proc.OFC,2011.
[81]Leonid G. Kazovsky, Lyn Curtis, William C. Young, Nim K. Cheung. All-fiber 900 optical hybrid for coherent communications[J]. Applied Optics,1987,26(3):437-439.
[82]E. Ip, A. Pak Tao Lau, D. J. F. Barros and J. M. Kahn. Coherent Detection in optical fiber systems[J]. Optics Express,2008,16:753-791.
[83]P. Poggiolini, A. Carena, V. Curri, F. Forghieri, Evaluation of the computational effort for chromatic dispersion compensation in coherent optical PM-OFDM and PM-QAM systems[J]. Opt. Express,2009,17(3):1385-1403.
[84]F. Yaman and Guifang Li. Nonlinear impairment compensation for polarization-division multiplexed WDM transmission using digital backward propagation[J]. IEEE Photonics Journal,2009,1:143-152.
[85]Jochen Leibrich, Werner Rosenkranz. Efficient numerical simulation of multichannel WDM transmission systems limited by XPM[J]. IEEE Photo. Technol. Lett.,2003,15(3):395-397.
[86]Fan Zhang, Yazhi Luo, Yandan Wang, Li Li, Lixin Zhu, Zhangyuan Chen, Chengbin Wu. Experimental comparison of different BER estimation methods for coherent optical QPSK transmission systems[J]. IEEE Photo. Technol. Lett.,2011,23(18):1343-1345.
[87]F. Yaman and G. Li. Nonlinear impairment compensation for polarization-division multiplexed WDM transmission using digital backward propagation[J]. IEEE Photonics Journal,2010,2:816-832.
[88]E. F. Mateo, X. Zhou and G. Li. Improved digital backward propagation for the compensation of inter-channel nonlinear effects in polarization-multiplexed WDM systems[J]. Optics Express,2011,19:570-583.
[89]Neal S. Bergano. Wavelength division multiplexing in long-haul transoceanic transmission systems[J]. J. Lightw. Technol.,2005,23(12):4125-4139.
[90]K. Iwatsuki, K. Suzuki, S. Nishi, M. Saruwatari.80 Gb/s optical soliton transmission over 80 km with time/polarization division multiplexing[J]. Photo. Technol. Lett.,1993,5(2):245-248.
[91]David Sandel, Frank Wust, Vitali Mirvoda, Reinhold Noe. Standard (NRZ 1 ×40Gb/s,210 km) and polarization multiplex (CS-RZ,2x40 Gb/s,212 km) transmissions with PMD compensation[J]. IEEE Photo. Technol. Lett.,2002,14(8):1181-1183.
[92]Ahmad Fauzi Abas, Ariya Hidayat, David Sandel, Biljana Milivojevic, Reinhold Noe.100 km fiber span in 292 km,2.38 Tb/s (16×160 Gb/s) WDM DQPSK polarization division multiplex transmission experiment without Raman amplification[J]. Optical Fiber Technology, 2007,13(1):46-50.
[93]B. Zhu, T. F. Taunay, M. Fishteyn, X. Liu, S. Chandrasekhar, M. F. Yan, J. M. Fini, E. M. Monberg, F. V. Dimarcello.112-TB/S space-division multiplexed DWDM transmission with 14-b/s/Hz aggregate spectral efficiency over a 76.8 km seven-core fiber [J]. Optics Express, 2011,19(17):16665-16671.
[94]A. H. Gnauck, P. J. Winzer, S. Chandrasekhar, X. Liu, B. Zhu, D. W. Peckham. Spectrally efficient long-haul WDM transmission using 224-Gb/s polarization-multiplexed 16-QAM[J]. J. Lightw. Technol.,2011,29(4):373-377.
[95]B. Crosignani, P. Di Porto. Intensity induced rotation of the polarization ellipse in low-birefringence, single mode optical fibers[J]. Opt. Acta.,1985,32:1251-1258.
[96]Curtis R. Menyuk. Nonlinear pulse propagation in birefringent optical fibers[J]. IEEE Journal of Quantum Electronics,1987, QE-23(2):174-178.
[97]D. Marcuse, C. R. Menyuk, P. K. A. Wai. Application of the Manakov-PMD equation to studies of signal propagation in optical fibers with randomly varying birefringence[J]. J. Lightw. Technol.,1997,15(9):1735-1746.
[98]P. K. A. Wai, W. L. Kath, C. R. Menyuk, J. W. Zhang. Nonlinear polarization-mode dispersion in optical fibers with randomly varying birefringence[J]. J. Opt. Soc. Amer. B, 1997,14(11):2967-2979.
[99]C. McKinstrie, H. Kogelnik, R. Jopson, S. Radic, A. Kanaev. Four-wave mixing in fibers with random birefringence[J]. Optics Express,2004,12(10):2033-2055.
[100]M. Karlsson, J. Brentel. Autocorrelation function of the polarization-mode dispersion vector[J]. Opt. Lett.,1999,24(14):939-941.
[101]S. Kumar. Effect of dispersion on nonlinear phase noise in optical transmission systems[J]. Optics Lettes,2005,30(24):3278-3280.
[102]K. P. Ho, H. C. Wang. Effect of dispersion on nonlinear phase noise[J]. Optics Letters, 2006,31(14):2109-2111.
[103]W. Mingchia, W. I. Way. Fiber nonlinearity limitations in ultra-dense WDM systems[J]. J. Lightw. Technol.,2004,22(6):1483-1498.
[104]K. Hoon, A. H. Gnauck. Experimental investigation of the performance limitation of DPSK systems due to nonlinear phase noise[J]. Photo. Technol. Lett.,2003,15(2):320-322.
[105]H. Keang-Po, W. Hsi-Cheng. Comparison of nonlinear phase noise and intrachannel four-wave mixing for RZ-DPSK signals in dispersive transmission systems[J]. Photo. Technol. Lett.,2005,17(7):1426-1428.
[106]H. Keang-Po. Performance degradation of phase-modulated systems due to nonlinear phase noise[J]. Photo. Technol. Lett.,2003,15(9):1213-1215.
[107]A. Mecozzi, M. Shtaif. On the capacity of intensity modulated systems using optical amplifiers[J]. IEEE Photon. Technol. Lett.,2001,13(9):1029-1031.
[108]J. Tang. The channel capacity of a multispan DWDM system employing dispersive nonlinear optical fibers and idearl coherent optical receiverfJ]. J. Lightw. Technol.,2002, 20(7):1095-1101.
[109]P. P. Mitra, J. B. Stark. Nonlinear limits to the information capacity of optical fibre communications[J]. Nature,2001,411(28):1027-1030.
[110]K. S. Turitsyn, S. A. Derevyanko, I. V. Yurkevich, S. K. Turitsyn. Information capacity of optical fiber channels with zero average dispersion[J]. Phys. Rev. Lett.,2003,91(20):1-4.
[111]J. Tang. The multispan effects of Kerr nonlinearity and amplifier noises on Shannon channel capacity of a dispersion-free nonlinear optical fiber[J]. J. Lightw. Technol.,2001, 19(8):1110-1115.
[112]I. B. Djordjevic, B. Vasic, M. Ivkovic, I. Gabitov. Achievable information rates for high-speed long-haul optical transmission[J]. J. Lightw. Technol.,2005,23(11):3755-3763.
[113]K.-P. Ho and J. M. Kahn. Channel capacity of WDM systems using constant-intensity modulation formats[C]. In Proc. Optical Fiber Communication (OFC), Anahim, CA,2002, Paper ThGG85:731-733.
[114]C. E. Shannon. A mathematical theory of communication[J]. Bell Syst. Tech. J.,1984, 27:379-423.
[115]E. E. Narimanov, P. Mitra. The channel capacity of a fiber optics communication system: Perturbation theory[J]. J. Lightw. Technol,2002,20(3):530-537.
[116]Lian Xiang, Xiao Ping Zhang. The study of information capacity in multispan nonlinear optical fiber communication systems using a developed perturbation technique[J]. J. Lightw. Technol.,2011,29(3):260-264.
[117]H. Wei, D. V. Plant. Intra-channel nonlinearity compensation with scaled translational symmetry[J]. Opt. Exp.,2004,12(18):4282-4296.
[118]L.G.L. Wegener, M.L.. Povinelli, A.G. Green, P.P. Mitra, J.B. Stark, P.B. Littlewood. The effect of propagation nonlinearities on the information capacity of WDM optical fiber systems:cross-phase modulation and four-wave mixing[J]. PHYSICA D,2004,189(2):81-99.
[119]Qi Xiaoqiong, Xiaoping Zhang. Nonlinear optical fiber channel capacity estimation[J]. Acta Photonica Sinica,2007,36:14-17.
[120]Bo Xu. Study of fiber nonlinear effects on fiber optic communication systems[D]. Ph. D. dissertation, University of Virginia,2003.
[121]Bo Xu, M. Brandt-Pearce. Modified volterra series transfer function method[J]. IEEE Photo. Technol. Lett.,14(1):47-49.
[122]Shmuel Fishman, Y. Krivolapov, Avy Soffer. Perturbation theory for the nonlinear Schrodinger equation with a random potential[J]. Nonlinearity,2009,22(12):1-28.
[123]O. V. Sinkin, R. Holzlohner, J. Zweck, C. R. Menyuk. Optimization of the split-step fourier method in modeling optical-fiber communications systems[J]. J. Lightw. Technol., 2003,21(1):61-68.
[124]E. Ciaramella, E. Forestieri. Analytical approximation of nonlinear distortions[J]. IEEE Photo. Technol. Lett.,2005,17(1):91-93.
[125]K. V. Peddannragari, Maite Brandt-Pearce. Volterra series transfer function of single-mode fibers[J]. J. Lightw. Technol.,1997,15(12):2232-2241.
[126]向练,李虎,张晓萍。多跨距非线性光纤链路中基于微扰理论的优化算法[J],中国激光,2010,37(4)：1033-1036
[2]K. C. Kao and G. A. Hockham. Dielectric-fiber surface waveguides for optical frequencies[J]. Proc.IEE,1966,113(7):1151-1158.
[3]C. Randy Giles, Emmanuel Desurvire. Modeling Erbium-Doped Fiber Amplifiers[J]. IEEE Journal of lightwave technology,1991,9(2):271-283.
[4]Jay Sharping, Yoshitomo Okawachi, Alexander Gaeta. Wide bandwidth slow light using a Raman fiber amplifier[J]. Optics Express,2005,16(16):6092-6098.
[5]Hideki Ishio, Junichiro Minowa, Kiyoshi Nosu. Review and status of wavelength-division-multiplexing technology and its application[J]. Journal of lightwave technology,1984,LT-2(4):448-462
[6]C. A. Brackett. Dense wavelength division multiplexing networks:principles and applications[J]. Journal on selected areas in communications,1990,8(6):948-964
[7]A. R. Chraplyvy. Limitations on lightwave communications imposed by optical-fber nonlinearities[J]. J. Lightw. Technol.,1990,8(10):1548-1557.
[8]N. S. Bergano. Wavelength division multiplexing in long-haul transoceanic transmission systems[J]. J. Lightw. Technol.,2005,23(12):4125-4139.
[9]M. Jinno, T. Sakamoto, J. Kani, S. Aisawa, K. Oda, M. Fukui, H. Ono, K. Oguchi. First demonstration of 1580 nm wavelength band WDM transmission for doubling usable bandwidth and suppressing FWM in DSF[J]. Electronics Letters,1997,33(10):882-883.
[10]K. O. Hill, F. Bilodeau, B. Malo, T. Kitagawa, S. Theriault, D. C. Johnson, J. Albert, K. Takiguchi. Chirped in-fber Bragg gratings for compensation of optical-fiber dispersion[J]. Opt. Lett.,1994,19:1314-1316.
[11]C. K. Madsen, G. Lenz. Optical all-pass filters for phase response design with applications for dispersion compensation[J]. Photonics Technology Letters,1998,10(7):994-996.
[12]A. Yariv, D. Fekete, D. M. Pepper. Compensation for channel dispersion by nonlinear optical phase conjugation[J]. Opt. Lett.,1979,4:52-54.
[13]S. Watanabe, T. Naito, T. Chikama. Compensation of chromatic dispersion in a single-mode fiber by optical phase conjugation[J]. Photonics Technology Letters,1993,5(1):92-95.
[14]C. D. Poole, J. M. Wiesenfeld, D. J. Digiovanni, A. M. Vengsarkar. Optical fiber-based dispersion compensation using higher order modes near cutoff[J]. J. Lightw. Technol.,1994, 12(10):1746-1758.
[15]Quang Le N. T., Torben Veng, Lars Gruner-Nielsen. New dispersion compensating module for compensation of dispersion and dispersion slope of non-zero dispersion fibres in the C-band[C]. OFC2000, paper TuH5-1.
[16]K. Mukasa, H. Moridaira, T. Yagi, K. Kokura. New type of dispersion management transmission line with MDFSD for long-haul 40 Gb/s transmission[C]. OFC2002, paper THGG2.
[17]Xiaoqiong Qi, Xiaoping Zhang, Haiqing Wei, David V. Plant. Linearity of nonlinear perturbations in fiber-optic transmission lines and its applications to nonlinear compensations[J]. J. Opt. Soc. Am. B.,2006,23(10):2032-2039.
[18]H. Wei and D. V. Plant. Fundamental equations of nonlinear fiber optics in optical modeling and performance predictions[C]. Proc. SPIE5178,2003:255-266.
[19]B. Xu, M. Brandt-Pearce. Analysis of noise amplification by a CW pump signal due to fiber nonlinearity[J]. Photonics Technology Letters,2004,16(4):1062-1064.
[20]J. P. Gordon, L. F. Mollenauer. Phase noise in photonic communications-systems using linear-amplifiers[J]. Optics Letters,1990,15(23):1351-1353.
[21]F. Zhang, C. A. Bunge, K. Petermann. Analysis of nonlinear phase noise in single-channel retum-to-zero differential phase-shift keying transmission systems[J]. Optics Letters,2006, 31(8):1038-1040.
[22]C. C. Wei, J. Chen. Convergence of phase fluctuation induced by intrachannel four-wave mixing in differential phase-shift keying transmission systems via phase fluctuation averaging[J]. Optics Lettes,2007,32(10):1217-1219.
[23]Xiao Qiong Qi, Xiaoping Zhang, Qun Feng Shao. Reduction of parametric amplified noise on nonlinear fiber channels by use of wiener filtering[J]. J. Lightw. Technol.,2008, 26(18):3210-3215.
[24]漆晓琼,邵群峰,张晓萍。基于沃尔泰拉理论的集总光纤非线性噪声补偿[J]。中国激光,2007,34(11)：1527-1532.
[25]Dong Yang, Shiva Kumar. Realization of optical OFDM using time lenses and its comparison with optical OFDM using FFT[J]. Opt. Express,2009,17:17214-17226.
[26]S. Kumar, D. Yang. Optical implementation of orthogonal frequency-division multiplexing using time lenses[J]. Opt. Lett.,2008,33(17):2002-2004.
[27]M. S. Afiad, Dirk van den Borne, Sander Lars Jansen, Torsten Wuth, Maxim Kuschnerov, Guido Grosso, Antonio Napoli, Huug de Waardt. A comparison of electrical and optical dispersion compensation for 111-Gb/s POLMUX-RZ-DQPSK[J]. J. Lightw. Technol.,2009, 27(16):3590-3598.
[28]K. Roberts, L. Chuandong, L. Strawczynski, M. O. Sullivan, I. Hardcastle. Electronic precompensation of optical nonlinearity[J]. IEEE Photon. Technol. Lett.,2006, 18(2):403-405.
[29]X. Li, X. Chen, G. Goldfarb, E. Mateo, I. Kim, F. Yaman, G. Li. Electronic post-compensation of WDM transmission impairments using coherent detection and digital signal processing[J]. Opt. Express,2008,16(2):880-888.
[30]G. Goldfarb, M. G. Taylor, G. Li. Experimental demonstration of fiber impairment compensation using the split-step finite-impulse-response filtering method[J]. IEEE Photon. Technol. Lett.,2008,20(22):1887-1889.
[31]E. Mateo, L. Zhu, G. Li. Impact of XPM and FWM on the digital implementation of impairment compensation for WDM transmission using backward propagation[J]. Opt. Express,2008,16(20):16124-16137.
[32]R.-J. Essiambre, P. J. Winzer, X. Q. Wang, W. Lee, C. A. White, E. C. Burrows. Electronic predistortion and fiber nonlinearity[J]. IEEE Photon. Technol. Lett.,2006,18:1804-1806.
[33]V. E. Zakharrov, A. B. Shabat. A scheme for intergrating the nonlinear equations of mathematical physics by the method of the inverse scattering problem[J]. Functional Analysis and its Applications,1974,8(3):226-235.
[34]J. A. C. Weidenman, B. M. Herbst. Split-step methods for the solution of the nonlinear schrodinger equation[J]. SIAM J. Numer. Anal,1986,23(3):485-507.
[35]Akira Hasegawa, Frederick Tappert. Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. I. Anomalous dispersion[J]. Applied Physics Letters,1973, 23(3):142-144.
[36]V. S. Shchesnovich, E. V. Doktorov. Perturbation theory for the modified nonlinear Schrodinger solitons[J]. Physica D,1999,129:115-129.
[37]Y. Kodama, S. Wabnitz. Analytical theory of guiding center nonreturn to zero and return to zero signal transmission in normally dispersive nonlinear optical fibers[J]. Opt. Lett.1995, 20:2291-2293.
[38]K. V. Peddannragari, Maite Brandt-Pearce. Volterra series approach for fiber optic communication system designs[J]. J. Lightw. Technol.,1998,16(11):2046-2055.
[39]Jacklyn D. Reis, A. L. Teixeira. Unveiling nonlinear effects in dense coherent optical WDM systems with volterra series[J]. Optics Express,2010,8660-8670.
[40]Armando Vannucci, Paolo Serna, Alberto Bononi. The RP method:a new tool for the iterative solution of the nonlinear Schrodinger equation[J]. J. Lightw. Technol.,2002, 20(7):1102-1112.
[41]Jong-Hyung Lee. Analysis and characterization of fiber nonlinearities with detecministic and stochastic signal sources[D]. Virginia Polytechnic Institute and State University,2000.
[42]Govind P. Agrawall. Nonlinear Fiber Optics (third edition)[M]. Beijing:World Publishing Corporation,2005.
[43]A. K. Atieh, P. Myslinski, J. Chrostowski, P. Galko. Measuring the Raman time constant (T_R) for soliton pulses in standard single-mode fiber[J]. J. Lightw. Technol.,1999, 17(2):216
[44]D. Zwillinger. Handbook of differential equations[M]. Boston Academic,1989:528-531.
[45]Finlay M. Knox, Wladek Forysiak, Nicholas J. Doran.10-Gbt/s soliton communication systems over standard fiber at 1.55 um and the use of dipersion compensation[J]. J. Lightw. Technol.,1995,13(10):1955-1962.
[46]Nicholas J. Smith, Nicholas J. Doran, Wladek Forysiak, Finlay M. Knox. Soliton transmission using periodic dispersion compensation[J]. J. Lightw. Technol.,1997, 15(10):1808-1822.
[47]A. R. Chrapyvy. Limitations on lightwave communications imposed by optical-fiber nonlinearities[J]. J. Lightw. Technol.,1990,8(10):1548-1557.
[48]Seb J. Savory, Giancarlo Gavioli, Robert I. Killey, Polina Bayvel. Electronic compensation of chromatic dispersion using a digital coherent receiver [J]. Optics express,2007, 15(5):2120-2126.
[49]Mike Sieben, Jan Conradi, David E. Dodds. Optical single sideband transmission at 10 Gb/s using only electrical dispersion compensation[J]. J. Lightw. Technol.,1999, 17(10):1742-1749.
[50]G. Charlet, N. Maaref, J. Renaudier, H. Mardoyan, P. Tran, S. Bigo. Transmission of 40 Gb/s QPSK with coherent detection over ultra-long distance improved by nonlinearity mitigation[C]. In Proc. Eur. Conf. Opt. Commun., Cannes France,2006.
[51]K. Roberts, L. Chuandong, L. Strawczynski, M. O'Sullivan, I. Hardcastle. Electronic precompensation of optical nonlinearity[J]. IEEE Photon. Technol. Lett.,2006,18:403-405.
[52]K. Kikuchi. Electronic post-compensation for nonlinear phase fluctuations in a 1000-km 20-Gbit/s optical quadrature phase-shift keying transmission system using the digital coherent receiver[J]. Opt. Express,2008,16:889-896.
[53]L. B. Y. Du, A. J. Lowery. Fiber nonlinearity precompensation for long-haul links using direct-detection optical OFDM[J]. Opt. Express,2008,16:6209-6215.
[54]E. Yamazaki, F. Inuzuka, K. Yonenaga, A. Takada, M. Koga. Compensation of interchannel crosstalk induced by optical fiber nonlinearity in carrier phase-locked WDM system[J]. IEEE Photon. Technol. Lett.,2007,19:9-11.
[55]C. Kurtzke. Suppression of fiber nonlinearities by appropriate dispersion management[J]. IEEE Photo. Technol. Lett.,1993,5(10):1250-1252.
[56]C. Behrens, R. I. Killy, S. J. Savory, P. Bayvel. Reducing the impact of intrachannel nonlinearities by pulse-width optimization in multi-level phase-shift-keyed transmission[C]. In Proc. EOCO,2009, pp.1-2.
[57]O. Kuzucu, Y. Okawachi, R. Salem, M. A. Foster, A. C. Tumer-Foster, M. Lipson, A. L. Gaeta, Spectral phase conjugation via temporal imaging[J]. Opt. Express,2009, 17(22):20605-20614.
[58]Y. Han, G. Li. Coherent optical communication using polarization multiple-input-multiple-output[J]. Opt. Express,2005,13(19):7527-7534.
[59]T. Pfau, S. Hoffmann, O. Adamczyk, R. Peveling, V. Herath, M. Porrmann, R. Noe. Coherent optical communication:towards realtime systems at 40 Gb/s and beyond[J]. Opt. Express,2008,16(2):866-872.
[60]L. B. Du and A. J. Lowery. Improved single channel backpropagation for intra-channel fiber nonlinearity compensation in long-haul optical communication systems[J].Optics Express, 2010,18:17075-17088.
[61]R. Waegemans, S. Herbst, L. Holbein, P. Watts, P. Bayvel, C. Furst and R. I. Killey.10.7 Gb/s electronic predistortion transmitter using commercial FPGAs and D/A converters implementing real-time DSP for chromatic dispension and SPM compensation[J]. Optics Express,2009,17:8630-8640.
[62]S. J. Savory. Digital filters for coherent optical receivers[J]. Optics Express,2008, 16:804-817.
[63]R. Asif, C. Y. Lin and B. Schmauss. Digital backward propagation:A Technique to Compensate Fiber Dispersion and Nonlinear Impairments. Digital Signal Processing[M], InTech-Book Publisher,2011.
[64]Mahdi Malekiha, Dong Yang, Shiva Kumar. Comparison of optical back propagation schemes for fiber-optic communications[J]. Optical Fiber Technology,2013,19:4-9.
[65]E. F. Mateo, G. Li. Compensation of interchannel nonlinearities using enhanced coupled equations for digital backward propagation[J]. Applied Optics,2009,48:6-10.
[66]X. Li, X. Chen, G. Goldfarb, E. Mateo, I. Kim, F. Yaman and G. Li. Electronic post-compensation of WDM transmission impairments using coherent detection and digital signal processing[J]. Optics Express,2008,16:880-888.
[67]E. Ip. Nonlinear compensation using backpropagation for polarization-multiplexed Transmission[J]. Journal of Lightwave Technology,2010,28:939-951.
[68]R. Asif, C. Y. Lin, M. Holtmannspoetter and B. Schmauss. Optimized digital backward propagation for phase modulated signals in mixed-optical fiber transmission link[J]. Optics Express,2010,18:22796-22807.
[69]S. J. Savory, G. Gavioli, E. Torrengo and P. Poggiolini. Impact of interchannel nonlinearities on a split-step intrachannel nonlinear equalizer[J]. IEEE Photonics Technology Letters,2010, 22:673-675.
[70]E. Ip and J. M. Kahn. Compensation of dispersion and nonlinear impairments using digital backpropagation[J]. J. Lightw. Technol.,2008,26:3416-3425.
[71]D. Rafique, A. Ellis. Impact of signal-ASE four-wave mixing on the effectiveness of digital back-propagation in 112 Gb/s PM-QPSK systems[J]. Optics Express,2011,19:3449-3454.
[72]E. F. Mateo, F. Yaman and G. Li. Efficient compensation of inter-channel nonlinear effects via digital backward propagation in WDM optical transmission[J]. Optics Express,2010, 18:15144-15154.
[73]D. Rafique, M. Mussolin, M. Forzati, J. Martensson, M. N. Chugtai and A. D. Ellis. Compensation of intra-channel nonlinear fibre impairments using simplified digital back-propagation algorithm[J]. Optics Express,2011,19:9453-9460.
[74]W. Yan, Z. Tao, L. Dou, L. Li, S. Oda, T. Tanimura, T. Hoshida and J. C. Rasmussen. Low complexity digital perturbation back-propagation[C]. In Proc. ECOC,2011.
[75]L. Zhu and G. Li. Nonlinearity compensation using dispersion-folded digital backward propagation[J]. Optics Express,2012,20(13):14362-14370.
[76]Hoon Kim, Alan H. Gnauck. Experimental investigation of the performance limitation of DPSK systems due to nonlinear phase noise[J]. IEEE Photo. Technol. Lett.,2003, 15(2):320-322.
[77]J. P. Gordon, L. F. Mollenauer. Phase noise in photonic communications systems using linear amplifiers[J]. Optics Letters,1990,15(33):1351-1353.
[78]C. Pare, A. Villeneuve, P.-A. Belanger. Compensating for dispersion and the nonlinear Kerr effect without phase conjugation[J]. Optics Letters,1996,21(7):459-461.
[79]B. Schmauss, R. Asif and C-Y. Lin. Recent advances in digital backward propagation algorithm for coherent transmission systems with higher order modulation formats[C]. In Proc. SPIE.2012.
[80]L. Lin, Z. Tao, L. Dou, W. Yan, S. Oda, T. Tanimura, T. Hoshida and J. Rasmussen. Implementation efficient non-linear equalizer based on correlated digital back-propagation[C]. In Proc.OFC,2011.
[81]Leonid G. Kazovsky, Lyn Curtis, William C. Young, Nim K. Cheung. All-fiber 900 optical hybrid for coherent communications[J]. Applied Optics,1987,26(3):437-439.
[82]E. Ip, A. Pak Tao Lau, D. J. F. Barros and J. M. Kahn. Coherent Detection in optical fiber systems[J]. Optics Express,2008,16:753-791.
[83]P. Poggiolini, A. Carena, V. Curri, F. Forghieri, Evaluation of the computational effort for chromatic dispersion compensation in coherent optical PM-OFDM and PM-QAM systems[J]. Opt. Express,2009,17(3):1385-1403.
[84]F. Yaman and Guifang Li. Nonlinear impairment compensation for polarization-division multiplexed WDM transmission using digital backward propagation[J]. IEEE Photonics Journal,2009,1:143-152.
[85]Jochen Leibrich, Werner Rosenkranz. Efficient numerical simulation of multichannel WDM transmission systems limited by XPM[J]. IEEE Photo. Technol. Lett.,2003,15(3):395-397.
[86]Fan Zhang, Yazhi Luo, Yandan Wang, Li Li, Lixin Zhu, Zhangyuan Chen, Chengbin Wu. Experimental comparison of different BER estimation methods for coherent optical QPSK transmission systems[J]. IEEE Photo. Technol. Lett.,2011,23(18):1343-1345.
[87]F. Yaman and G. Li. Nonlinear impairment compensation for polarization-division multiplexed WDM transmission using digital backward propagation[J]. IEEE Photonics Journal,2010,2:816-832.
[88]E. F. Mateo, X. Zhou and G. Li. Improved digital backward propagation for the compensation of inter-channel nonlinear effects in polarization-multiplexed WDM systems[J]. Optics Express,2011,19:570-583.
[89]Neal S. Bergano. Wavelength division multiplexing in long-haul transoceanic transmission systems[J]. J. Lightw. Technol.,2005,23(12):4125-4139.
[90]K. Iwatsuki, K. Suzuki, S. Nishi, M. Saruwatari.80 Gb/s optical soliton transmission over 80 km with time/polarization division multiplexing[J]. Photo. Technol. Lett.,1993,5(2):245-248.
[91]David Sandel, Frank Wust, Vitali Mirvoda, Reinhold Noe. Standard (NRZ 1 ×40Gb/s,210 km) and polarization multiplex (CS-RZ,2x40 Gb/s,212 km) transmissions with PMD compensation[J]. IEEE Photo. Technol. Lett.,2002,14(8):1181-1183.
[92]Ahmad Fauzi Abas, Ariya Hidayat, David Sandel, Biljana Milivojevic, Reinhold Noe.100 km fiber span in 292 km,2.38 Tb/s (16×160 Gb/s) WDM DQPSK polarization division multiplex transmission experiment without Raman amplification[J]. Optical Fiber Technology, 2007,13(1):46-50.
[93]B. Zhu, T. F. Taunay, M. Fishteyn, X. Liu, S. Chandrasekhar, M. F. Yan, J. M. Fini, E. M. Monberg, F. V. Dimarcello.112-TB/S space-division multiplexed DWDM transmission with 14-b/s/Hz aggregate spectral efficiency over a 76.8 km seven-core fiber [J]. Optics Express, 2011,19(17):16665-16671.
[94]A. H. Gnauck, P. J. Winzer, S. Chandrasekhar, X. Liu, B. Zhu, D. W. Peckham. Spectrally efficient long-haul WDM transmission using 224-Gb/s polarization-multiplexed 16-QAM[J]. J. Lightw. Technol.,2011,29(4):373-377.
[95]B. Crosignani, P. Di Porto. Intensity induced rotation of the polarization ellipse in low-birefringence, single mode optical fibers[J]. Opt. Acta.,1985,32:1251-1258.
[96]Curtis R. Menyuk. Nonlinear pulse propagation in birefringent optical fibers[J]. IEEE Journal of Quantum Electronics,1987, QE-23(2):174-178.
[97]D. Marcuse, C. R. Menyuk, P. K. A. Wai. Application of the Manakov-PMD equation to studies of signal propagation in optical fibers with randomly varying birefringence[J]. J. Lightw. Technol.,1997,15(9):1735-1746.
[98]P. K. A. Wai, W. L. Kath, C. R. Menyuk, J. W. Zhang. Nonlinear polarization-mode dispersion in optical fibers with randomly varying birefringence[J]. J. Opt. Soc. Amer. B, 1997,14(11):2967-2979.
[99]C. McKinstrie, H. Kogelnik, R. Jopson, S. Radic, A. Kanaev. Four-wave mixing in fibers with random birefringence[J]. Optics Express,2004,12(10):2033-2055.
[100]M. Karlsson, J. Brentel. Autocorrelation function of the polarization-mode dispersion vector[J]. Opt. Lett.,1999,24(14):939-941.
[101]S. Kumar. Effect of dispersion on nonlinear phase noise in optical transmission systems[J]. Optics Lettes,2005,30(24):3278-3280.
[102]K. P. Ho, H. C. Wang. Effect of dispersion on nonlinear phase noise[J]. Optics Letters, 2006,31(14):2109-2111.
[103]W. Mingchia, W. I. Way. Fiber nonlinearity limitations in ultra-dense WDM systems[J]. J. Lightw. Technol.,2004,22(6):1483-1498.
[104]K. Hoon, A. H. Gnauck. Experimental investigation of the performance limitation of DPSK systems due to nonlinear phase noise[J]. Photo. Technol. Lett.,2003,15(2):320-322.
[105]H. Keang-Po, W. Hsi-Cheng. Comparison of nonlinear phase noise and intrachannel four-wave mixing for RZ-DPSK signals in dispersive transmission systems[J]. Photo. Technol. Lett.,2005,17(7):1426-1428.
[106]H. Keang-Po. Performance degradation of phase-modulated systems due to nonlinear phase noise[J]. Photo. Technol. Lett.,2003,15(9):1213-1215.
[107]A. Mecozzi, M. Shtaif. On the capacity of intensity modulated systems using optical amplifiers[J]. IEEE Photon. Technol. Lett.,2001,13(9):1029-1031.
[108]J. Tang. The channel capacity of a multispan DWDM system employing dispersive nonlinear optical fibers and idearl coherent optical receiverfJ]. J. Lightw. Technol.,2002, 20(7):1095-1101.
[109]P. P. Mitra, J. B. Stark. Nonlinear limits to the information capacity of optical fibre communications[J]. Nature,2001,411(28):1027-1030.
[110]K. S. Turitsyn, S. A. Derevyanko, I. V. Yurkevich, S. K. Turitsyn. Information capacity of optical fiber channels with zero average dispersion[J]. Phys. Rev. Lett.,2003,91(20):1-4.
[111]J. Tang. The multispan effects of Kerr nonlinearity and amplifier noises on Shannon channel capacity of a dispersion-free nonlinear optical fiber[J]. J. Lightw. Technol.,2001, 19(8):1110-1115.
[112]I. B. Djordjevic, B. Vasic, M. Ivkovic, I. Gabitov. Achievable information rates for high-speed long-haul optical transmission[J]. J. Lightw. Technol.,2005,23(11):3755-3763.
[113]K.-P. Ho and J. M. Kahn. Channel capacity of WDM systems using constant-intensity modulation formats[C]. In Proc. Optical Fiber Communication (OFC), Anahim, CA,2002, Paper ThGG85:731-733.
[114]C. E. Shannon. A mathematical theory of communication[J]. Bell Syst. Tech. J.,1984, 27:379-423.
[115]E. E. Narimanov, P. Mitra. The channel capacity of a fiber optics communication system: Perturbation theory[J]. J. Lightw. Technol,2002,20(3):530-537.
[116]Lian Xiang, Xiao Ping Zhang. The study of information capacity in multispan nonlinear optical fiber communication systems using a developed perturbation technique[J]. J. Lightw. Technol.,2011,29(3):260-264.
[117]H. Wei, D. V. Plant. Intra-channel nonlinearity compensation with scaled translational symmetry[J]. Opt. Exp.,2004,12(18):4282-4296.
[118]L.G.L. Wegener, M.L.. Povinelli, A.G. Green, P.P. Mitra, J.B. Stark, P.B. Littlewood. The effect of propagation nonlinearities on the information capacity of WDM optical fiber systems:cross-phase modulation and four-wave mixing[J]. PHYSICA D,2004,189(2):81-99.
[119]Qi Xiaoqiong, Xiaoping Zhang. Nonlinear optical fiber channel capacity estimation[J]. Acta Photonica Sinica,2007,36:14-17.
[120]Bo Xu. Study of fiber nonlinear effects on fiber optic communication systems[D]. Ph. D. dissertation, University of Virginia,2003.
[121]Bo Xu, M. Brandt-Pearce. Modified volterra series transfer function method[J]. IEEE Photo. Technol. Lett.,14(1):47-49.
[122]Shmuel Fishman, Y. Krivolapov, Avy Soffer. Perturbation theory for the nonlinear Schrodinger equation with a random potential[J]. Nonlinearity,2009,22(12):1-28.
[123]O. V. Sinkin, R. Holzlohner, J. Zweck, C. R. Menyuk. Optimization of the split-step fourier method in modeling optical-fiber communications systems[J]. J. Lightw. Technol., 2003,21(1):61-68.
[124]E. Ciaramella, E. Forestieri. Analytical approximation of nonlinear distortions[J]. IEEE Photo. Technol. Lett.,2005,17(1):91-93.
[125]K. V. Peddannragari, Maite Brandt-Pearce. Volterra series transfer function of single-mode fibers[J]. J. Lightw. Technol.,1997,15(12):2232-2241.
[126]向练,李虎,张晓萍。多跨距非线性光纤链路中基于微扰理论的优化算法[J],中国激光,2010,37(4)：1033-1036