基于Volterra级数的光正交频分复用系统中四波混频效应的研究
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摘要
随着人们对互联网的使用逐渐增加,高流量的应用程序的出现对网络传输速率提出了更高的新的要求,使光纤通信系统向着100Gbit/s甚至更高的传输速率演进。光正交频分复用技术以其频谱利用率高、抗色散的优势成为了高速光纤通信系统的方案之一,引起了广泛的研究热情。本文对影响光正交频分复用系统信号传输质量的光纤非线性效应进行了研究,尤其是对影响光正交频分复用系统信号传输质量最为严重的四波混频效应进行了具体的研究。
本文通过利用基于Volterra级数的非线性薛定谔方程的闭式半解析解对光正交频分复用系统进行求解,得到了包含线性项和非线性项的光正交频分复用系统的传播方程的近似解,利用四波混频效应的定义,从非线性项中分离出了对光正交频分复用系统影响最大的四波混频效应的表达式。该表达式可体现色散和非线性效应的相互作用,并且包含了相位失配,较之以往的结论更为贴近实际情况,分析结果更为精确。对所得表达式进行数值仿真,验证了本文所给出的光正交频分复用中的四波混频的表达式更为贴近实际系统。数值仿真的结果还表明,光正交频分复用系统中某一子载波所受的四波混频的影响主要来源于与其相临近的子载波,而与它频率间隔较大的子载波的影响可以忽略,因此可以对基于Volterra级数传递函数的光正交频分复用系统四波混频效应的表达式进行简化,降低其计算复杂度,为通过Volterra级数传递函数设计光正交频分复用系统的优化方案提供了理论依据。
With the use of the Internet is gradually increased, the application of high flow forward higher and new requirements for the network transmission rate, the optical fiber communication system to100Gbit/s or even higher transmission rate evolution. One of the high-speed optical fiber communication system as Optical Orthogonal Frequency Division Multiplexing(OOFDM) technology due to its high rate of resistance to dispersion spectrum, the advantages, attracted extensive research enthusiasm. In this paper, fiber nonlinear effect on Optical Orthogonal Frequency Division Multiplexing system signal transmission quality were studied, especially for the most important effection:Four Wave Mixing (FWM) effect.
In this paper, Volterra series Transfer Function model of nonlinear Schrodinger equation was used to study Optical Orthogonal Frequency Division Multiplexing system. The approximate solution is obtained propagation equation contains linear term and nonlinear term, and then based on the defination of the four wave mixing effect, isolated the expression of four wave mixing effect on Optical Orthogonal Frequency Division Multiplexing system. The expression to represent the Four Wave Mixing in Optical Orthogonal Frequency Division Multiplexing system was obtained, with considering dispersion and phase mismatch. The results of computer simulation show that the power of Four Wave Mixing products are different from each other, and Four Wave Mixing effect in a certain subcarrier only derives its adjoining subcarriers, the effect of other subcarriers could be ignored. So in practical application, the expression of Four Wave Mixing in Optical Orthogonal Frequency Division Multiplexing system could be simplified, to reduce the computational complexity, and provides a theoretical basis for the optimization of Volterra series transfer function design of optical orthogonal frequency division multiplexing system.
本文通过利用基于Volterra级数的非线性薛定谔方程的闭式半解析解对光正交频分复用系统进行求解,得到了包含线性项和非线性项的光正交频分复用系统的传播方程的近似解,利用四波混频效应的定义,从非线性项中分离出了对光正交频分复用系统影响最大的四波混频效应的表达式。该表达式可体现色散和非线性效应的相互作用,并且包含了相位失配,较之以往的结论更为贴近实际情况,分析结果更为精确。对所得表达式进行数值仿真,验证了本文所给出的光正交频分复用中的四波混频的表达式更为贴近实际系统。数值仿真的结果还表明,光正交频分复用系统中某一子载波所受的四波混频的影响主要来源于与其相临近的子载波,而与它频率间隔较大的子载波的影响可以忽略,因此可以对基于Volterra级数传递函数的光正交频分复用系统四波混频效应的表达式进行简化,降低其计算复杂度,为通过Volterra级数传递函数设计光正交频分复用系统的优化方案提供了理论依据。
With the use of the Internet is gradually increased, the application of high flow forward higher and new requirements for the network transmission rate, the optical fiber communication system to100Gbit/s or even higher transmission rate evolution. One of the high-speed optical fiber communication system as Optical Orthogonal Frequency Division Multiplexing(OOFDM) technology due to its high rate of resistance to dispersion spectrum, the advantages, attracted extensive research enthusiasm. In this paper, fiber nonlinear effect on Optical Orthogonal Frequency Division Multiplexing system signal transmission quality were studied, especially for the most important effection:Four Wave Mixing (FWM) effect.
In this paper, Volterra series Transfer Function model of nonlinear Schrodinger equation was used to study Optical Orthogonal Frequency Division Multiplexing system. The approximate solution is obtained propagation equation contains linear term and nonlinear term, and then based on the defination of the four wave mixing effect, isolated the expression of four wave mixing effect on Optical Orthogonal Frequency Division Multiplexing system. The expression to represent the Four Wave Mixing in Optical Orthogonal Frequency Division Multiplexing system was obtained, with considering dispersion and phase mismatch. The results of computer simulation show that the power of Four Wave Mixing products are different from each other, and Four Wave Mixing effect in a certain subcarrier only derives its adjoining subcarriers, the effect of other subcarriers could be ignored. So in practical application, the expression of Four Wave Mixing in Optical Orthogonal Frequency Division Multiplexing system could be simplified, to reduce the computational complexity, and provides a theoretical basis for the optimization of Volterra series transfer function design of optical orthogonal frequency division multiplexing system.
引文
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[38]Artur James Lowery, Shunjie Wang, Malin Premrate, Calculation of power limit due to fiber nonlinearity in optical OFDM system[J], Optics Express,2007,15(20):13282-13287
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[41]Jacklyn D.Reis, Antonio L. Teixeira, Unveiling nonlinear effects in dense coherent optical WDM systems with Volterra series[J], Optics Express,2010,18(8):8660-8670
[42]Ling Liu, Liangchuan Li, Yuanda Huang, Kai Cui, Qianjin Xiong, Fabian N.Hauske,Intrachannel nonlinearity compensation by inverse Volterra Series Transfer Function[J], J.Lightwave Technol,2012,30(3):310-316
[43]Jie Pan and Chi-Hao Cheng, Nonlinear Electrical Compensation for the Coherent Optical OFDM System[J], J.Lightwave Technol,2011,29(2):215-221.
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[2]Gnauck AH, Tkach RW, Chraplyvy AR, Li T. High-capacity optical transmission systems[J]. J. Lightwave Technol.2008,26:1032-45.
[3]Giuseppe Talli and Paul D. Townsend. Hybrid DWDM-TDM Long-Reach PON for Next-Generation Optical Access[J]. J. Lightwave Technol.2006,24(7):2827-34
[4]Kobayash T, Sano A, Yamada E. Electro-optically subcarrier multiplexed 110 Gb/s OFDM signal transmission over 80 km SMF without dispersion compensation[J]. IET Electron Lett 2008,44:225-226.
[5]Jansen S.L, Morita I, Tanaka H.10×121.9-Gb/s PDM-OFDM transmission with 2-b/s/Hz spectral efficiency over 1000 km of SSMF[J]. J. Lightwave Technol.2009,27(3):177-88.
[6]Shieh W, Yang Q, Ma Y.107 Gb/s coherent optical OFDM transmission over 1000-km SSMF fiber using orthogonal band multiplexing[J]. Opt Express 2008,16:6378-86.
[7]Peter J.Winzer, Greg Raybon, and Mareus Deuk,107Gbit/s optical ETDM transmitter for 100G Ethernet transport[C].ECOC2005,6:1-2.
[8]Itsuro Morit, Sander L Janse, High Speed Transmission Technologies for 100-Gbit/s-class Etherne[C], ECOC2007:1-4.
[9]Wuth. T, Chbat. M.W, kamalov. V.F, Multi-rate (100G/40G/10G) Transport Over DePloyed Optical Networks[C], OFC2008:1-9.
[10]Hill. P.M, Olshansky. R, Burns. W.K. Optical polarization division multiplexing at 4 Gb/s[J]. Photonics Technology Letters.1992,4(5):500-502.
[11]Noe. R, PLL-free synchronous QPSK polarization multiplex/diversity receiver concept with digital I&Q baseband processing[J]. Photonics Technology Letters.2005,17(4):887-889.
[12]Fischer. J.K., Molle. L., Nolle. M., Schmidt-Langhorst. C., Hilt. J., Ludwig. R, Peckham. D.W., Schubert. C.8×448-Gb/s WDM Transmission of 56-GBd PDM 16-QAM OTDM Signals Over 250-km Ultralarge Effective Area Fiber[J]. Photonics Technology Letters.2011,23(4):239-241.
[13]Sander L. Jansen, Itsuro Morita, Kamyar Forozesh, Sebastian Randel, Dirk van den Borne, Optical OFDM, a hype or is it for real[C], ECOC 2008:21-25
[14]Gnauck. A. H. and Jopson. R. M. Dispersion compensation for optical fiber systems[J]. Communications Magazine.33(6):96-102.
[15]Forghieri. F., Tkach. R. W. and Chraplyvy. A. R. Fiber nonlinearities and their impact on transmission systems[C]. in Optical Fiber Telecommunications Ⅲ A, Ⅰ. P. Kaminow and T. L. Koch, eds.(Academic Press, San Diego,1997)
[16]Hill. K. O., Bilodeau. F., Malo. B., Kitagawa. T., Theriault. S., Johnson. D. C., Albert. J., and Takiguchi. K. Chirped in-fiber Bragg gratings for compensation of optical-fiber dispersion[J]. Opt. Lett.1994,19:1314-1316.
[17]Madsen, C.K.; Lenz, G. Optical all-pass filters for phase response design with applications for dispersion compensation[J]. Photonics Technology Letters.1998,10(7):994-996.
[18]Yariv. A., Fekete. D., and Pepper. D. M.. Compensation for channel dispersion by nonlinear optical phase conjugation[J]. Opt. Lett.1979,4,:52-54.
[19]Watanabe, S.; Naito, T.; Chikama, T. Compensation of chromatic dispersion in a single-mode fiber by optical phase conjugation[J]. Photonics Technology Letters.1993,5(1):92-95.
[20]周志强,唐余亮,谢崇进.色散补偿光纤传输系统的最佳补偿方案[J].激光技术,2000,24(5)：265-269
[21]Poole, C.D.; Wiesenfeld, J.M.; DiGiovanni, D.J.; Vengsarkar, A.M. Optical fiber-based dispersion compensation using higher order modes near cutoff[J]. Journal of Lightwave Technology,1994,12 (10):1746-1758.
[22]Srikant. V. Broadband dispersion and dispersion slope compensation in high bit rate and ultra
long haul systems[C]. OFC 2001, paper TuHl.
[23]Knudsen.. S. N. and Veng. T. Large effective area dispersion compensating fiber for cabled compensation of standard single mode fiber[C]. OFC 2000, paper TuG5
[24]Quang. Le, Lucent Technol N.T., Denmark, Broendby, Denmark, Veng. T., and L. Gruner-Nielsen. New dispersion compensating module for compensation of dispersion and dispersion slope of non-zero dispersion fibres in the C-band[C]. OFC 2001, paper TuH5..
[25]Mukasa. K., Moridaira. H., Yagi. T., and Kokura. K. New type of dispersion management transmission line with MDFSD for long-haul 40 Gb/s transmission[C]. OFC 2002, paper ThGG2.
[26]Ho. K. P., Phase-modulated optical communication systems[M], Springer, U.S.:New York,2005
[27]Gordon. J. P., and Mollenauer. L. F.phase noise in photonic communications-systems using linear-amplifiers[J]. Optics Letters,1990,15(23):1351-1353,.
[28]B. Xu, and Brandt-Pearce. M. Analysis of noise amplification by a CW pump signal due to fiber nonlinearity[J]. IEEE Photonics Technology Letters,2004,16(4):1062-1064.
[29]S. Kumar. Effect of dispersion on nonlinear phase noise in optical transmission systems[J]. Optics Letters,2005,30(24):3278-3280.
[30]F. Zhang, C. A. Bunge, and K. Petermann. Analysis of nonlinear phase noise in single-channel return-to-zero differential phase-shift keying transmission systems[J]. Optics Letters,2006,31(8): 1038-1040.
[31]Ho. K. P., and Wang. H. C. Effect of dispersion on nonlinear phase noise[J]. Optics Letters,2006,31, (14):2109-2111.
[32]Lowery J, Armstrong J.Orthogonal-frequency-division Multiplexing for Dispersion Compensation of Long-haul Optical Systems [J]. Optics Express,2006,14:2079-2084.
[33]Shieh. W., Bao H., and Tang Y., Coherent optical OFDM:theory and design[J], Optics Express,2008, Vol.16, No.2, pp.841-859.
[34]Jean Armstrong, OFDM for Optical Communications[J], J.Lightwave Technol.,2009,27(3):189-204
[35]邵群峰,基于时域透镜的高速非线性光纤通信链路的优化研究[博士论文],兰州：兰州大学,2011
[36]Nori Shibata, Ralf P. Braun,Robert G. Waarts, Phase-mismatch dependence of efficiency of wave generation through four-wave mixing in a single-mode optical fiber[J] Journal of Quantum Electronics,1987,23(7):1205-1210..
[37]Tkach. R. W., Chraplyvy. A. R., Fabrizio Forghieri, Gnauck. A. H., and Derosier. R.M., Four-photon mixing and high-speed WDM systems[J], J.Lightwave Technol.1995,13(5):841-849
[38]Artur James Lowery, Shunjie Wang, Malin Premrate, Calculation of power limit due to fiber nonlinearity in optical OFDM system[J], Optics Express,2007,15(20):13282-13287
[39]Peddannragari. K.V., Maite Brandt-Pearce, Volterra series transfer function of single-model fiber[J],J.Lightwave Technol,1997,15(12):2232-2241
[40]Peddannragari. K.V., Maite Brandt-Pearce, Volterra series approach for optimizing fiber-optic communications system designs[J], J,Lightwave Technol,1998,16(11):2046-2055
[41]Jacklyn D.Reis, Antonio L. Teixeira, Unveiling nonlinear effects in dense coherent optical WDM systems with Volterra series[J], Optics Express,2010,18(8):8660-8670
[42]Ling Liu, Liangchuan Li, Yuanda Huang, Kai Cui, Qianjin Xiong, Fabian N.Hauske,Intrachannel nonlinearity compensation by inverse Volterra Series Transfer Function[J], J.Lightwave Technol,2012,30(3):310-316
[43]Jie Pan and Chi-Hao Cheng, Nonlinear Electrical Compensation for the Coherent Optical OFDM System[J], J.Lightwave Technol,2011,29(2):215-221.
[44]Govind P. Agrawal.非线性光纤光学原理及应用[M].贾东方,余震虹译.北京：电子工业出版社,2003
[45]Agrawal. G. P. Fiber-Optic Communication Systems[M]. Number ISBN 0-471-17540-4 in Wiley Series in Microwave and Optical Engineering. John Wiley and Sons, Inc.,3 edition,2002
[46]Agrawal. G. P. Nonlinear Fiber Optics[M]. Number ISBN 0-12-045143-3. Academic Press,3 edition, 2001.
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