Simulation of 1 550 nm Femtosecond Pulse Self-similar Fiber Amplification Enhanced Publication

{ "defaultlang": "zh", "titlegroup": { "articletitle": [ { "lang": "zh", "data": [ { "name": "text", "data": "1 550 nm飞秒脉冲自相似光纤放大仿真模拟" } ] }, { "lang": "en", "data": [ { "name": "text", "data": "Simulation of 1 550 nm Femtosecond Pulse Self-similar Fiber Amplification" } ] } ] }, "contribgroup": { "author": [ { "name": [ { "lang": "zh", "surname": "白", "givenname": "笑羽", "namestyle": "eastern", "prefix": "" }, { "lang": "en", "surname": "BAI", "givenname": "Xiao-yu", "namestyle": "eastern", "prefix": "" } ], "stringName": [], "aff": [ { "rid": "aff1", "text": "1" } ], "role": [ "first-author" ], "bio": [ { "lang": "zh", "text": [ "白笑羽(1997-)，女，吉林四平人，硕士研究生，2019年于长春电子科技学院获得学士学位，主要从事光纤激光器及放大器方面的研究。E-mail: bxy971011@163.com" ], "graphic": [ { "print": "http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24623165&type=", "small": "http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24623167&type=", "big": 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"graphic": [ { "print": "http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24623174&type=", "small": "http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24623179&type=", "big": "http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24623184&type=" } ], "data": [ [ { "name": "text", "data": "王蓟" }, { "name": "text", "data": "(1978-)，女，山东青岛人，博士，副教授，2007年于中国科学院长春光学精密机械与物理研究所获得博士学位，主要从事光纤激光器及放大器方面的研究。E-mail: " }, { "name": "text", "data": "24169973@qq.com" } ] ] } ], "email": "24169973@qq.com", "deceased": false }, { "name": [ { "lang": "zh", "surname": "孙", "givenname": "旭东", "namestyle": "eastern", "prefix": "" }, { "lang": "en", "surname": "SUN", "givenname": "Xu-dong", "namestyle": "eastern", "prefix": "" } ], "stringName": [], "aff": [ { "rid": "aff1", "text": "1" } ], "role": [], "deceased": false }, { "name": [ { "lang": "zh", "surname": "贾", "givenname": "苏蒙", "namestyle": "eastern", "prefix": "" }, { "lang": "en", "surname": "JIA", "givenname": "Su-meng", "namestyle": "eastern", "prefix": "" } ], "stringName": [], "aff": [ { "rid": "aff1", "text": "1" } ], "role": [], "deceased": false }, { "name": [ { "lang": "zh", "surname": "郭", "givenname": "欣宇", "namestyle": "eastern", "prefix": "" }, { "lang": "en", "surname": "GUO", "givenname": "Xin-yu", "namestyle": "eastern", "prefix": "" } ], "stringName": [], "aff": [ { "rid": "aff1", "text": "1" } ], "role": [], "deceased": false }, { "name": [ { "lang": "zh", "surname": "张", "givenname": "永熙", "namestyle": "eastern", "prefix": "" }, { "lang": "en", "surname": "ZHANG", "givenname": "Yong-xi", "namestyle": "eastern", "prefix": "" } ], "stringName": [], "aff": [ { "rid": "aff1", "text": "1" } ], "role": [], "deceased": false }, { "name": [ { "lang": "zh", "surname": "王", "givenname": "国政", "namestyle": "eastern", "prefix": "" }, { "lang": "en", "surname": "WANG", "givenname": "Guo-zheng", "namestyle": "eastern", "prefix": "" } ], "stringName": [], "aff": [ { "rid": "aff1", "text": "1" } ], "role": [], "deceased": false } ], "aff": [ { "id": "aff1", "intro": [ { "lang": "zh", "label": "1", "text": "长春理工大学　物理学院，吉林　长春　130022", "data": [ { "name": "text", "data": "长春理工大学　物理学院，吉林　长春　130022" } ] }, { "lang": "en", "label": "1", "text": "School of Science, Changchun University of Science and Technology, Changchun 130022, China", "data": [ { "name": "text", "data": "School of Science, Changchun University of Science and Technology, Changchun 130022, China" } ] } ] }, { "id": "aff2", "intro": [ { "lang": "zh", "label": "2", "text": "鹏城实验室　数学与理论部，广东　深圳　518000", "data": [ { "name": "text", "data": "鹏城实验室　数学与理论部，广东　深圳　518000" } ] }, { "lang": "en", "label": "2", "text": "Department of Mathematics and Theories, Peng Cheng Laboratory, Shenzhen 518000, China", "data": [ { "name": "text", "data": "Department of Mathematics and Theories, Peng Cheng Laboratory, Shenzhen 518000, China" } ] } ] } ] }, "abstracts": [ { "lang": "zh", "data": [ { "name": "p", "data": [ { "name": "text", "data": "针对全光纤的超短脉冲掺铒光纤放大器进行了仿真模拟，对正常色散条件下掺铒光纤自相似脉冲放大过程进行了详细分析。在光纤预放大器中，使用高正色散掺铒光纤对脉冲形状进行预整形，将重复频率43 MHz、脉冲宽度600 fs、平均输出功率1.2 mW的孤子型锁模脉冲预整形为抛物线型脉冲，预整形后的脉冲通过光纤主放大器进行功率放大。经两级光纤放大后，1.2 mW的信号光功率放大为102 mW，放大增益19.3 dB。分析了掺铒光纤长度、放大功率对脉冲自相似演化过程的影响。放大后的脉冲经4.4 m长单模光纤将脉冲宽度压缩至53 fs，峰值功率为44.8 kW。" } ] } ] }, { "lang": "en", "data": [ { "name": "p", "data": [ { "name": "text", "data": "In this paper, an all-fiber structure of ultrashort pulse erbium-doped fiber amplifier was simulated, and the self-similar pulse amplification processed of erbium-doped fiber under normal dispersion conditions was analyzed in detail. In the fiber pre-amplifier, a high positive dispersion erbium-doped fiber was be used to pre-shape the pulse shape. The soliton mode-locked pulse with the repetition frequency of 43 MHz, pulse width of 600 fs, and average output power of 1.2 mW was pre-shaped into a parabolic pulse. The pre-shaped pulse is amplified by the optical fiber main amplifier. After two-stage optical fiber amplification, the signal optical power of 1.2 mW was amplified to 102 mW, and the amplification gain was 19.3 dB. The influence of erbium-doped fiber length and amplification power on the evolution of pulse self-similarity was analyzed in this article. The amplified pulse was compressed to 53 fs through 4.4 m long single-mode fiber and the peak power was 44.8 kW." } ] } ] } ], "keyword": [ { "lang": "zh", "data": [ [ { "name": "text", "data": "光纤放大器" } ], [ { "name": "text", "data": "自相似" } ], [ { "name": "text", "data": "正常色散掺铒光纤" } ], [ { "name": "text", "data": "超短脉冲" } ], [ { "name": "text", "data": "仿真模拟" } ] ] }, { "lang": "en", "data": [ [ { "name": "text", "data": "fiber amplifier" } ], [ { "name": "text", "data": "self-similarity" } ], [ { "name": "text", "data": "normal dispersion erbium-doped fiber" } ], [ { "name": "text", "data": "ultrashort pulse" } ], [ { "name": "text", "data": "simulation" } ] ] } ], "highlights": [], "body": [ { "name": "sec", "data": [ { "name": "sectitle", "data": { "label": [ { "name": "text", "data": "1" } ], "title": [ { "name": "text", "data": "引言" } ], "level": "1", "id": "s1" } }, { "name": "p", "data": [ { "name": "text", "data": "自相似抛物线型脉冲是指由于光纤中的色散、非线性效应、增益的共同作用，脉冲会产生很高的线性啁啾，且能量被显著放大，脉冲的形状呈现抛物线型" }, { "name": "sup", "data": [ { "name": "text", "data": "[" }, { "name": "xref", "data": { "text": "1", "type": "bibr", "rid": "R1", "data": [ { "name": "text", "data": "1" } ] } }, { "name": "text", "data": "]" } ] }, { "name": "text", "data": "。" } ] }, { "name": "p", "data": [ { "name": "text", "data": "从理论角度出发，通过求解非线性薛定谔方程的自相似渐近解，能够得出自相似光纤放大的典型特征及脉冲的演化条件。由于其脉冲呈抛物线形状，故在传输过程中能够很好地抵御光波分裂。自相似脉冲的放大及传输过程只与入射脉冲的初始能量有关，因而易获得较高的能量输出。抛物线型脉冲放大时积累的啁啾是线性正啁啾，有利于后续的脉冲压缩" }, { "name": "sup", "data": [ { "name": "text", "data": "[" }, { "name": "xref", "data": { "text": "2", "type": "bibr", "rid": "R2", "data": [ { "name": "text", "data": "2" } ] } }, { "name": "text", "data": "]" } ] }, { "name": "text", "data": "。2000年，Fermann等首次证明，脉冲在足够长的正色散增益光纤中传输及放大时，其包络形状最终会演化成抛物线型。随后他们将实验中产生的抛物线型脉冲进行了压缩，得到了70 fs的超短脉冲输出，峰值功率高达80 kW" }, { "name": "sup", "data": [ { "name": "text", "data": "[" }, { "name": "xref", "data": { "text": "3", "type": "bibr", "rid": "R3", "data": [ { "name": "text", "data": "3" } ] } }, { "name": "text", "data": "]" } ] }, { "name": "text", "data": "。2008年，南开大学涂成厚等首次给出了实现脉冲自相似演化的具体条件，同时研究了增益系数对脉冲自相似演化形成和放大传输的影响" }, { "name": "sup", "data": [ { "name": "text", "data": "[" }, { "name": "xref", "data": { "text": "4", "type": "bibr", "rid": "R4", "data": [ { "name": "text", "data": "4" } ] } }, { "name": "text", "data": "]" } ] }, { "name": "text", "data": "。2010年，Ortac等搭建了一套孤子-自相似子光纤激光器(Soliton-similariton fiber laser)。这是自相似脉冲放大技术在掺铒光纤激光器中的首次实现，他们最终获得了能量为3.1 nJ、脉冲宽度110 fs的激光输出" }, { "name": "sup", "data": [ { "name": "text", "data": "[" }, { "name": "xref", "data": { "text": "5", "type": "bibr", "rid": "R5", "data": [ { "name": "text", "data": "5" } ] } }, { "name": "text", "data": "]" } ] }, { "name": "text", "data": "。2015年，Liu等设计了一套通过预啁啾管理的掺镱光纤自相似放大器，输出重复频率75 MHz，输出脉冲经光栅对压缩至60 fs，平均功率高达100 W" }, { "name": "sup", "data": [ { "name": "text", "data": "[" }, { "name": "xref", "data": { "text": "6", "type": "bibr", "rid": "R6", "data": [ { "name": "text", "data": "6" } ] } }, { "name": "text", "data": "]" } ] }, { "name": "text", "data": "。2018年，Song等报道了关于皮秒脉冲自相似放大系统的数值模拟和实验研究。该系统得到了30 MHz的重复频率，66 fs的脉冲宽度，平均功率为6.1 W" }, { "name": "sup", "data": [ { "name": "text", "data": "[" }, { "name": "xref", "data": { "text": "7", "type": "bibr", "rid": "R7", "data": [ { "name": "text", "data": "7" } ] } }, { "name": "text", "data": "]" } ] }, { "name": "text", "data": "。2020年，贺明洋等基于自相似光纤激光放大技术，选用大模场增益光纤，最终得到中心波长1 030 nm、重复频率40 MHz、平均功率34 W、脉冲宽度50 fs的高质量脉冲输出，对应峰值功率17 MW" }, { "name": "sup", "data": [ { "name": "text", "data": "[" }, { "name": "xref", "data": { "text": "8", "type": "bibr", "rid": "R8", "data": [ { "name": "text", "data": "8" } ] } }, { "name": "text", "data": "]" } ] }, { "name": "text", "data": "。" } ] }, { "name": "p", "data": [ { "name": "text", "data": "本文模拟了孤子型脉冲在一段高正色散掺铒光纤中被预先整形为抛物线型，然后经主放大器进行自相似放大，最后使用一段负色散的普通单模光纤对放大后的脉冲进行压缩的过程。" } ] } ] }, { "name": "sec", "data": [ { "name": "sectitle", "data": { "label": [ { "name": "text", "data": "2" } ], "title": [ { "name": "text", "data": "非线性薛定谔方程及自相似抛物型脉冲渐近解" } ], "level": "1", "id": "s2" } }, { "name": "p", "data": [ { "name": "text", "data": "脉冲在光纤放大器中的演化可以用带有常增益系数且不考虑光纤吸收损耗和高阶色散的非线性薛定谔方程描述" }, { "name": "sup", "data": [ { "name": "text", "data": "[" }, { "name": "xref", "data": { "text": "3", "type": "bibr", "rid": "R3", "data": [ { "name": "text", "data": "3" } ] } }, { "name": "text", "data": "," }, { "name": "xref", "data": { "text": "9", "type": "bibr", "rid": "R9", "data": [ { "name": "text", "data": "9" } ] } }, { "name": "text", "data": "]" } ] }, { "name": "text", "data": ":" }, { "name": "dispformula", "data": { "label": [ { "name": "text", "data": "(1)" } ], "data": [ { "name": "math", "data": { "graphicsData": { "print": "http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24623186&type=", "small": "http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24623190&type=", "big": "http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24623194&type=" } } } ], "id": "DF1" } }, { "name": "text", "data": "我们暂不考虑增益饱和以及增益带宽限制的影响，" }, { "name": "italic", "data": [ { "name": "text", "data": "Ψ" } ] }, { "name": "text", "data": "(" }, { "name": "italic", "data": [ { "name": "text", "data": "z" } ] }, { "name": "text", "data": "," }, { "name": "italic", "data": [ { "name": "text", "data": "T" } ] }, { "name": "text", "data": ")为延时系中的慢变脉冲包络，" }, { "name": "italic", "data": [ { "name": "text", "data": "γ" } ] }, { "name": "text", "data": "为非线性参量，" }, { "name": "italic", "data": [ { "name": "text", "data": "g" } ] }, { "name": "text", "data": "为放大器平均分布增益系数，" }, { "name": "italic", "data": [ { "name": "text", "data": "β" } ] }, { "name": "sub", "data": [ { "name": "text", "data": "2" } ] }, { "name": "text", "data": "为群速度色散参量。在群速度色散" }, { "name": "italic", "data": [ { "name": "text", "data": "β" } ] }, { "name": "sub", "data": [ { "name": "text", "data": "2" } ] }, { "name": "italic", "data": [ { "name": "text", "data": ">" } ] }, { "name": "text", "data": "0时，只要传输距离足够长，非线性薛定谔方程就存在一种带有线性啁啾的自相似渐近解" }, { "name": "sup", "data": [ { "name": "text", "data": "[" }, { "name": "xref", "data": { "text": "3", "type": "bibr", "rid": "R3", "data": [ { "name": "text", "data": "3" } ] } }, { "name": "text", "data": "]" } ] }, { "name": "text", "data": "。" } ] }, { "name": "p", "data": [ { "name": "text", "data": "经推导可以得出脉冲相位项：" }, { "name": "dispformula", "data": { "label": [ { "name": "text", "data": "(2)" } ], "data": [ { "name": "math", "data": { "graphicsData": { "print": "http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24623201&type=", "small": "http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24623205&type=", "big": "http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24623209&type=" } } } ], "id": "DF2" } }, { "name": "text", "data": "其中" }, { "name": "italic", "data": [ { "name": "text", "data": "φ" } ] }, { "name": "sub", "data": [ { "name": "text", "data": "0" } ] }, { "name": "text", "data": "为任意常数，进而可得脉冲时域强度：" }, { "name": "dispformula", "data": { "label": [ { "name": "text", "data": "(3)" } ], "data": [ { "name": "math", "data": { "graphicsData": { "print": "http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24623213&type=", "small": "http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24623216&type=", "big": "http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24623218&type=" } } } ], "id": "DF3" } }, { "name": "text", "data": "以及脉冲峰值强度：" }, { "name": "dispformula", "data": { "label": [ { "name": "text", "data": "(4)" } ], "data": [ { "name": "math", "data": { "graphicsData": { "print": "http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24623226&type=", "small": "http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24623231&type=", "big": "http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24623237&type=" } } } ], "id": "DF4" } }, { "name": "text", "data": "公式(3)说明脉冲具有抛物线型的时域形状，并且随着传输距离的增大仍然可以保持该形状。公式(2)和(4)表示随着传输距离的增长，脉冲宽度和脉冲的峰值功率都呈指数增长" }, { "name": "sup", "data": [ { "name": "text", "data": "[" }, { "name": "xref", "data": { "text": "10", "type": "bibr", "rid": "R10", "data": [ { "name": "text", "data": "10" } ] } }, { "name": "text", "data": "]" } ] }, { "name": "text", "data": "。在放大器的参数固定不变时，自相似的放大过程只与入射脉冲的初始能量" }, { "name": "italic", "data": [ { "name": "text", "data": "U" } ] }, { "name": "sub", "data": [ { "name": "text", "data": "in" } ] }, { "name": "text", "data": "有关，不受入射脉冲形状、宽度等参数影响" }, { "name": "sup", "data": [ { "name": "text", "data": "[" }, { "name": "blockXref", "data": { "data": [ { "name": "xref", "data": { "text": "11", "type": "bibr", "rid": "R11", "data": [ { "name": "text", "data": "11" } ] } }, { "name": "text", "data": "-" }, { "name": "xref", "data": { "text": "12", "type": "bibr", "rid": "R12", "data": [ { "name": "text", "data": "12" } ] } } ], "rid": [ "R11", "R12" ], "text": "11-12", "type": "bibr" } }, { "name": "text", "data": "]" } ] }, { "name": "text", "data": "。根据静态相位理论，脉冲频谱强度可以表示为：" }, { "name": "dispformula", "data": { "label": [ { "name": "text", "data": "(5)" } ], "data": [ { "name": "math", "data": { "graphicsData": { "print": "http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24623242&type=", "small": "http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24623245&type=", "big": "http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24623249&type=" } } } ], "id": "DF5" } }, { "name": "text", "data": "其中，" }, { "name": "italic", "data": [ { "name": "text", "data": "ω" } ] }, { "name": "sub", "data": [ { "name": "text", "data": "p" } ] }, { "name": "text", "data": "(" }, { "name": "italic", "data": [ { "name": "text", "data": "z" } ] }, { "name": "text", "data": ")为脉冲频谱宽度，其表达式如公式(6)所示：" }, { "name": "dispformula", "data": { "label": [ { "name": "text", "data": "(6)" } ], "data": [ { "name": "math", "data": { "graphicsData": { "print": "http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24623252&type=", "small": "http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24623255&type=", "big": "http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24623260&type=" } } } ], "id": "DF6" } }, { "name": "text", "data": "从公式(5)和(6)可知，自相似脉冲的频谱呈抛物线型，且随着传输距离的增长，频谱宽度呈指数增长" }, { "name": "sup", "data": [ { "name": "text", "data": "[" }, { "name": "xref", "data": { "text": "10", "type": "bibr", "rid": "R10", "data": [ { "name": "text", "data": "10" } ] } }, { "name": "text", "data": "]" } ] }, { "name": "text", "data": "。根据上述分析，可以发现自相似脉冲在时域以及频域都呈抛物线型。随着传输距离的增长，脉冲的峰值功率、时域及频域的宽度都呈指数增长。此外，其线性啁啾量不受传输距离影响。" } ] }, { "name": "p", "data": [ { "name": "text", "data": "上述分析过程是基于" }, { "name": "italic", "data": [ { "name": "text", "data": "β" } ] }, { "name": "sub", "data": [ { "name": "text", "data": "2" } ] }, { "name": "italic", "data": [ { "name": "text", "data": "γ>" } ] }, { "name": "text", "data": "0，目前已知的稀土掺杂光纤" }, { "name": "italic", "data": [ { "name": "text", "data": "γ" } ] }, { "name": "text", "data": "均大于0，也就是基于" }, { "name": "italic", "data": [ { "name": "text", "data": "β" } ] }, { "name": "sub", "data": [ { "name": "text", "data": "2" } ] }, { "name": "italic", "data": [ { "name": "text", "data": ">" } ] }, { "name": "text", "data": "0的前提，可以得到上述自相似脉冲放大理论。" } ] } ] }, { "name": "sec", "data": [ { "name": "sectitle", "data": { "label": [ { "name": "text", "data": "3" } ], "title": [ { "name": "text", "data": "自相似脉冲演化仿真模拟" } ], "level": "1", "id": "s3" } }, { "name": "p", "data": [ { "name": "text", "data": "仿真模拟使用的软件是MATLAB，模拟过程通过改变器件尾纤长度、增益光纤长度、小信号增益系数这些参数，研究光纤放大器中的色散、非线性效应、增益对输出脉冲及光谱的影响。整个过程是在预放大器中使用高正色散的掺铒光纤，目的是将脉冲初步整形为抛物线型；然后在主放大器中将功率放大；最后使用一段单模光纤完成脉冲压缩。" }, { "name": "xref", "data": { "text": "图1", "type": "fig", "rid": "F1", "data": [ { "name": "text", "data": "图1" } ] } }, { "name": "text", "data": "为光纤放大器的主要结构，信号光源是一个孤子锁模掺铒光纤激光器，信号光经过隔离器(ISO1)，与泵浦光同时经波分复用器(WDM1)耦合进增益光纤(EDF1)，再由隔离器(ISO2)输出便完成一级预放大，随后使用双向泵浦进行主放大过程，最后经过一段单模光纤(SMF)完成脉冲压缩。" } ] }, { "name": "fig", "data": { "id": "F1", "caption": [ { "lang": "zh", "label": [ { "name": "text", "data": "图1" } ], "title": [ { "name": "text", "data": "掺铒光纤放大器结构图" } ] }, { "lang": "en", "label": [ { "name": "text", "data": "Fig.1" } ], "title": [ { "name": "text", "data": "Structure diagram of erbium-doped fiber amplifier" } ] } ], "subcaption": [], "note": [], "graphics": [ { "print": "http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24623266&type=", "small": "http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24623276&type=", "big": "http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24623273&type=" } ] } }, { "name": "p", "data": [ { "name": "text", "data": "信号光源为基于碳纳米管可饱和吸收体锁模的孤子型掺铒光纤激光器，中心波长为1 550 nm，平均输出功率1.2 mW，重复频率43 MHz，脉冲宽度600 fs，脉冲形状为双曲正割型，信噪比为45 dB。预放大级使用的掺铒光纤主要参数为：峰值吸收率80 dB/m@1 530 nm，模场直径4.3 μm@1 550 nm，色散值" }, { "name": "italic", "data": [ { "name": "text", "data": "D" } ] }, { "name": "text", "data": "=-48 ps/(km·nm)，可以计算出" }, { "name": "italic", "data": [ { "name": "text", "data": "β" } ] }, { "name": "sub", "data": [ { "name": "text", "data": "2" } ] }, { "name": "text", "data": "=61 ps" }, { "name": "sup", "data": [ { "name": "text", "data": "2" } ] }, { "name": "text", "data": "/km，根据掺铒光纤的经验值，其非线性折射率为" }, { "name": "italic", "data": [ { "name": "text", "data": "n" } ] }, { "name": "sub", "data": [ { "name": "text", "data": "2" } ] }, { "name": "text", "data": "=2.2×10" }, { "name": "sup", "data": [ { "name": "text", "data": "-20" } ] }, { "name": "text", "data": " m" }, { "name": "sup", "data": [ { "name": "text", "data": "2" } ] }, { "name": "text", "data": "/W，主放大级所使用的掺铒光纤与预放大级相同。脉冲压缩光纤主要参数为：模场直径为10.4 μm@1 550 nm，色散值" }, { "name": "italic", "data": [ { "name": "text", "data": "D" } ] }, { "name": "text", "data": "=18 ps/(km·nm)，计算得到" }, { "name": "italic", "data": [ { "name": "text", "data": "β" } ] }, { "name": "sub", "data": [ { "name": "text", "data": "2" } ] }, { "name": "text", "data": "=-22.96 ps" }, { "name": "sup", "data": [ { "name": "text", "data": "2" } ] }, { "name": "text", "data": "/km。" } ] } ] }, { "name": "sec", "data": [ { "name": "sectitle", "data": { "label": [ { "name": "text", "data": "4" } ], "title": [ { "name": "text", "data": "结果与讨论" } ], "level": "1", "id": "s4" } }, { "name": "sec", "data": [ { "name": "sectitle", "data": { "label": [ { "name": "text", "data": "4.1" } ], "title": [ { "name": "text", "data": "预放大级仿真结果分析" } ], "level": "2", "id": "s4a" } }, { "name": "p", "data": [ { "name": "text", "data": "如" }, { "name": "xref", "data": { "text": "图2", "type": "fig", "rid": "F2", "data": [ { "name": "text", "data": "图2" } ] } }, { "name": "text", "data": "所示，在预放大过程中，增益光纤的长度对脉冲的演变结果有影响。在色散和自相位调制的共同作用下，增益光纤越长，脉冲就会展得越宽。但模拟数据" }, { "name": "xref", "data": { "text": "图2", "type": "fig", "rid": "F2", "data": [ { "name": "text", "data": "图2" } ] } }, { "name": "text", "data": "显示，脉冲呈现顶端逐渐平缓且两侧越来越陡峭的类似抛物线的形状。结果显示，随着增益光纤长度的增加，脉冲形状从信号光的双曲正割型逐步演化为抛物线型，模拟结果与理论分析一致" }, { "name": "sup", "data": [ { "name": "text", "data": "[" }, { "name": "xref", "data": { "text": "8", "type": "bibr", "rid": "R8", "data": [ { "name": "text", "data": "8" } ] } }, { "name": "text", "data": "]" } ] }, { "name": "text", "data": "。" } ] }, { "name": "fig", "data": { "id": "F2", "caption": [ { "lang": "zh", "label": [ { "name": "text", "data": "图2" } ], "title": [ { "name": "text", "data": "不同增益光纤长度下预放大级的脉冲变化" } ] }, { "lang": "en", "label": [ { "name": "text", "data": "Fig.2" } ], "title": [ { "name": "text", "data": "Pulse variation of the pre-amplifier stage at different gain fiber lengths" } ] } ], "subcaption": [], "note": [], "graphics": [ { "print": "http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24623280&type=", "small": "http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24623292&type=", "big": "http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24623287&type=" } ] } }, { "name": "p", "data": [ { "name": "text", "data": "脉冲被放大的同时，其光谱也具有良好的抛物线形状，才能为后续的主放大过程提供有利条件。因此，我们进一步模拟了信号脉冲经过不同长度增益光纤时的情况。如" }, { "name": "xref", "data": { "text": "图3", "type": "fig", "rid": "F3", "data": [ { "name": "text", "data": "图3" } ] } }, { "name": "text", "data": "所示，我们对强度进行了归一化处理。通过改变增益光纤的长度，观察光谱的演变，随着增益光纤长度逐渐增加，光谱不断被展宽。增益光纤长度由1 m增加至2.6 m，光谱宽度由4.1 nm展宽至10.9 nm，脉冲宽度由600 fs展宽至1 406 fs。可以发现，在增益光纤长度为2.4 m时，光谱的形状也呈现出类似抛物线的形状。增益光纤长度增加至2.6 m后，光谱产生了畸变。故我们采用在增益光纤长度为2.4 m时的类抛物型脉冲作为信号，进行后续的主放大模拟。" } ] }, { "name": "fig", "data": { "id": "F3", "caption": [ { "lang": "zh", "label": [ { "name": "text", "data": "图3" } ], "title": [ { "name": "text", "data": "不同增益光纤长度下预放大级的光谱变化" } ] }, { "lang": "en", "label": [ { "name": "text", "data": "Fig.3" } ], "title": [ { "name": "text", "data": "Spectral variation of the pre-amplification stage at different gain fiber lengths" } ] } ], "subcaption": [], "note": [], "graphics": [ { "print": "http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24623293&type=", "small": "http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24623302&type=", "big": "http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24623299&type=" } ] } }, { "name": "p", "data": [ { "name": "text", "data": "为观察预放大级放大后脉冲及光谱形状随平均功率的增大而变化的情况，模拟了输出功率不断增加时脉冲及光谱形状的演化过程。" }, { "name": "xref", "data": { "text": "图4", "type": "fig", "rid": "F4", "data": [ { "name": "text", "data": "图4" } ] } }, { "name": "text", "data": "、" }, { "name": "xref", "data": { "text": "5", "type": "fig", "rid": "F5", "data": [ { "name": "text", "data": "5" } ] } }, { "name": "text", "data": "为增益光纤长度2.4 m时，不同输出功率下脉冲及光谱的变化。由" }, { "name": "xref", "data": { "text": "图4", "type": "fig", "rid": "F4", "data": [ { "name": "text", "data": "图4" } ] } }, { "name": "text", "data": "、" }, { "name": "xref", "data": { "text": "5", "type": "fig", "rid": "F5", "data": [ { "name": "text", "data": "5" } ] } }, { "name": "text", "data": "可见，在增益、色散、自相位调制效应的共同作用下，脉冲及光谱宽度逐渐展宽。但同时，由于放大功率增加，光谱曲线形状发生畸变。经过归一化处理的" }, { "name": "xref", "data": { "text": "图5", "type": "fig", "rid": "F5", "data": [ { "name": "text", "data": "图5" } ] } }, { "name": "text", "data": "显示，当输出功率达到29 mW时，光谱顶端不再平滑，产生畸变，因而在进行主放大模拟时，将预放大级的输出功率定为19 mW。" } ] }, { "name": "fig", "data": { "id": "F4", "caption": [ { "lang": "zh", "label": [ { "name": "text", "data": "图4" } ], "title": [ { "name": "text", "data": "增益光纤长度2.4 m时预放大级在不同增益下的脉冲变化" } ] }, { "lang": "en", "label": [ { "name": "text", "data": "Fig.4" } ], "title": [ { "name": "text", "data": "Pulse variation of pre-amplification stage at different gains when the length of gain fiber is 2.4 m" } ] } ], "subcaption": [], "note": [], "graphics": [ { "print": "http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24623306&type=", "small": "http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24623313&type=", "big": "http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24623308&type=" } ] } }, { "name": "fig", "data": { "id": "F5", "caption": [ { "lang": "zh", "label": [ { "name": "text", "data": "图5" } ], "title": [ { "name": "text", "data": "增益光纤长度2.4 m时预放大级在不同增益下的光谱变化" } ] }, { "lang": "en", "label": [ { "name": "text", "data": "Fig.5" } ], "title": [ { "name": "text", "data": "Spectral variation of the pre-amplifier stage at different gains when the gain fiber length is 2.4 m" } ] } ], "subcaption": [], "note": [], "graphics": [ { "print": "http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24623315&type=", "small": "http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24623320&type=", "big": "http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24623319&type=" } ] } }, { "name": "p", "data": [ { "name": "text", "data": "信号脉冲在经预放大器后，主要目的是将形状整形为抛物线型，不过仍然要保证光谱展至合适宽度且不发生畸变。因此，通过综合分析可知，作为预放大器，应选用2.4 m长的增益光纤，并将脉冲平均功率放大至19 mW最为合适。如" }, { "name": "xref", "data": { "text": "图6", "type": "fig", "rid": "F6", "data": [ { "name": "text", "data": "图6" } ] } }, { "name": "text", "data": "所示，此时的脉冲自相关曲线经归一化处理后又进行了抛物线拟合，脉宽被初步展宽至1.3 ps。拟合曲线也证明预放大的输出脉冲形状为类抛物线型。" } ] }, { "name": "fig", "data": { "id": "F6", "caption": [ { "lang": "zh", "label": [ { "name": "text", "data": "图6" } ], "title": [ { "name": "text", "data": "预放大自相关模拟曲线" } ] }, { "lang": "en", "label": [ { "name": "text", "data": "Fig.6" } ], "title": [ { "name": "text", "data": "Pre-amplified autocorrelation simulation curve" } ] } ], "subcaption": [], "note": [], "graphics": [ { "print": "http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24623325&type=", "small": "http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24623330&type=", "big": "http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24623327&type=" } ] } } ] }, { "name": "sec", "data": [ { "name": "sectitle", "data": { "label": [ { "name": "text", "data": "4.2" } ], "title": [ { "name": "text", "data": "主放大级仿真结果分析" } ], "level": "2", "id": "s4b" } }, { "name": "p", "data": [ { "name": "text", "data": "主放大器的主要功能是实现功率放大，因而采用双向泵浦的方式，使掺铒光纤中的铒离子能够充分地被激发，噪声系数小。主放大的模拟过程中，群速度色散为正，仍然是改变器件尾纤长度、增益光纤长度、小信号增益系数这些参数，来研究光纤放大器的色散、非线性效应、增益对输出脉冲和光谱的影响。主放大级所用的光纤参数与预放大级相同。" } ] }, { "name": "p", "data": [ { "name": "text", "data": "由于自相位调制(SPM)、色散效应的影响会引起光谱展宽。在主放大过程中，要选择最佳增益光纤长度，要求既能保证光谱展宽，又不会发生严重的畸变。" }, { "name": "xref", "data": { "text": "图7", "type": "fig", "rid": "F7", "data": [ { "name": "text", "data": "图7" } ] } }, { "name": "text", "data": "、" }, { "name": "xref", "data": { "text": "8", "type": "fig", "rid": "F8", "data": [ { "name": "text", "data": "8" } ] } }, { "name": "text", "data": "所示是基于预放大的输出结果，模拟在不同长度的增益光纤中脉冲及光谱的演化过程。随着增益光纤长度不断增加，脉冲及光谱均不断被展宽，脉冲顶部逐渐变得平缓。由于非线性效应的影响，这时的脉冲具有上啁啾，上啁啾脉冲的前沿频率低于后沿，而高频分量集中于脉冲的后部，因而就会将光谱展得越来越宽。" } ] }, { "name": "fig", "data": { "id": "F7", "caption": [ { "lang": "zh", "label": [ { "name": "text", "data": "图7" } ], "title": [ { "name": "text", "data": "不同增益光纤长度下主放大级的脉冲形状" } ] }, { "lang": "en", "label": [ { "name": "text", "data": "Fig.7" } ], "title": [ { "name": "text", "data": "Pulse shape of the main amplifier stage at different gain fiber lengths" } ] } ], "subcaption": [], "note": [], "graphics": [ { "print": "http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24623334&type=", "small": "http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24623338&type=", "big": "http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24623337&type=" } ] } }, { "name": "fig", "data": { "id": "F8", "caption": [ { "lang": "zh", "label": [ { "name": "text", "data": "图8" } ], "title": [ { "name": "text", "data": "不同增益光纤长度下主放大级的光谱形状" } ] }, { "lang": "en", "label": [ { "name": "text", "data": "Fig.8" } ], "title": [ { "name": "text", "data": "Spectral shape of the main amplifier stage at different gains fiber lengths" } ] } ], "subcaption": [], "note": [], "graphics": [ { "print": "http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24623341&type=", "small": "http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24623350&type=", "big": "http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24623346&type=" } ] } }, { "name": "p", "data": [ { "name": "text", "data": "增益光纤越长会累积越多的非线性相移，而使光谱展宽" }, { "name": "sup", "data": [ { "name": "text", "data": "[" }, { "name": "xref", "data": { "text": "13", "type": "bibr", "rid": "R13", "data": [ { "name": "text", "data": "13" } ] } }, { "name": "text", "data": "]" } ] }, { "name": "text", "data": "。但在传输过程中，由于有限增益带宽的限制，随着传输距离逐渐变长，光谱宽度将超过增益谱宽度，则脉冲光谱各部分获得的增益不均，脉冲的自相似特性将无法保持" }, { "name": "sup", "data": [ { "name": "text", "data": "[" }, { "name": "blockXref", "data": { "data": [ { "name": "xref", "data": { "text": "14", "type": "bibr", "rid": "R14", "data": [ { "name": "text", "data": "14" } ] } }, { "name": "text", "data": "-" }, { "name": "xref", "data": { "text": "15", "type": "bibr", "rid": "R15", "data": [ { "name": "text", "data": "15" } ] } } ], "rid": [ "R14", "R15" ], "text": "14-15", "type": "bibr" } }, { "name": "text", "data": "]" } ] }, { "name": "text", "data": "。结合" }, { "name": "xref", "data": { "text": "图7", "type": "fig", "rid": "F7", "data": [ { "name": "text", "data": "图7" } ] } }, { "name": "text", "data": "、" }, { "name": "xref", "data": { "text": "8", "type": "fig", "rid": "F8", "data": [ { "name": "text", "data": "8" } ] } }, { "name": "text", "data": "分析，随着铒纤长度的不断增加，脉冲以及光谱都不断地被展宽，这符合我们此前的分析。但铒纤长度达到2.0 m时，脉冲及光谱形状的前、后沿发生明显畸变，底端已经不呈抛物线型，而且顶端也不如1.5 m时平滑。另外，群速度失配会引起波长不同的光在光纤内传输时速度不同。根据时间带宽积理论，光谱的展宽程度会影响脉冲压缩的结果。脉冲越窄，光谱越宽，受色散效应影响越严重。高阶色散会引入非线性啁啾，导致脉冲在展宽时发生畸变，而非线性啁啾无法得到补偿，脉冲就会出现部分不能压缩的基座。" } ] }, { "name": "p", "data": [ { "name": "text", "data": "模拟结果总结：主放大级的铒纤长度由0.5 m增加至2.0 m时，脉冲宽度由1.8 ps展宽至3.4 ps，光谱宽度由16 nm展宽至33 nm。在增益光纤长度为1.5 m时，光谱展宽至约26 nm，足以将脉冲宽度压窄；而在增益光纤长度为2.0 m时，脉冲及光谱形状均发生畸变，不如1.5 m时良好。" }, { "name": "xref", "data": { "text": "图9", "type": "fig", "rid": "F9", "data": [ { "name": "text", "data": "图9" } ] } }, { "name": "text", "data": "、" }, { "name": "xref", "data": { "text": "10", "type": "fig", "rid": "F10", "data": [ { "name": "text", "data": "10" } ] } }, { "name": "text", "data": "所示，此时输出功率由30 mW增大到125 mW，脉冲宽度被展宽至3.4 ps。脉冲及光谱宽度的变化是随着平均输出功率的增加而展宽的。但在输出功率放大到125 mW时，脉冲底端前、后沿发生畸变，光谱顶部畸变明显。结合后续模拟发现，若将主放大输出功率定为125 mW，脉冲压缩结果也没有放大到102 mW时好。" } ] }, { "name": "fig", "data": { "id": "F9", "caption": [ { "lang": "zh", "label": [ { "name": "text", "data": "图9" } ], "title": [ { "name": "text", "data": "增益光纤长度为1.5 m时主放大级在不同增益下的脉冲变化" } ] }, { "lang": "en", "label": [ { "name": "text", "data": "Fig.9" } ], "title": [ { "name": "text", "data": "The pulse variation of the main amplifier stage at different gains when the gain fiber length is 1.5 m" } ] } ], "subcaption": [], "note": [], "graphics": [ { "print": "http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24623353&type=", "small": "http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24623361&type=", "big": "http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24623357&type=" } ] } }, { "name": "fig", "data": { "id": "F10", "caption": [ { "lang": "zh", "label": [ { "name": "text", "data": "图10" } ], "title": [ { "name": "text", "data": "增益光纤长度为1.5 m时主放大级在不同增益下的光谱变化" } ] }, { "lang": "en", "label": [ { "name": "text", "data": "Fig.10" } ], "title": [ { "name": "text", "data": "Spectral variation of the main amplifier stage at different gains when the gain fiber length is 1.5 m" } ] } ], "subcaption": [], "note": [], "graphics": [ { "print": "http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24623365&type=", "small": "http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24623371&type=", "big": "http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24623366&type=" } ] } }, { "name": "p", "data": [ { "name": "text", "data": "主放大器的目的是实现功率放大和光谱展宽，以便在后面的压缩过程中得到窄脉冲宽度和高峰值功率。理论上，越长的增益光纤越能够获得宽光谱，压缩后可以得到窄脉宽，不过也会带来严重的畸变。但由于有限增益带宽的限制以及高阶色散的影响，并结合后续压缩模拟发现，过长的光纤或过高的增益均会导致光谱前、后沿及顶部发生畸变，压缩结果变差" }, { "name": "sup", "data": [ { "name": "text", "data": "[" }, { "name": "xref", "data": { "text": "13", "type": "bibr", "rid": "R13", "data": [ { "name": "text", "data": "13" } ] } }, { "name": "text", "data": "]" } ] }, { "name": "text", "data": "。因此，主放大级采用1.5 m长的铒纤，放大到102 mW，脉宽放大至2.8 ps。" }, { "name": "xref", "data": { "text": "图11", "type": "fig", "rid": "F11", "data": [ { "name": "text", "data": "图11" } ] } }, { "name": "text", "data": "为放大功率为102 mW时的归一化脉冲自相关曲线。对曲线进行了抛物线拟合后，可见经主放大级后脉冲仍然保持类抛物线形状。" } ] }, { "name": "fig", "data": { "id": "F11", "caption": [ { "lang": "zh", "label": [ { "name": "text", "data": "图11" } ], "title": [ { "name": "text", "data": "主放大自相关模拟曲线" } ] }, { "lang": "en", "label": [ { "name": "text", "data": "Fig.11" } ], "title": [ { "name": "text", "data": "Main amplified autocorrelation simulation curve" } ] } ], "subcaption": [], "note": [], "graphics": [ { "print": "http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24623374&type=", "small": "http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24623380&type=", "big": "http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24623377&type=" } ] } } ] }, { "name": "sec", "data": [ { "name": "sectitle", "data": { "label": [ { "name": "text", "data": "4.3" } ], "title": [ { "name": "text", "data": "自相似脉冲压缩仿真结果分析" } ], "level": "2", "id": "s4c" } }, { "name": "p", "data": [ { "name": "text", "data": "在脉冲功率放大、光谱展宽后，需要补偿在放大过程中积累的色散，我们使用具有负色散的普通单模光纤作为脉冲压缩器，光纤型号为SMF-28e。" } ] }, { "name": "p", "data": [ { "name": "text", "data": "在压缩过程中，将压缩光纤SMF-28e的长度从1 m开始逐渐加长至10 m，发现长度在4.4 m时得到了最窄的脉冲宽度。" }, { "name": "xref", "data": { "text": "图12", "type": "fig", "rid": "F12", "data": [ { "name": "text", "data": "图12" } ] } }, { "name": "text", "data": "给出了压缩光纤4~5 m脉冲自相关演化图，在4.4 m时，脉冲宽度由放大后的2.8 ps压缩至最窄，脉冲形状最好，峰值功率最高。" }, { "name": "xref", "data": { "text": "图13", "type": "fig", "rid": "F13", "data": [ { "name": "text", "data": "图13" } ] } }, { "name": "text", "data": "给出了此时脉冲的自相关图，脉冲宽度为53 fs，由于高阶色散带来的非线性啁啾导致了较小的基座。" } ] }, { "name": "fig", "data": { "id": "F12", "caption": [ { "lang": "zh", "label": [ { "name": "text", "data": "图12" } ], "title": [ { "name": "text", "data": "压缩脉冲自相关模拟图" } ] }, { "lang": "en", "label": [ { "name": "text", "data": "Fig.12" } ], "title": [ { "name": "text", "data": "The autocorrelation simulation diagram of compressed pulse" } ] } ], "subcaption": [], "note": [], "graphics": [ { "print": "http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24623382&type=", "small": "http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24623388&type=", "big": "http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24623385&type=" } ] } }, { "name": "fig", "data": { "id": "F13", "caption": [ { "lang": "zh", "label": [ { "name": "text", "data": "图13" } ], "title": [ { "name": "text", "data": "经4.4 m单模光纤压缩后的脉冲自相关曲线" } ] }, { "lang": "en", "label": [ { "name": "text", "data": "Fig.13" } ], "title": [ { "name": "text", "data": "Pulse autocorrelation curve after compression by 4.4 m single-mode fiber" } ] } ], "subcaption": [], "note": [], "graphics": [ { "print": "http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24623391&type=", "small": "http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24623397&type=", "big": "http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24623394&type=" } ] } } ] } ] }, { "name": "sec", "data": [ { "name": "sectitle", "data": { "label": [ { "name": "text", "data": "5" } ], "title": [ { "name": "text", "data": "结论" } ], "level": "1", "id": "s5" } }, { "name": "p", "data": [ { "name": "text", "data": "本文通过仿真模拟系统地讨论了掺铒光纤放大器在正色散区进行自相似放大过程。首先，讨论非线性薛定谔方程的渐近解，分析获得自相似脉冲的条件以及自相似放大脉冲的特点。随即进行数值模拟，探讨飞秒种子脉冲在经由不同长度增益光纤以及放大到不同的功率时，放大脉冲及光谱的变化。模拟的设计思路是先用正色散的掺铒增益光纤对信号光脉冲进行预整形，使其形状由双曲正割型变为抛物线型。经过二次放大实现功率放大和光谱展宽，以期在后续的脉冲压缩中获得更高的输出功率和更窄的脉冲宽度。由于自相似放大过程累积的啁啾是线性的，可以用线性的色散器件补偿，因而我们选用了带有负色散的普通单模光纤进行脉冲压缩模拟。最终获得平均输出功率102 mW、脉冲宽度53 fs、峰值功率为44.8 kW的高功率超短脉冲输出。" } ] }, { "name": "p", "data": [ { "name": "text", "data": "本文专家审稿意见及作者回复内容的下载地址：http://cjl.lightpublishing.cn/thesisDetails#10.37188/CJL.20210319." } ] } ] } ], "footnote": [], "reflist": { "title": [ { "name": "text", "data": 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