四波混频泵浦消耗过程的相位匹配条件研究
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摘要
采用解析方法分析讨论泵浦消耗情形下的准相位匹配范围以及相位匹配条件的变化,并给出相位匹配条件的表达式.比较分析小信号近似和泵浦消耗两种情形下四波混频增益演化过程.研究表明,在泵浦消耗情形下,随转移功率的增大,满足总相位匹配的线性失配因子从负值逐渐趋于0,准相位匹配范围也越来越小;确定四波混频的准相位匹配范围,可简化波分复用或空分复用系统中级联四波混频的分析过程;小信号近似模型只适合于转移功率远小于泵浦功率的情形,满足总相位匹配的线性失配因子不依赖于光纤长度.
The analytic method is used to analyze the range of quasi-phase matching and the evolution of the phase matching in the case of pump depletion,and the expression for the phase matching is given.The evolution process of four-wave mixing gain under pump depletion is compared to the case in smallsignal approximation.In the case of pump depletion,with the increase of the transfer power,the linear mismatch factor corresponding to the total phase matching gradually tends to 0and the quasi-phase matching range also becomes narrower.By determining the quasi-phase matching rang,the cascaded four-wave mixing process in wavelength division multiplex or space division multiplexing systems can be simplified for analysis.The small signal approximation model is only suitable for the case that the transfer power is far less than the pump power,and the linear mismatch factor at the total phase matching is not dependent on the length of the fiber.
The analytic method is used to analyze the range of quasi-phase matching and the evolution of the phase matching in the case of pump depletion,and the expression for the phase matching is given.The evolution process of four-wave mixing gain under pump depletion is compared to the case in smallsignal approximation.In the case of pump depletion,with the increase of the transfer power,the linear mismatch factor corresponding to the total phase matching gradually tends to 0and the quasi-phase matching range also becomes narrower.By determining the quasi-phase matching rang,the cascaded four-wave mixing process in wavelength division multiplex or space division multiplexing systems can be simplified for analysis.The small signal approximation model is only suitable for the case that the transfer power is far less than the pump power,and the linear mismatch factor at the total phase matching is not dependent on the length of the fiber.
引文
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[20]CHEN Y.Four-wave mixing in optical fibers:exact solution[J].Journal of the Optical Society of America B,1989,6(11):1986-1993.
[2]XU X,YAO Y,ZHAO X,et al.Multiple four-wave-mixing processes and their application to multiwavelength Erbiumdoped fiber lasers[J].Journal of Lightwave Technology,2009,27(14):2876-2885.
[3]FEVE J P.Phase-matching and mitigationof four-wave mixing in fibers with positive gain[J].Optics Express,2007,15(2):577-582.
[4]ASO O,TADAKUMA M,SHU N.Four-wave mixing in optical fibers and its applications[J].Furukawa Review,1999,1(19):63-68.
[5]MATEO E,YAMAN F,LI G.Control of four-wave mixing phase-matching condition using the Brillouin slow-light effect in fibers[J].Optics Letters,2008,33(5):488-490.
[6]WILLNER A E,KHALEGHI S,CHITGARHA M R,et al.All-optical signal processing[J].Journal of Lightwave Technology,2014,32(4):660-680.
[7]TURITSYN S K,BEDNYAKOVA A E,FEDORUK M P,et al.Inverse four-wave mixing and self-parametric amplification in optical fibre[J].Nature Photonics,2015,9(9):608-614.
[8]CAO Ya-min,WU Bao-jian,WAN Feng,et al.Principle and noise performance of optical phase arithmetic devices using four wave mixing[J].Acta Physica Sinica,2018,67(9):94208.曹亚敏,武保剑,万峰,等.四波混频光相位运算器原理及其噪声性能研究[J].物理学报,2018,67(9):94208.
[9]DUAN Jie,XIE Xiao-ping,DUAN Tao,et al.An all-optical exclusive-OR gate based on terahertz optical asymmetric demultiplexer-four wave mixing effect[J].Acta Photonica Sinica,2013,42(9):1031-1038.段杰,谢小平,段弢,等.基于太赫兹光解复用器-四波混频效应的全光异或门方案[J].光子学报,2013,42(9):1031-1038.
[10]SHAH N M,MATSUMOTO M.2Rregeneration of time-interleaved multiwavelength signals based on higher order four-wave mixing in a fiber[J].IEEE Photonics Technology Letters,2010,22(1):27-29.
[11]AN Jun-ge,WU Bao-jian,ZHOU Xing-yu.Assessment of performance for all-optical reshapers based on the power transfer function[J].Acta Photonica Sinica,2013,42(1):38-42.安俊鸽,武保剑,周星宇.基于功率转移函数的全光整形器性能评估[J].光子学报,2013,42(1):38-42.
[12]JIA Liang,ZHANG Fan,LI Ming,et al.Numerical analysis for four-wave mixing based wavelength conversion of differential phase-shift keying signals[J].Chinese Optics Letters,2009,7(7):617-620.
[13]AHMED J,HUSSAIN A,SIYAL M Y,et al.Parametric analysis of four wave mixing in DWDM systems[J].OptikInternational Journal for Light and Electron Optics,2014,125(7):1853-1859.
[14]REDYUK A,STEPHENS M F C,DORAN N J.Suppression of WDM four-wave mixing crosstalk in fibre optic parametric amplifier using Raman-assisted pumping[J].Optics Express,2015,23(21):27240-27249.
[15]LAWAN S H,MOHAMMAD A B.Reduction of four wave mixing efficiency in DWDM systems using optimal PMD[J].Optical and Quantum Electronics,2018,50(2):91
[16]SHARMA V,KAUR R.Implementation of DWDM system in the presence of four wave mixing(FWM)under the impact of channel spacing[J].Optik-International Journal for Light and Electron Optics,2013,124(17):3112-3114.
[17]WANG J,SUN Q,SUN J.All-optical 40Gbit/s CSRZ-DPSK logic XOR gate and format conversion using four-wave mixing[J].Optics Express,2009,17(15):12555-12563.
[18]LI Zhi,WU Bao-jian,WEN Feng et al.Measurement method of fiber nonlinear coefficient based on four wave mixing[J].Acta Photonica Sinica,2012,41(5):536-540.李智,武保剑,文峰,等.基于四波混频的光纤非线性系数测量方法[J].光子学报,2012,41(5):536-540.
[19]WANG Yan-bin,XIONG Chun-le,HOU Jing et al.Modeling of four-wave mixing and supercontinuum with long pulses in photonic crystal fibers[J].Acta Physica Sinica,2011,60(1):14201.王彦斌,熊春乐,侯静,等.长脉冲抽运光子晶体光纤四波混频和超连续谱的理论研究[J].物理学报,2011,60(1):14201.
[20]CHEN Y.Four-wave mixing in optical fibers:exact solution[J].Journal of the Optical Society of America B,1989,6(11):1986-1993.