【《空芯微结构光纤光流控微腔激光器的理论基础综述》8300字】

空芯微结构光纤光流控微腔激光器的理论基础综述目录TOC\o"1-3"\h\u23454空芯微结构光纤光流控微腔激光器的理论基础综述 130323第一节空芯微结构光纤的模式特性 125703第二节空芯微结构光纤微腔理论 514052第三节光流控激光理论 890392.3.1激光能级理论 8183252.3.2光学微谐振腔对自发辐射的影响 9空芯微结构光纤光流控微腔激光器的主要特征是采用空芯微结构光纤作为光学微腔实现激光输出。本章就空芯微结构光纤光流控微腔激光器所涉及的理论基础进行简单介绍，具体包括空芯微结构光纤的模式特性、空芯微结构光纤微腔理论及光流控激光理论。通过分析空芯微结构光纤的模式特性，可得知空芯微结构光纤中纤芯及薄壁石英环的模式分布；分析空芯微结构光纤微腔的工作原理、谐振条件、微腔品质因子等理论，为设计和搭建基于空芯微结构光纤的光流控微腔激光器奠定了理论基础；在光流控激光理论中从激光的角度分析光微流激光的产生原理，通过介绍激光能级理论和微腔对自发辐射的影响，有利于理解微腔激光器的优势。空芯微结构光纤的模式特性空芯微结构光纤（hollow-coremicrostructuredopticalfiber，HC-MOFs），也叫空芯光子晶体光纤，与传统光纤或固芯微结构光纤最大的区别在于将光限制在空气中传输而非在固体材料中传输。空芯微结构光纤包括空芯光子带隙微结构光纤和空芯反谐振微结构光纤，前者通过光子带隙效应将光限制在空气纤芯中传输，后者通过纤芯周围石英薄层的反谐振效应将光限制在空气纤芯中。从其研究及发展历史来看，相比于空芯反谐振微结构光纤，空芯光子带隙微结构光纤被更早的研究。空芯微结构光纤与光子晶体密切相关，自科学家S.JohnADDINEN.CITE<EndNote><Cite><Author>John</Author><Year>1987</Year><RecNum>239</RecNum><DisplayText><styleface="superscript">[190]</style></DisplayText><record><rec-number>239</rec-number><foreign-keys><keyapp="EN"db-id="fsp2sprfses59ge9tf3xezao9xp909p92tdw"timestamp="1613871384">239</key></foreign-keys><ref-typename="JournalArticle">17</ref-type><contributors><authors><author>John,Sajeev</author></authors></contributors><titles><title>Stronglocalizationofphotonsincertaindisordereddielectricsuperlattices</title><secondary-title>Physicalreviewletters</secondary-title></titles><periodical><full-title>Physicalreviewletters</full-title></periodical><pages>2486</pages><volume>58</volume><number>23</number><dates><year>1987</year></dates><urls></urls></record></Cite></EndNote>[\o"John,1987#239"190]和E.YablonovitchADDINEN.CITE<EndNote><Cite><Author>Yablonovitch</Author><Year>1987</Year><RecNum>238</RecNum><DisplayText><styleface="superscript">[191]</style></DisplayText><record><rec-number>238</rec-number><foreign-keys><keyapp="EN"db-id="fsp2sprfses59ge9tf3xezao9xp909p92tdw"timestamp="1613871225">238</key></foreign-keys><ref-typename="JournalArticle">17</ref-type><contributors><authors><author>Yablonovitch,Eli</author></authors></contributors><titles><title>Inhibitedspontaneousemissioninsolid-statephysicsandelectronics</title><secondary-title>Physicalreviewletters</secondary-title></titles><periodical><full-title>Physicalreviewletters</full-title></periodical><pages>2059</pages><volume>58</volume><number>20</number><dates><year>1987</year></dates><urls></urls></record></Cite></EndNote>[\o"Yablonovitch,1987#238"191]在1987年讨论光子局域及研究抑制自发辐射时各自提出光子晶体概念后，学术界围绕光子晶体开展了大量的研究工作。介电常数在光波长量级呈周期性分布的光子晶体，其最根本的特征是存在光子禁带，与半导体的禁带相类似，当光入射到光子晶体中时，特定波段的光会呈指数衰减而无法传播，从而在频谱上形成带隙，当光子晶体的周期性结构存在缺陷时，与缺陷态同频率的光被限制在缺陷处沿特定方向传播，这种光子局域效应为科研人员研究导光机理提供了新的思路，光子晶体结构也因此被尝试引入到光纤设计中，便出现了光子带隙型微结构光纤ADDINEN.CITEADDINEN.CITE.DATA[\o"Roberts,2005#15"4,\o"Cregan,1999#74"192-198]。典型的空芯光子带隙型微结构光纤结构图见2.1（a-c），通常空芯光子带隙光纤需要大于90%的空气填充比，且光纤包层需要严格的周期性结构，使得对光纤的制备工艺要求比较高，限制了空芯光子带隙光纤性能的提升。且空芯光子带隙光纤的带宽通常较窄，其损耗虽不断地被降低，但和最初光纤损耗的预测（7×10-4dB/km）相比，仍有很大差距。为进一步提升空芯微结构光纤的性能，人们开始将目光转向空芯反谐振微结构光纤。最早被报道的空芯反谐振微结构光纤是由巴斯大学的F.Benabid等人在2002年拉制的Kagomé空芯微结构光纤ADDINEN.CITE<EndNote><Cite><Author>Benabid</Author><Year>2002</Year><RecNum>233</RecNum><DisplayText><styleface="superscript">[199]</style></DisplayText><record><rec-number>233</rec-number><foreign-keys><keyapp="EN"db-id="fsp2sprfses59ge9tf3xezao9xp909p92tdw"timestamp="1613802834">233</key></foreign-keys><ref-typename="JournalArticle">17</ref-type><contributors><authors><author>Benabid,F.</author><author>Knight,J.C.</author><author>Antonopoulos,G.</author><author>Russell,P.St.J.</author></authors></contributors><titles><title>StimulatedRamanScatteringinHydrogen-FilledHollow-CorePhotonicCrystalFiber</title><secondary-title>Science</secondary-title></titles><periodical><full-title>Science</full-title></periodical><pages>399-402</pages><volume>298</volume><number>5592</number><dates><year>2002</year></dates><urls><related-urls><url>/content/sci/298/5592/399.full.pdf</url></related-urls></urls><electronic-resource-num>10.1126/science.1076408</electronic-resource-num></record></Cite></EndNote>[\o"Benabid,2002#233"199]，该光纤的包层栅格结构呈“六芒星”形排列，三组薄壁石英管以120º角交叉排列。虽然该光纤的损耗稍高于空芯光子带隙光纤的损耗，但它具有较多的传输带以及更宽的光谱覆盖范围，吸引了人们的关注。如图2.2（a）所示，巴斯大学的F.Couny等人在2006年拉制了大间距Kagomé空芯微结构光纤ADDINEN.CITE<EndNote><Cite><Author>Couny</Author><Year>2006</Year><RecNum>258</RecNum><DisplayText><styleface="superscript">[5]</style></DisplayText><record><rec-number>258</rec-number><foreign-keys><keyapp="EN"db-id="fsp2sprfses59ge9tf3xezao9xp909p92tdw"timestamp="1614072819">258</key></foreign-keys><ref-typename="JournalArticle">17</ref-type><contributors><authors><author>Couny,F.</author><author>Benabid,F.</author><author>Light,P.S.</author></authors></contributors><titles><title>Large-pitchkagome-structuredhollow-corephotoniccrystalfiber</title><secondary-title>OpticsLetters</secondary-title><alt-title>Opt.Lett.</alt-title></titles><periodical><full-title>OpticsLetters</full-title><abbr-1>Opt.Lett.</abbr-1></periodical><alt-periodical><full-title>OpticsLetters</full-title><abbr-1>Opt.Lett.</abbr-1></alt-periodical><pages>3574-3576</pages><volume>31</volume><number>24</number><keywords><keyword>Fibercharacterization</keyword><keyword>Fiberdesignandfabrication</keyword><keyword>Fiberoptics</keyword><keyword>Electromagneticallyinducedtransparency</keyword><keyword>Highharmonicgeneration</keyword><keyword>Hollowcorefibers</keyword><keyword>Largepitchfibers</keyword><keyword>Photonicbandgapfibers</keyword><keyword>Quantumoptics</keyword></keywords><dates><year>2006</year><pub-dates><date>2006/12/15</date></pub-dates></dates><publisher>OSA</publisher><urls><related-urls><url>/abstract.cfm?URI=ol-31-24-3574</url></related-urls></urls><electronic-resource-num>10.1364/OL.31.003574</electronic-resource-num></record></Cite></EndNote>[\o"Couny,2006#258"5]，进一步提升了Kagomé空芯微结构光纤的带宽性能。为了进一步降低该类光纤的损耗，巴斯大学的Y.Y.Wang等人在2011年提出了下摆线型Kagomé空芯微结构光纤ADDINEN.CITE<EndNote><Cite><Author>Wang</Author><Year>2011</Year><RecNum>261</RecNum><DisplayText><styleface="superscript">[6]</style></DisplayText><record><rec-number>261</rec-number><foreign-keys><keyapp="EN"db-id="fsp2sprfses59ge9tf3xezao9xp909p92tdw"timestamp="1614077267">261</key></foreign-keys><ref-typename="JournalArticle">17</ref-type><contributors><authors><author>Wang,Y.Y.</author><author>Wheeler,N.V.</author><author>Couny,F.</author><author>Roberts,P.J.</author><author>Benabid,F.</author></authors></contributors><titles><title>Lowlossbroadbandtransmissioninhypocycloid-coreKagomehollow-corephotoniccrystalfiber</title><secondary-title>OpticsLetters</secondary-title><alt-title>Opt.Lett.</alt-title></titles><periodical><full-title>OpticsLetters</full-title><abbr-1>Opt.Lett.</abbr-1></periodical><alt-periodical><full-title>OpticsLetters</full-title><abbr-1>Opt.Lett.</abbr-1></alt-periodical><pages>669-671</pages><volume>36</volume><number>5</number><keywords><keyword>Fiberdesignandfabrication</keyword><keyword>Photoniccrystalfibers</keyword><keyword>Attenuation</keyword><keyword>Fiberfabrication</keyword><keyword>Finiteelementmethod</keyword><keyword>Hollowcorefibers</keyword><keyword>Phasematching</keyword><keyword>Whisperinggallerymodes</keyword></keywords><dates><year>2011</year><pub-dates><date>2011/03/01</date></pub-dates></dates><publisher>OSA</publisher><urls><related-urls><url>/abstract.cfm?URI=ol-36-5-669</url></related-urls></urls><electronic-resource-num>10.1364/OL.36.000669</electronic-resource-num></record></Cite></EndNote>[\o"Wang,2011#261"6]，如图2.2（b）所示。对比前述两种Kagomé空芯微结构光纤，它们的主要区别在于紧邻空气纤芯的石英壁一个为正曲率的六边形，一个为负曲率的下摆线型，且负曲率结构更有利于降低空芯微结构光纤的损耗。为解决这两种Kagomé空芯微结构光纤对拉制工艺要求高的问题，人们不断地研究并发现，负曲率空芯微结构光纤的包层结构可以进一步简化成只有一层空气孔的结构，如图2.2（c）所示，该空芯反谐振微结构光纤仍然可以较好地实现光的低损耗传导ADDINEN.CITE<EndNote><Cite><Author>Kolyadin</Author><Year>2013</Year><RecNum>260</RecNum><DisplayText><styleface="superscript">[8]</style></DisplayText><record><rec-number>260</rec-number><foreign-keys><keyapp="EN"db-id="fsp2sprfses59ge9tf3xezao9xp909p92tdw"timestamp="1614073695">260</key></foreign-keys><ref-typename="JournalArticle">17</ref-type><contributors><authors><author>Kolyadin,AntonN.</author><author>Kosolapov,AlexeyF.</author><author>Pryamikov,AndreyD.</author><author>Biriukov,AlexanderS.</author><author>Plotnichenko,VictorG.</author><author>Dianov,EvgenyM.</author></authors></contributors><titles><title>Lighttransmissioninnegativecurvaturehollowcorefiberinextremelyhighmateriallossregion</title><secondary-title>OpticsExpress</secondary-title></titles><periodical><full-title>OpticsExpress</full-title></periodical><pages>9514-9519</pages><volume>21</volume><number>8</number><dates><year>2013</year><pub-dates><date>Apr22</date></pub-dates></dates><isbn>1094-4087</isbn><accession-num>WOS:000318151600033</accession-num><urls><related-urls><url><GotoISI>://WOS:000318151600033</url></related-urls></urls><electronic-resource-num>10.1364/oe.21.009514</electronic-resource-num></record></Cite></EndNote>[\o"Kolyadin,2013#260"8]。相比空芯光纤带隙微结构光纤，负曲率空芯反谐振微结构光纤因具有：包层结构简单，相对而言更易于制备；光能量更集中在空气纤芯中；更宽的传输带宽；对制备材料要求低等独特优点，是近些年空芯微结构光纤的研究热点ADDINEN.CITEADDINEN.CITE.DATA[\o"Pryamikov,2011#262"7,\o"Belardi,2014#264"200-204]。图2.1（a）第一根空气导光的空芯光子带隙光纤ADDINEN.CITE<EndNote><Cite><Author>Cregan</Author><Year>1999</Year><RecNum>10</RecNum><DisplayText><styleface="superscript">[192]</style></DisplayText><record><rec-number>10</rec-number><foreign-keys><keyapp="EN"db-id="wtrfdstsp200t2e9t0nvdvrfrdsrde20e5rp"timestamp="1613883078">10</key></foreign-keys><ref-typename="JournalArticle">17</ref-type><contributors><authors><author>Cregan,R.F.</author><author>Mangan,B.J.</author><author>Knight,J.C.</author><author>Birks,T.A.</author><author>Roberts,P.J.</author><author>Allan,D.C.</author></authors></contributors><titles><title>Single-ModePhotonicBandGapGuidanceofLightinAir</title><secondary-title>Science</secondary-title></titles><pages>1537-9</pages><volume>285</volume><number>5433</number><dates><year>1999</year></dates><urls></urls></record></Cite></EndNote>[\o"Cregan,1999#74"192]；（b）损耗降至13dB/km的7芯-空芯光子带隙光纤ADDINEN.CITE<EndNote><Cite><Author>Smith</Author><Year>2003</Year><RecNum>12</RecNum><DisplayText><styleface="superscript">[193]</style></DisplayText><record><rec-number>12</rec-number><foreign-keys><keyapp="EN"db-id="wtrfdstsp200t2e9t0nvdvrfrdsrde20e5rp"timestamp="1613883078">12</key></foreign-keys><ref-typename="JournalArticle">17</ref-type><contributors><authors><author>Smith,CharleneM,</author><author>Natesan,Venkataraman</author><author>Gallagher,MichaelT,</author><author>Dirk,Müller</author><author>West,JamesA,</author><author>Borrelli,NicholasF,</author><author>Allan,DouglasC,</author><author>Koch,KarlW,</author></authors></contributors><titles><title>Low-losshollow-coresilica/airphotonicbandgapfibre</title><secondary-title>Nature</secondary-title></titles><pages>657-9</pages><volume>424</volume><number>6949</number><dates><year>2003</year></dates><urls></urls></record></Cite></EndNote>[\o"Smith,2003#13"193]；（c）损耗降至1.2dB/km的19芯-空芯光子带隙光纤ADDINEN.CITE<EndNote><Cite><Author>Roberts</Author><Year>2005</Year><RecNum>14</RecNum><DisplayText><styleface="superscript">[4]</style></DisplayText><record><rec-number>14</rec-number><foreign-keys><keyapp="EN"db-id="wtrfdstsp200t2e9t0nvdvrfrdsrde20e5rp"timestamp="1613883078">14</key></foreign-keys><ref-typename="JournalArticle">17</ref-type><contributors><authors><author>Roberts,P,</author><author>Couny,F,</author><author>Sabert,H,</author><author>Mangan,B,</author><author>Williams,D,</author><author>Farr,L,</author><author>Mason,M,</author><author>Tomlinson,A,</author><author>Birks,T,</author><author>Knight,J,</author></authors></contributors><titles><title>Ultimatelowlossofhollow-corephotoniccrystalfibres</title><secondary-title>OpticsExpress</secondary-title></titles><pages>236-44</pages><volume>13</volume><number>1</number><dates><year>2005</year></dates><urls></urls></record></Cite></EndNote>[\o"Roberts,2005#15"4]图2.2（a）Kagomé空芯微结构光纤ADDINEN.CITE<EndNote><Cite><Author>Couny</Author><Year>2006</Year><RecNum>258</RecNum><DisplayText><styleface="superscript">[5]</style></DisplayText><record><rec-number>258</rec-number><foreign-keys><keyapp="EN"db-id="fsp2sprfses59ge9tf3xezao9xp909p92tdw"timestamp="1614072819">258</key></foreign-keys><ref-typename="JournalArticle">17</ref-type><contributors><authors><author>Couny,F.</author><author>Benabid,F.</author><author>Light,P.S.</author></authors></contributors><titles><title>Large-pitchkagome-structuredhollow-corephotoniccrystalfiber</title><secondary-title>OpticsLetters</secondary-title><alt-title>Opt.Lett.</alt-title></titles><periodical><full-title>OpticsLetters</full-title><abbr-1>Opt.Lett.</abbr-1></periodical><alt-periodical><full-title>OpticsLetters</full-title><abbr-1>Opt.Lett.</abbr-1></alt-periodical><pages>3574-3576</pages><volume>31</volume><number>24</number><keywords><keyword>Fibercharacterization</keyword><keyword>Fiberdesignandfabrication</keyword><keyword>Fiberoptics</keyword><keyword>Electromagneticallyinducedtransparency</keyword><keyword>Highharmonicgeneration</keyword><keyword>Hollowcorefibers</keyword><keyword>Largepitchfibers</keyword><keyword>Photonicbandgapfibers</keyword><keyword>Quantumoptics</keyword></keywords><dates><year>2006</year><pub-dates><date>2006/12/15</date></pub-dates></dates><publisher>OSA</publisher><urls><related-urls><url>/abstract.cfm?URI=ol-31-24-3574</url></related-urls></urls><electronic-resource-num>10.1364/OL.31.003574</electronic-resource-num></record></Cite></EndNote>[\o"Couny,2006#258"5]；（b）下摆线型Kagomé空芯微结构光纤ADDINEN.CITE<EndNote><Cite><Author>Wang</Author><Year>2011</Year><RecNum>261</RecNum><DisplayText><styleface="superscript">[6]</style></DisplayText><record><rec-number>261</rec-number><foreign-keys><keyapp="EN"db-id="fsp2sprfses59ge9tf3xezao9xp909p92tdw"timestamp="1614077267">261</key></foreign-keys><ref-typename="JournalArticle">17</ref-type><contributors><authors><author>Wang,Y.Y.</author><author>Wheeler,N.V.</author><author>Couny,F.</author><author>Roberts,P.J.</author><author>Benabid,F.</author></authors></contributors><titles><title>Lowlossbroadbandtransmissioninhypocycloid-coreKagomehollow-corephotoniccrystalfiber</title><secondary-title>OpticsLetters</secondary-title><alt-title>Opt.Lett.</alt-title></titles><periodical><full-title>OpticsLetters</full-title><abbr-1>Opt.Lett.</abbr-1></periodical><alt-periodical><full-title>OpticsLetters</full-title><abbr-1>Opt.Lett.</abbr-1></alt-periodical><pages>669-671</pages><volume>36</volume><number>5</number><keywords><keyword>Fiberdesignandfabrication</keyword><keyword>Photoniccrystalfibers</keyword><keyword>Attenuation</keyword><keyword>Fiberfabrication</keyword><keyword>Finiteelementmethod</keyword><keyword>Hollowcorefibers</keyword><keyword>Phasematching</keyword><keyword>Whisperinggallerymodes</keyword></keywords><dates><year>2011</year><pub-dates><date>2011/03/01</date></pub-dates></dates><publisher>OSA</publisher><urls><related-urls><url>/abstract.cfm?URI=ol-36-5-669</url></related-urls></urls><electronic-resource-num>10.1364/OL.36.000669</electronic-resource-num></record></Cite></EndNote>[\o"Wang,2011#261"6]；（c）负曲率空芯反谐振微结构光纤ADDINEN.CITE<EndNote><Cite><Author>Kolyadin</Author><Year>2013</Year><RecNum>260</RecNum><DisplayText><styleface="superscript">[8]</style></DisplayText><record><rec-number>260</rec-number><foreign-keys><keyapp="EN"db-id="fsp2sprfses59ge9tf3xezao9xp909p92tdw"timestamp="1614073695">260</key></foreign-keys><ref-typename="JournalArticle">17</ref-type><contributors><authors><author>Kolyadin,AntonN.</author><author>Kosolapov,AlexeyF.</author><author>Pryamikov,AndreyD.</author><author>Biriukov,AlexanderS.</author><author>Plotnichenko,VictorG.</author><author>Dianov,EvgenyM.</author></authors></contributors><titles><title>Lighttransmissioninnegativecurvaturehollowcorefiberinextremelyhighmateriallossregion</title><secondary-title>OpticsExpress</secondary-title></titles><periodical><full-title>OpticsExpress</full-title></periodical><pages>9514-9519</pages><volume>21</volume><number>8</number><dates><year>2013</year><pub-dates><date>Apr22</date></pub-dates></dates><isbn>1094-4087</isbn><accession-num>WOS:000318151600033</accession-num><urls><related-urls><url><GotoISI>://WOS:000318151600033</url></related-urls></urls><electronic-resource-num>10.1364/oe.21.009514</electronic-resource-num></record></Cite></EndNote>[\o"Kolyadin,2013#260"8]与普通光纤相比，空芯微结构光纤，不管是空芯光子带隙微结构光纤还是空芯反谐振微结构光纤，具有设计自由度高的截面结构，表现出丰富的模式特性。由于空芯微结构光纤的特殊性，使得在求解其模式特性时无法得到解析解，也不能直接利用传统光纤的模式分析方法。因此，只能采用全矢量数值模拟方法对微结构光纤进行模式分析。目前，比较常用的数值模拟方法有：有限元法ADDINEN.CITE<EndNote><Cite><Author>Cucinotta</Author><Year>2002</Year><RecNum>329</RecNum><DisplayText><styleface="superscript">[205]</style></DisplayText><record><rec-number>329</rec-number><foreign-keys><keyapp="EN"db-id="fsp2sprfses59ge9tf3xezao9xp909p92tdw"timestamp="1614777313">329</key></foreign-keys><ref-typename="JournalArticle">17</ref-type><contributors><authors><author>A.Cucinotta</author><author>S.Selleri</author><author>L.Vincetti</author><author>M.Zoboli</author></authors></contributors><titles><title>Holeyfiberanalysisthroughthefinite-elementmethod</title><secondary-title>IEEEPhotonicsTechnologyLetters</secondary-title></titles><periodical><full-title>IEEEPhotonicsTechnologyLetters</full-title></periodical><pages>1530-1532</pages><volume>14</volume><number>11</number><keywords><keyword>photonicbandgap</keyword><keyword>opticalfibretheory</keyword><keyword>finiteelementanalysis</keyword><keyword>opticalfibredispersion</keyword><keyword>opticalfibrepolarisation</keyword><keyword>vectors</keyword><keyword>geometry</keyword><keyword>holeyfiberanalysis</keyword><keyword>finite-elementmethod</keyword><keyword>complexholegeometry</keyword><keyword>numericalsimulator</keyword><keyword>modalanalysis</keyword><keyword>photoniccrystalfibers</keyword><keyword>polarizationproperties</keyword><keyword>dispersionproperties</keyword><keyword>fullvectorfielddistribution</keyword><keyword>fundamentalmode</keyword><keyword>Holeyfibers</keyword><keyword>Finiteelementmethods</keyword><keyword>Opticalfiberpolarization</keyword><keyword>Hafnium</keyword><keyword>Polarizationmodedispersion</keyword><keyword>Shape</keyword><keyword>Numericalsimulation</keyword><keyword>Siliconcompounds</keyword></keywords><dates><year>2002</year></dates><isbn>1941-0174</isbn><urls></urls><electronic-resource-num>10.1109/LPT.2002.803375</electronic-resource-num></record></Cite></EndNote>[\o"Cucinotta,2002#329"205]、光束传播法ADDINEN.CITE<EndNote><Cite><Author>Saitoh</Author><Year>2002</Year><RecNum>163</RecNum><DisplayText><styleface="superscript">[206]</style></DisplayText><record><rec-number>163</rec-number><foreign-keys><keyapp="EN"db-id="dtsfaeex9st5axets06paxfaefse0fzrs95f">163</key></foreign-keys><ref-typename="JournalArticle">17</ref-type><contributors><authors><author>Saitoh,K.</author><author>Koshiba,M.</author></authors></contributors><titles><title>Full-vectorialimaginary-distancebeampropagationmethodbasedonafiniteelementscheme:Applicationtophotoniccrystalfibers</title><secondary-title>IEEEJournalofQuantumElectronics</secondary-title></titles><periodical><full-title>IEEEJournalofQuantumElectronics</full-title></periodical><pages>927-33</pages><volume>38</volume><number>7</number><dates><year>2002</year></dates><urls></urls></record></Cite></EndNote>[\o"Saitoh,2002#163"206]、有限时域差分法ADDINEN.CITE<EndNote><Cite><Author>Min</Author><Year>2001</Year><RecNum>168</RecNum><DisplayText><styleface="superscript">[207]</style></DisplayText><record><rec-number>168</rec-number><foreign-keys><keyapp="EN"db-id="dtsfaeex9st5axets06paxfaefse0fzrs95f">168</key></foreign-keys><ref-typename="JournalArticle">17</ref-type><contributors><authors><author>Min,Qiu</author></authors></contributors><titles><title>Analysisofguidedmodesinphotoniccrystalfibersusingthefinite‐differencetime‐domainmethod</title><secondary-title>Microwave&OpticalTechnologyLetters</secondary-title></titles><periodical><full-title>Microwave&OpticalTechnologyLetters</full-title></periodical><pages>327-30</pages><volume>30</volume><number>5</number><dates><year><styleface="normal"font="default"size="100%">20</style><styleface="normal"font="default"charset="134"size="100%">01</style></year></dates><urls></urls></record></Cite></EndNote>[\o"Min,2001#168"207]、平面波展开法ADDINEN.CITE<EndNote><Cite><Author>Maradudin</Author><Year>1994</Year><RecNum>165</RecNum><DisplayText><styleface="superscript">[208]</style></DisplayText><record><rec-number>165</rec-number><foreign-keys><keyapp="EN"db-id="dtsfaeex9st5axets06paxfaefse0fzrs95f">165</key></foreign-keys><ref-typename="JournalArticle">17</ref-type><contributors><authors><author>Maradudin,A.A.</author><author>Mcgurn,A.R.</author></authors></contributors><titles><title>OutofPlanePropagationofElectromagneticWavesinaTwo-dimensionalPeriodicDielectricMedium</title><secondary-title>JournalofModernOptics</secondary-title></titles><periodical><full-title>JournalofModernOptics</full-title></periodical><pages>275-84</pages><volume>41</volume><number>2</number><dates><year>1994</year></dates><urls></urls></record></Cite></EndNote>[\o"Maradudin,1994#165"208]等。其中有限元法作为一个成熟而精确的数值模拟方法，能够计算和分析截面复杂的空芯微结构光纤所支持的模式及多种模式特性，如损耗、色散、电磁场分布和偏振特性，是本文分析空芯微结构光纤的数值分析方法。有限元法出现于20世纪50、60年代，是一种高效能的常用数值计算方法，随着ANSYS、COMSOLMultiphysics等有限元分析软件的出现，有限元法被广泛用于结构力学、流体力学、电磁学等领域。在光纤光学方面，有限元方法由M.Koshiba等人于2001年首次引入到微结构光纤的分析中，在设定好光波长、折射率分布、边界条件、网格划分形式的基础上，就能计算出微结构光纤的传输模式、模场分布等。其基本思路是：将连续的求解域离散为有限个不同尺寸大小的单元（如三角形单元、四方形单元），在每个单元内假设的近似函数分片地表示全部求解区域上待求的场函数，之后通过Galerkin法或泛函的变分方法将电磁场的波动方程转换为特征值方程再进行求解，最终得到所求微结构光纤的传输模式和模场分布特性。以三角形单元为例，在对求解域中单个单元进行分析时，其中的磁场可以表示为ADDINEN.CITE<EndNote><Cite><Author>王志</Author><Year>2005</Year><RecNum>267</RecNum><DisplayText><styleface="superscript">[209]</style></DisplayText><record><rec-number>267</rec-number><foreign-keys><keyapp="EN"db-id="dtsfaeex9st5axets06paxfaefse0fzrs95f">267</key></foreign-keys><ref-typename="Thesis">32</ref-type><contributors><authors><author>王志</author></authors></contributors><titles><title>光子晶体光纤及其功能型器件的研究</title></titles><dates><year>2005</year></dates><publisher>南开大学</publisher><urls></urls></record></Cite></EndNote>[\o"王志,2005#267"209]： (2.1.1)其中 (2.1.2) (2.1.3)式中和分别每个单元在横截面边上的变量和节点上轴向磁场分量，、、是形函数矢量，而磁场波动方程的泛函为： (2.1.4)其中s为波导横截面，为波矢量，指相对介电常数张量。将式(2.1.1)代入到(2.1.4)中并使用变分原理，可以得到关于传播常数的特征值问题如下所示： (2.1.5) (2.1.6)其中 (2.1.7) (2.1.8) (2.1.9) (2.1.10)将式(2.1.6)代入式(2.1.5)中，就可以得到如下的特征值问题： (2.1.11)其中 (2.1.12)而对式(2.1.11)的特征方程进行求解就可以得到特征值和特征向量，即和。因为特征值为传播常数的平方，所以可以直接得到光纤在一定波长下的传导特性。本章中，采用COMSOLMultiphysics有限元分析软件对如图2.3（a）所示的简化空芯微结构光纤的模式特性进行分析。该光纤的结构可以看作是Kagomé空芯微结构光纤的简化结构，由一层空气孔包围着中心孔。光纤的实际传导机制主要由中心孔的周围结构决定。环绕中心孔的二氧化硅环是特殊结构，形成一个反谐振反射光学波导ADDINEN.CITE<EndNote><Cite><Author>Gérôme</Author><Year>2010</Year><RecNum>328</RecNum><DisplayText><styleface="superscript">[210]</style></DisplayText><record><rec-number>328</rec-number><foreign-keys><keyapp="EN"db-id="fsp2sprfses59ge9tf3xezao9xp909p92tdw"timestamp="1614777015">328</key></foreign-keys><ref-typename="JournalArticle">17</ref-type><contributors><authors><author>Gérôme,Frédéric</author><author>Jamier,Raphaël</author><author>Auguste,Jean-Louis</author><author>Humbert,Georges</author><author>Blondy,Jean-Marc</author></authors></contributors><titles><title>Simplifiedhollow-corephotoniccrystalfiber</title><secondary-title>OpticsLetters</secondary-title><alt-title>Opt.Lett.</alt-title></titles><periodical><full-title>OpticsLetters</full-title><abbr-1>Opt.Lett.</abbr-1></periodical><alt-periodical><full-title>OpticsLetters</full-title><abbr-1>Opt.Lett.</abbr-1></alt-periodical><pages>1157-1159</pages><volume>35</volume><number>8</number><keywords><keyword>Fibercharacterization</keyword><keyword>Fiberdesignandfabrication</keyword><keyword>Bendloss</keyword><keyword>Fiberdesign</keyword><keyword>Fiberdevices</keyword><keyword>Hollowcorefibers</keyword><keyword>Phasemodulation</keyword><keyword>Photoniccrystals</keyword></keywords><dates><year>2010</year><pub-dates><date>2010/04/15</date></pub-dates></dates><publisher>OSA</publisher><urls><related-urls><url>/abstract.cfm?URI=ol-35-8-1157</url></related-urls></urls><electronic-resource-num>10.1364/OL.35.001157</electronic-resource-num></record></Cite></EndNote>[\o"Gérôme,2010#328"210]，阻止中心模式和包层模式的耦合，进而影响光纤中对光场的限制。在有限元分析软件中建立的简化空芯微结构光纤模型如图2.3（b）所示，设置光纤模型的参数与实际光纤相符合。外包层直径为170µm，中空区域直径为40µm，中心六边形石英环的边长为16µm，石英壁厚为400nm。图中紫色区域为外部完美匹配层，厚度5µm。在模拟计算中，包层孔的折射率为空气折射率1，中心孔的折射率改为荧光染料折射率1.357，另外其他部分设置为二氧化硅折射率1.45。我们设置的网格分布图见图2.3（c），为了重点分析纤芯和石英壁中的传导模式并在保证精度的前提下节省计算时间，在纤芯和石英壁结构中设置较密集的三角网格，在其他区域设置较稀疏的三角网格。图2.4（a-e）表明空芯微结构光纤在532nm波长处支持的一些典型的中心模式图，（a）-（e）分别对应LP01、LP11、LP21、LP31及LP32模式。图2.4（f）是在570nm波长计算得到的石英环高阶模式图，说明功率流密度在二氧化硅微环中可形成一个接近环的分布，也表明微环具有较强的光场限制能力，这是其作为激光谐振腔的前提条件。图2.3（a）简化空芯微结构光纤的截面扫描电镜图；（b）模拟的简化空芯微结构光纤的结构图；（c）网格分布图图2.4纤芯填充增益介质的简化空芯微结构光纤中的典型模式分布情况：（a）-（e）泵浦波长下液芯中的模式；（f）谐振波长下石英环中的高阶模空芯微结构光纤微腔理论随着光纤拉丝技术的发展，空芯微结构光纤得到了迅速发展，其独特的结构和性能为研究高性能光学器件和光纤光子器件提供了更多的可能，促进了新型高灵敏度传感器和有源器件的发展。将具有特殊光、电、磁、热等特性的功能材料填充入空芯微结构光纤中，可实现光纤优异的导光特性和填充材料特殊的物理性能的有机结合，进而可以调控空芯微结构光纤的传导机制、模式耦合、双折射、色散等光学特性，不仅对研究空芯微结构光纤中光与填充物质的相互作用规律以及研制高性能可调控的光纤通信和传感器件具有重要意义，而且对生化物检测、光流控学和集成光子学的发展同样具有重要意义。空芯微结构光纤特殊的空气纤芯和多孔结构使其具有易与功能性材料等物质结合、高激光损伤阈值、低非线性等优势，以及将光限制在中心空气孔中减小了光与光纤材料的相互作用，可以实现一系列应用，如：（1）在光通信方面，由传统光纤的非线性及损耗导致传输容量逐渐接近其容量极限不能被提升，而空芯微结构光纤具有低非线性、低时延及理论上的低损耗，成为了光纤通信更加理想的传输介质。意大利LINKSFoundation的A.Nespola等人展示了叠加有L波段噪声信号的61路速率为32GBaud、调制格式为PM-QPSK的C波段信号，经过618km低损耗无节点嵌套型负曲率空芯反谐振光纤传输后，平均GMI为3.44bit/symbol，证明了100G相干信号在空芯微结构光纤上进行近1000km的长距传输能力ADDINEN.CITE<EndNote><Cite><Author>Nespola</Author><Year>2020</Year><RecNum>273</RecNum><DisplayText><styleface="superscript">[211]</style></DisplayText><record><rec-number>273</rec-number><foreign-keys><keyapp="EN"db-id="fsp2sprfses59ge9tf3xezao9xp909p92tdw"timestamp="1614164115">273</key></foreign-keys><ref-typename="ConferenceProceedings">10</ref-type><contributors><authors><author>A.Nespola</author><author>S.Straullu</author><author>T.D.Bradley</author><author>K.Harrington</author><author>H.Sakr</author><author>G.T.Jasion</author><author>E.N.Fokoua</author><author>Y.Jung</author><author>Y.Chen</author><author>J.R.Hayes</author><author>F.Forghieri</author><author>D.J.Richardson</author><author>F.Poletti</author><author>G.Bosco</author><author>P.Poggiolini</author></authors></contributors><titles><title>Transmissionof61C-BandChann