基于硅基光子器件的Fano共振研究进展

鹿利单; 祝连庆; 曾周末; 崔一平; 张东亮; 袁配

doi:10.7498/aps.70.20200550

摘要

硅基光子技术的发展为新型微纳光学功能器件和片上系统提供了高可靠、高精度的实现手段. 采用硅基光子技术构建的具有连续(准连续)模式微腔与离散模式的微腔耦合产生的Fano共振现象得到了广泛关注. Fano共振光谱在共振波长附近具有不对称且尖锐的谐振峰, 传输光的强度在共振波长附近从0突变为1, 该机制可显著提高硅基光开关、探测器、传感器, 以及光非互易性全光信号处理的性能. 本综述分析了Fano共振的一般数学表述, 总结了当前硅基光子微腔耦合产生Fano共振的理论模型研究现状, 讨论了不同类型硅光器件实现Fano共振的方法, 比较各种方案优劣及适用场合, 梳理了Fano共振在全光信号处理方面的应用研究情况. 最后探讨存在的一些问题及未来可能的相关研究方向.

关键词:

Abstract

The development of silicon photonics provides a method of implementing high reliability and high precision for new micro-nano optical functional devices and system-on-chips. The asymmetric Fano resonance phenomenon caused by the mutual coupling of optical resonant cavities is extensively studied. The spectrum of Fano resonance has an asymmetric and sharp slope near the resonance wavelength. The wavelength range for tuning the transmission from zero to one is much narrow in Fano lineshape, therefore improving the figure of merits of power consumption, sensing sensitivity, and extinction ratio. The mechanism can significantly improve silicon-based optical switches, detectors, sensors, and optical non-reciprocal all-optical signal processing. Therefore, the mechanism and method of generating the Fano resonance, the applications of silicon-based photonic technology, and the physical meaning of the Fano formula’s parameters are discussed in detail. It can be concluded that the primary condition for creating the Fano resonance is that the dual-cavity coupling is a weak coupling, and the detuning of resonance frequency of the two cavities partly determines Fano resonance lineshapes. Furthermore, the electromagnetically induced transparency is generated when the frequency detuning is zero. The methods of generating Fano resonance by using different types of devices in silicon photonics (besides the two-dimensional photonic crystals) and the corresponding evolutions of Fano resonance are introduced and categorized, including simple photonic crystal nanobeam, micro-ring resonator cavity without sacrificing the compact footprint, micro-ring resonator coupling with other structures (mainly double micro-ring resonators), adjustable Mach-Zehnder interferometer, and others such as slit waveguide and self-coupling waveguide. Then, we explain the all-optical signal processing based on the Fano resonance phenomenon, and also discuss the differences among the design concepts of Fano resonance in optimizing optical switches, modulators, optical sensing, and optical non-reciprocity. Finally, the future development direction is discussed from the perspective of improving Fano resonance parameters. The topology structure can improve the robustness of the Fano resonance spectrum; the bound states in continuous mode can increase the slope of Fano spectrum; the Fano resonance can expand the bandwidth of resonance spectrum by combining other material systems besides silicon photonics; the multi-mode Fano resonances can enhance the capability of the spectral multiplexing; the reverse design methods can improve the performance of the device. We believe that this review can provide an excellent reference for researchers who are studying the silicon photonic devices.

Keywords:

作者及机构信息

1.
天津大学, 精密测试技术及仪器国家重点实验室, 天津　300072

2.
北京信息科技大学, 光电测试技术及仪器教育部重点实验室, 北京　100192

3.
东南大学, 先进光子学中心, 南京　210096

通信作者: 祝连庆, lqzhu_bistu@sina.com ; 曾周末, zhmzeng@tju.edu.cn ;

基金项目: 高等学校学科创新引智计划(批准号: D17021)、北京市科技新星计划(批准号: Z191100001119052)和北京实验室纵向课题(批准号: GXKF2019002)资助的课题

Authors and contacts

1.
State Key Laboratory of Precision Measurement Technology and Instruments, Tianjin University, Tianjin 300072, China

2.
Key Laboratory of the Ministry of Education for Optoelectronic Measurement Technology and Instrument, Beijing Information Science & Technology University, Beijing 100192, China

3.
Advanced Photonics Center, Southeast University, Nanjing 210096, China

Corresponding author: Zhu Lian-Qing, lqzhu_bistu@sina.com ; Zeng Zhou-Mo, zhmzeng@tju.edu.cn ;

Funds: Project supported by the 111 Project of China (Grant No. D17021), the Beijing New-star Plan of Science and Technology of China (Grant No. Z191100001119052), and the Vertical Subject of Beijing Laboratory of China (Grant No. GXKF2019002)

文章全文 : translate this paragraph

参考文献

[1]	Lide D R 2017 A Century of Excellence in Measurements, Standards, and Technology (Boston: Government Printing Office) pp116−119
[2]	Fano U 1935 Nuovo Cimento 12 154 Google Scholar
[3]	Fano U 1961 Phys. Rev. A 124 1866 Google Scholar
[4]	Miroshnichenko A E, Flach S, Kivshar Y S 2010 Rev. Mod. Phys. 82 2257 Google Scholar
[5]	Limonov M F, Rybin M V, Poddubny A N, Kivshar Y S 2017 Nat. Photonics 11 543 Google Scholar
[6]	Holfeld C, Löser F, Sudzius M, Leo K, Whittaker D, Köhler K 1998 Phys. Rev. Lett. 81 874 Google Scholar
[7]	Luk'yanchuk B, Zheludev N I, Maier S A, Halas N J, Nordlander P, Giessen H, Chong C T 2010 Nat. Mater. 9 707 Google Scholar
[8]	Khanikaev A B, Wu C, Shvets G 2013 Nanophotonics 2 247 Google Scholar
[9]	Rahmani M, Luk'yanchuk B, Hong M 2013 Laser Photon. Rev. 7 329 Google Scholar
[10]	Zhou W, Zhao D, Shuai Y C, Yang H, Chuwongin S, Chadha A, Seo J H, Wang K X, Liu V, Ma Z 2014 Prog. Quantum Electron. 38 1 Google Scholar
[11]	涂鑫, 陈震旻, 付红岩 2019 物理学报 68 104210 Google Scholar Tu X, Chen Z M, Fu H Y 2019 Acta Phys. Sin. 68 104210 Google Scholar
[12]	Kanbara N, Suzuki K, Watanabe T, Iwaoka 2002 H IEEE/LEOS International Conference on Optical MEMs Lugano, Switzerland, August 20–23, 2002 p173
[13]	Fang Q, Liow T Y, Song J F, Ang K W, Yu M B, Lo G Q, Kwong D L 2010 Opt. Express 18 5106 Google Scholar
[14]	Ayazi A, Baehr Jones T, Liu Y, Lim A E J, Hochberg M 2012 Opt. Express 20 13115 Google Scholar
[15]	Wade J H, Alsop A T, Vertin N R, Yang H, Johnson M D, Bailey R C 2015 ACS Central Sci. 1 374 Google Scholar
[16]	Sasi M, Sophia d A, Randy R, Carli C, Alice W, Jue W, Martin A G, Muzammil I, Rufus W B 2017 J. Immunol. Methods 448 34 Google Scholar
[17]	Bekele D, Yu Y, Yvind K, Mork J 2019 Laser Photon. Rev. 13 1900054 Google Scholar
[18]	Genet C, van Exter M P, Woerdman J 2003 Opt. Commun. 225 331 Google Scholar
[19]	Connerade J P, Lane A 1988 Rep. Prog. Phys. 51 1439 Google Scholar
[20]	Gu L, Fang L, Fang H, Li J, Zheng J, Zhao J, Zhao Q, Gan X 2020 APL Photonics 5 016108 Google Scholar
[21]	Fan S 2002 Appl. Phys. Lett. 80 908 Google Scholar
[22]	Liu X, Yu Y, Zhang X 2019 Opt. Lett. 44 251 Google Scholar
[23]	Smith D D, Chang H, Fuller K A, Rosenberger A, Boyd R W 2004 Phys. Rev. A 69 063804 Google Scholar
[24]	Mahan G D 2013 Many-particle Physics (Boston: Springer) pp205−218
[25]	Miroshnichenko A E, Mingaleev S F, Flach S, Kivshar Y S 2005 Phys. Rev. E 71 036626 Google Scholar
[26]	Manolatou C, Khan M, Fan S, Villeneuve P R, Haus H, Joannopoulos J 1999 IEEE J. Quantum Electron. 35 1322 Google Scholar
[27]	Fan S, Suh W, Joannopoulos J D 2003 J. Opt. Soc. Am. A 20 569 Google Scholar
[28]	Li Q, Wang T, Su Y, Yan M, Qiu M 2010 Opt. Express 18 8367 Google Scholar
[29]	Du H, Zhang X, Chen G, Deng J, Chau F S, Zhou G 2016 Sci. Rep. 6 24766 Google Scholar
[30]	Du H, Zhang W, Littlejohns C, Stankovic S, Yan X, Tran D, Sharp G, Gardes F, Thomson D, Sorel M 2019 Opt. Express 27 7365 Google Scholar
[31]	Zhu B, Zhang W, Pan S, Yao J 2018 J. Lightwave Technol. 37 2527 Google Scholar
[32]	Xu Z, Wu Z, Chen Y, Zhang S, Liu L, Zhou L, Yang C, Zhang Y, Yu S 2019 Asia Communications and Photonics Conference Chengdu, China, November 2–5, 2019 p294
[33]	Dong G, Wang Y, Zhang X 2018 Opt. Lett. 43 5977 Google Scholar
[34]	Gu L, Fang H, Li J, Fang L, Chua S J, Zhao J, Gan X 2019 Nanophotonics 8 841 Google Scholar
[35]	Li A, Bogaerts W 2020 Optica 7 7 Google Scholar
[36]	Tu X, Mario L Y, Mei T 2010 Opt. Express 18 18820 Google Scholar
[37]	Lin T, Chau F S, Deng J, Zhou G 2015 Appl. Phys. Lett. 107 223105 Google Scholar
[38]	Mehta K K, Orcutt J S, Ram R J 2013 Appl. Phys. Lett. 102 081109 Google Scholar
[39]	Yu P, Hu T, Qiu H, Ge F, Yu H, Jiang X, Yang J 2013 Appl. Phys. Lett. 103 091104 Google Scholar
[40]	Meng Z M, Liang A, Li Z Y 2017 J. Appl. Phys. 121 193102 Google Scholar
[41]	Meng Z M, Li Z Y 2018 J. Phys. D-Appl. Phys. 51 095106 Google Scholar
[42]	Meng Z M, Chen C B, Qin F 2020 J. Phys. D-Appl. Phys. 53 205105 Google Scholar
[43]	Burr J R, Wood M G, Reano R M 2016 IEEE Photonics J. 8 1 Google Scholar
[44]	Chang C M, Solgaard O 2013 Opt. Express 21 27209 Google Scholar
[45]	Cheng Z, Dong J, Zhang X 2020 Opt. Lett. 45 2363 Google Scholar
[46]	Chao C Y, Guo L J 2003 Appl. Phys. Lett. 83 1527 Google Scholar
[47]	Ruege A C, Reano R M 2010 J. Lightwave Technol. 28 2964 Google Scholar
[48]	Yi H, Citrin D, Zhou Z 2010 Opt. Express 18 2967 Google Scholar
[49]	Lu Y, Fu X, Chu D, Wen W, Yao J 2011 Opt. Commun. 284 476 Google Scholar
[50]	Zhao G, Zhao T, Xiao H, Liu Z, Liu G, Yang J, Ren Z, Bai J, Tian Y 2016 Opt. Express 24 20187 Google Scholar
[51]	Huang Q, Ma K, He S 2015 IEEE Photonics Technol. Lett. 27 1402 Google Scholar
[52]	Zhang W, Li W, Yao J 2016 Opt. Lett. 41 2474 Google Scholar
[53]	Zhang Z, Ng G I, Hu T, Qiu H, Guo X, Wang W, Rouifed M S, Liu C, Wang H 2017 Appl. Phys. Lett. 111 081105 Google Scholar
[54]	Tu Z, Gao D, Zhang M, Zhang D 2017 Opt. Express 25 20911 Google Scholar
[55]	Zhao C Y, Zhang L, Zhang C M 2018 Opt. Commun. 414 212 Google Scholar
[56]	Peng F, Wang Z, Yuan G, Guan L, Peng Z 2018 IEEE Photonics J. 10 1 Google Scholar
[57]	Xiao Y F, Li M, Liu Y C, Li Y, Sun X, Gong Q 2010 Phys. Rev. A 82 065804 Google Scholar
[58]	Zhou J, Han W, Meng Y, Song H, Mu D, Park W 2014 J. Lightwave Technol. 32 4104 Google Scholar
[59]	Qiu C, Yu P, Hu T, Wang F, Jiang X, Yang J 2012 Appl. Phys. Lett. 101 021110 Google Scholar
[60]	Wang G, Dai T, Jiang J, Yu H, Hao Y, Wang Y, Li Y, Jiang X, Yang J 2017 J. Opt. 19 025803 Google Scholar
[61]	Wang G, Shen A, Zhao C, Yang L, Dai T, Wang Y, Li Y, Jiang X, Yang J 2016 Opt. Lett. 41 544 Google Scholar
[62]	Zhou X, Zhang L, Armani A M, Beausoleil R G, Willner A E, Pang W 2013 Opt. Express 21 20179 Google Scholar
[63]	Zhou X Y, Zhang L, Armani A M, Zhang D, Duan X, Liu J, Zhang H, Pang W 2013 IEEE J. Sel. Top. Quantum Electron. 20 35 Google Scholar
[64]	Zhou X Y, Zhang L, Armani A M, Liu J, Duan X, Zhang D, Zhang H, Pang W 2015 J. Lightwave Technol. 33 4521 Google Scholar
[65]	Dotan I E, Scheuer J 2012 Opt. Commun. 285 3475 Google Scholar
[66]	Yu C, Tian H, Qian Z, Bai R, Zhu L, Zhang Y 2017 Appl. Phys. Express 10 122202 Google Scholar
[67]	Xiao H, Wu X, Liu Z, Zhao G, Guo X, Meng Y, Deng L, Chen W, Tian Y, Yang J 2017 Appl. Phys. Lett. 111 091901 Google Scholar
[68]	Wen Y, Sun Y, Deng C, Huang L, Hu G, Yun B, Zhang R, Cui Y 2019 Opt. Commun. 446 141 Google Scholar
[69]	Zhao T, Xiao H, Li Y, Yang J, Jia H, Ren G, Mitchell A, Tian Y 2019 Opt. Lett. 44 3154 Google Scholar
[70]	Chaudhry M R, Zakwan M, Onbasli M C, Serpengüzel A 2019 IEEE J. Sel. Top. Quantum Electron. 26 1 Google Scholar
[71]	Thomas R, Makri E, Kottos T, Shapiro B, Vitebskiy I 2018 Phys. Rev. A 98 053806 Google Scholar
[72]	Whitlock M C, Phillips P C, Moore F B G, Tonsor S J 1995 Annu. Rev. Ecol. Syst. 26 601 Google Scholar
[73]	Li J, Yu R, Ding C, Wu Y 2016 Phys. Rev. A 93 023814 Google Scholar
[74]	Lu Y, Xu L, Yu Y, Wang P, Yao J 2006 J. Opt. Soc. Am. A 23 1718 Google Scholar
[75]	Zheng S, Ruan Z, Gao S, Long Y, Li S, He M, Zhou N, Du J, Shen L, Cai X, Wang J 2017 Opt. Express 25 25655 Google Scholar
[76]	Li A, Bogaerts W 2017 APL Photonics 2 096101 Google Scholar
[77]	Li A, Bogaerts W 2017 Opt. Express 25 31688 Google Scholar
[78]	Li A, Bogaerts W 2019 Laser Photon. Rev. 13 1800244 Google Scholar
[79]	Yang J, Wang F, Jiang X, Qu H, Wang M, Wang Y 2004 Opt. Express 12 4178 Google Scholar
[80]	Chen S, Zhou G, Zhou L, Lu L, Chen J 2020 J. Lightwave Technol. 18 3395 Google Scholar
[81]	Troia B, Penades J S, Qu Z, Khokhar A Z, Osman A, Wu Y, Stirling C, Nedeljkovic M, Passaro V M, Mashanovich G Z 2017 Appl. Optics 56 8769 Google Scholar
[82]	Zheng S, Cao X, Wang J 2020 Opt. Lett. 45 1035 Google Scholar
[83]	Zhou L, Poon A W 2007 Opt. Lett. 32 781 Google Scholar
[84]	Lu Y, Xu L, Shu M, Wang P, Yao J 2008 IEEE Photonics Technol. Lett. 20 529 Google Scholar
[85]	Le T T, Cahill L 2013 Opt. Commun. 301 100 Google Scholar
[86]	Wang F, Wang X, Zhou H, Zhou Q, Hao Y, Jiang X, Wang M, Yang J 2009 Opt. Express 17 7708 Google Scholar
[87]	Hu T, Yu P, Qiu C, Qiu H, Wang F, Yang M, Jiang X, Yu H, Yang J 2013 Appl. Phys. Lett. 102 011112 Google Scholar
[88]	Guo X, Dai T, Chen B, Yu H, Wang Y, Yang J 2019 Opt. Lett. 44 4527 Google Scholar
[89]	Zhang W, Yao J 2018 Opt. Lett. 43 5415 Google Scholar
[90]	Zhou L, Ye T, Chen J 2011 Opt. Lett. 36 13 Google Scholar
[91]	Tang H, Zhou L, Xie J, Lu L, Chen J 2018 J. Lightwave Technol. 36 2188 Google Scholar
[92]	Bera A, Kuittinen M, Honkanen S, Roussey M 2018 Opt. Lett. 43 3489 Google Scholar
[93]	Yu Y, Heuck M, Hu H, Xue W, Peucheret C, Chen Y, Oxenløwe L K, Yvind K, Mork J 2014 Appl. Phys. Lett. 105 061117 Google Scholar
[94]	Poulton C V, Zeng X, Wade M T, Popović M A 2015 Opt. Lett. 40 4206 Google Scholar
[95]	Xie X, Khurgin J, Kang J, Chow F S 2003 IEEE Photonics Technol. Lett. 15 531 Google Scholar
[96]	Tazawa H, Steier W H 2005 IEEE Photonics Technol. Lett. 17 1851 Google Scholar
[97]	Cardenas J, Morton P A, Khurgin J B, Griffith A, Poitras C B, Preston K, Lipson M 2013 Opt. Express 21 22549 Google Scholar
[98]	Zhang J, Leroux X, Duraán-Valdeiglesias E, Alonso-Ramos C, Marris-Morini D, Vivien L, He S, Cassan E 2018 ACS Photonics 5 4229 Google Scholar
[99]	Terrel M, Digonnet M J, Fan S 2009 Appl. Optics 48 4874 Google Scholar
[100]	Yu Y, Chen Y, Hu H, Xue W, Yvind K, Mork J 2015 Laser Photon. Rev. 9 241 Google Scholar
[101]	Yang K Y, Skarda J, Cotrufo M, Dutt A, Ahn G H, Sawaby M, Vercruysse D, Arbabian A, Fan S, Alù A J 2019 Conference on Lasers and Electro-Optics (CLEO) San Jose, USA, May 1–5, 2019 pSW4J.3
[102]	Kivshar Y, Rybin M 2017 Nat. Photonics 11 212 Google Scholar
[103]	An Y, Fu T, Liu Q, Ouyang Z 2020 Appl. Phys. Express 13 032006 Google Scholar
[104]	Zangeneh-Nejad F, Fleury R 2019 Phys. Rev. Lett. 122 014301 Google Scholar

施引文献

图 1 (a) q与相移δ之间的关系曲线; (b)—(f) q → $ -\infty $, q = –1, q = 0, q = +1, q → $ +\infty $时对应的传输光谱; (g)不同半高宽Γ对Fano线形的影响; (h)不同共振波长ω₀对应的光谱

Fig. 1. (a) Relationship between q and the phase shift δ; (b)–(f) transmitted spectra corresponding to q → $ -\infty $, q =–1, q = 0, q = + 1, q → $ +\infty $, respectively; (g) effect of different half-widths Γ on Fano lineshapes; (h) different spectra corresponding to different resonance wavelengths ω₀.

下载: 全尺寸图片幻灯片

图 2 硅基光子谐振腔不同耦合方式的简化模型　(a)—(c) 侧边直接耦合腔; (d) 端面耦合腔; (e)侧边间接耦合腔

Fig. 2. A simplified model of different coupling modes of the silicon-based photonic resonator: (a)–(c) Directly side coupled cavities; (d) end-coupled cavities; (e) indirectly side coupled cavities.

下载: 全尺寸图片幻灯片

图 3 (a) Fano共振形成条件; (b) ω₂– ω₁的失谐量对Fano共振线形的影响

Fig. 3. (a) Formation conditions for Fano resonance; (b) the effect of ω₂– ω₁ on Fano resonance.

下载: 全尺寸图片幻灯片

图 4 各种PCNC产生Fano共振的方法　(a)单PCNC^[38]; (b) PCNC侧耦合F-P谐振器^[39]; (c)纳米微机电结构动态控制Fano共振光谱^[37]; (d) PCN的带隙边缘模式耦合PCNC^[40]; (e)具有简并带隙边缘模式的双PCNC^[43]; (f)双排PCN构建的布拉格反射结构的(i)整体结构图和(ii)俯视图^[44]

Fig. 4. Various PCNC structures for Fano resonance: (a) Single PCNC^[38]; (b) PCNC side coupled F-P resonator^[39]; (c) dynamic control of Fano resonance with a nanoelectromechanical structure^[37]; (d) band edge mode of PCN couple with PCNC^[40]; (e) double PCNCs with degenerate band edges mode^[43]; (f) the overall structure (i) and top view (ii) Bragg reflection structure constructed with double-row PCN^[44].

下载: 全尺寸图片幻灯片

图 5 紧凑型MRR产生Fano共振的方法　(a)错位总线波导耦合MRR^[46]; (b)双模式总线波导耦合MRR^[47]; (c)直波导端面反射耦合MRR^[48]; (d) 反馈直波导耦合MRR^[50]; (e)直波导耦合带有相移布拉格光栅的MRR^[51]; (f)总线波导结合光栅/空气孔/狭缝耦合MRR^{[20,34,54-56]}

Fig. 5. Various MRRs with compact footprint for Fano resonance: (a) Straight waveguide with misalignment^[46]; (b) dual-mode bus waveguide^[47]; (c) straight waveguide with end face reflection^[48]; (d) straight waveguide with feedback^[50]; (e) MRR with phase-shifted Bragg grating^[51]; (f) bus waveguide combined Bragg grating/air holes/slits^{[20,34,54-56]}.

下载: 全尺寸图片幻灯片

图 6 各种复合MRR产生Fano共振的方法　(a)耦合模式理论分析双MRR结构^[57]; (b)等效F-P单元分析多环耦合结构^[36]; (c)双环嵌套结构^[59-64]; (d)双环反馈耦合结构^[67,68]; (e) Sagnac形成F-P腔耦合MRR^[75]; (f)等效双马赫-曾德尔干涉仪^[35,76-78]

Fig. 6. Various complex MRRs for Fano resonance: (a) Analysis of double MRR using coupling mode theory^[57]; (b) analysis of multi-ring coupling with equivalent F-P unit^[36]; (c) double-MRRs nested structure^[59-64]; (d) double-MRRs with feedback configuration^[67,68]; (e) Sagnac formed F-P cavity couples MRR^[75]; (f) equivalent double Mach-Zehnder interferometer^[35,76-78].

下载: 全尺寸图片幻灯片

图 7 MRR与各种变异结构MZI耦合产生Fano共振的方法　(a) MZI耦合MRR模型^[79]; (b) MZI侧边耦合MRR^[83]; (c) 双4 × 4多模耦合器组成双MZI^[85]; (d) MZI双臂耦合交叉环^[86]; (e) MZI双臂耦合MRR及交叉波导^[87]; (f)双MZI耦合双MRR^[22]

Fig. 7. MRR coupled with variant MZI for Fano resonance: (a) Model for MZI coupled MRR^[79]; (b) MZI side coupled MRR^[83]; (c) dual 4 × 4 multimode couplers form dual MZI^[85]; (d) dual-arm of MZI coupled cross-loop waveguide^[86]; (e) dual-arm of MZI coupled MRR and cross waveguide^[87]; (f) dual MZI coupled dual MRR^[22].

下载: 全尺寸图片幻灯片

图 8 (a)自耦合波导^[90]; (b)狭缝波导耦合光栅式F-P^[92]

Fig. 8. (a) Self-coupling waveguide^[90]; (b) slot waveguide coupling F-P composed by Bragg grating^[92].

下载: 全尺寸图片幻灯片

图 9 Fano共振与Lorentzian线形的开关性能

Fig. 9. Switching performance of Fano resonance and Lorentzian lineshapes.

下载: 全尺寸图片幻灯片

图 10 Fano共振硅光开关^[42]　(a) PCNC耦合PCN; (b) PCNC耦合PCN的光谱

Fig. 10. Silicon optical switch based on Fano resonant^[42]: (a) PCNC couple PCN; (b) corresponding spectra.

下载: 全尺寸图片幻灯片

图 11 Fano共振硅基电光调制器　(a) MZI耦合MRR^[80]; (b)单波导PCNC^[98]

Fig. 11. Silicon electro-optic modulator based on Fano resonant: (a) MZI couple MRR^[80]; (b) single waveguide PCNC^[98].

下载: 全尺寸图片幻灯片

图 12 Fano共振传感　(a)波导截面^[46]; (b)光栅式MRR^[68]; (c)传感测试装置^[63,64]; (d) Fano共振光谱随折射率传感变化曲线, 图中RI (refractive index)代表折射率^[56]

Fig. 12. Fano resonance for sensing applications: (a) Cross section of waveguide^[46]; (b) MRR composed of grating^[68]; (c) setup for sensor^[63,64]; (d) spectrum of Fano resonance versus refractive index (RI)^[56].

下载: 全尺寸图片幻灯片

图 13 基于EIT的光非互易性传输　(a) 微环形成双MZI结构^[35]; (b)非互易性光谱特征^[35]; (c)端口1波长随输入功率变化曲线^[35]; (d) 端口2波长随输入功率变化曲线^[101]

Fig. 13. EIT-based optical nonreciprocal transmission: (a) Microrings forming a dual MZIs^[35]; (b) characteristics of optical nonreciprocity spectral^[35]; (c) wavelength of port 1 versus input power^[35]; (d) wavelength of port 2 versus input power^[101].

下载: 全尺寸图片幻灯片

表 1 不同PCNC产生Fano共振的参数表

Table 1. Parameters for Fano resonance based on different PCNCs.

结构	尺寸/(μm × μm)	消光比/dB	斜率/(dB·nm^–1)	应用	文献
PCNC结合光纤	～13.2 × 0.47	17			[38]
F-P 侧边耦合 PCNC	～6 × 0.45	7.3	5.3		[39]
F-P 侧边耦合 PCNC	～18 × 0.72	14—18			[37]
F-P 侧边耦合 PCNC	～10.5 × 1.5	22			[40]
F-P 侧边耦合狭缝 PCNC	～10.5 × 1.5	24		折射率灵敏度778 nm/RIU	[41]
双 PCNs	～5.18 × 0.74	20			[43]
交叉耦合四端口PCNC	～4	16		光开关	[45]

下载: 导出CSV

表 2 不同紧凑型MRR产生Fano共振的参数表

Table 2. Parameters for Fano resonance based on different compact MRRs.

结构	尺寸/(μm×μm)	消光比/dB	斜率	性能	文献
总线错位波导耦合MRR	～20×30	30		葡萄糖灵敏度24 mg/dl	[46]
多模总线波导耦合MRR	～1020×230	6	27.1/nm		[47]
端面反射总线波导耦合MRR	～22×10000	30		折射率探测极限～10^–8 RIU	[48]
MRR耦合反馈总线波导	～20×350	30.8	226.5 dB/nm		[49,50]
MRR耦合相移光栅	～60×60	20			[51]
MRR耦合由两个布拉格光栅形成的F-P腔	～17×140	22.54	250.4 dB/nm		[52]
MRR耦合由光子晶体形成的F-P腔	～6×10	23		折射率灵敏度～1.76 × 10^–4	[56]
亚波长光栅耦合MRR	～6×10	12		折射率灵敏度366 nm/RIU	[54]
狭缝F-P耦合狭缝MRR	～4×10	20		折射率灵敏度297.13 nm/RIU	[55]
PCNC侧耦合结合Kerr 非线性材料的PCN	～16			关开关功耗0.76 pJ, 切换时间0.707 ps	[42]

下载: 导出CSV

表 3 多MRR产生Fano共振的参数表

Table 3. Parameters for Fano resonance based on multiple MRRs.

结构	尺寸/(μm×μm)	消光比/dB	斜率	性能	文献
MRR嵌入跑道微环	～5×40	20			[59]
热调MRR嵌入跑道微环	～5 × 40	40	35—93 dB/nm		[60]
亚波长光栅式MRR嵌入跑道微环	～20×100	21.53		折射率灵敏度500 nm/RIU	[68]
Sagnac形成的双F-P耦合	～100×300	20	770 dB/pm		[30]
Sagnac形成的F-P耦合MRR	～25×30	23.22	252 dB/nm		[75]

下载: 导出CSV

表 4 不同基于MZI 单元产生Fano共振的参数表

Table 4. Parameters for Fano resonance based on MZI unit.

结构	尺寸/(μm×μm)	消光比/dB	斜率/(dB·nm^–1)	应用	文献
多模MZI耦合MRR	～65×85	33	113	模式开关	[82]
双总线耦合交叉MRR形成的等效MZI				光开关	[86]
MRR结合“十”交叉波导作为MZI的干涉臂	～100×370	20			[87]
MRR的两总线波导反馈形成MZI	～390×850	30.2	41		[88]
双MRR辅助双MZI		56.8	3388.1		[22]

下载: 导出CSV

表 5 各种硅光器件产生Fano共振的方法对比

Table 5. Comparation of diffrent silicon waveguide unit for Fano resonance.

方法	尺寸	消光比	斜率	工艺要求	应用
PCNC	小	适中	小	高	光开关/传感
MRR	中	适中	大	一般	传感/滤波器
MZI	大	大	大	一般	调制器/隔离器

下载: 导出CSV

[1]	Lide D R 2017 A Century of Excellence in Measurements, Standards, and Technology (Boston: Government Printing Office) pp116−119
[2]	Fano U 1935 Nuovo Cimento 12 154 Google Scholar
[3]	Fano U 1961 Phys. Rev. A 124 1866 Google Scholar
[4]	Miroshnichenko A E, Flach S, Kivshar Y S 2010 Rev. Mod. Phys. 82 2257 Google Scholar
[5]	Limonov M F, Rybin M V, Poddubny A N, Kivshar Y S 2017 Nat. Photonics 11 543 Google Scholar
[6]	Holfeld C, Löser F, Sudzius M, Leo K, Whittaker D, Köhler K 1998 Phys. Rev. Lett. 81 874 Google Scholar
[7]	Luk'yanchuk B, Zheludev N I, Maier S A, Halas N J, Nordlander P, Giessen H, Chong C T 2010 Nat. Mater. 9 707 Google Scholar
[8]	Khanikaev A B, Wu C, Shvets G 2013 Nanophotonics 2 247 Google Scholar
[9]	Rahmani M, Luk'yanchuk B, Hong M 2013 Laser Photon. Rev. 7 329 Google Scholar
[10]	Zhou W, Zhao D, Shuai Y C, Yang H, Chuwongin S, Chadha A, Seo J H, Wang K X, Liu V, Ma Z 2014 Prog. Quantum Electron. 38 1 Google Scholar
[11]	涂鑫, 陈震旻, 付红岩 2019 物理学报 68 104210 Google Scholar Tu X, Chen Z M, Fu H Y 2019 Acta Phys. Sin. 68 104210 Google Scholar
[12]	Kanbara N, Suzuki K, Watanabe T, Iwaoka 2002 H IEEE/LEOS International Conference on Optical MEMs Lugano, Switzerland, August 20–23, 2002 p173
[13]	Fang Q, Liow T Y, Song J F, Ang K W, Yu M B, Lo G Q, Kwong D L 2010 Opt. Express 18 5106 Google Scholar
[14]	Ayazi A, Baehr Jones T, Liu Y, Lim A E J, Hochberg M 2012 Opt. Express 20 13115 Google Scholar
[15]	Wade J H, Alsop A T, Vertin N R, Yang H, Johnson M D, Bailey R C 2015 ACS Central Sci. 1 374 Google Scholar
[16]	Sasi M, Sophia d A, Randy R, Carli C, Alice W, Jue W, Martin A G, Muzammil I, Rufus W B 2017 J. Immunol. Methods 448 34 Google Scholar
[17]	Bekele D, Yu Y, Yvind K, Mork J 2019 Laser Photon. Rev. 13 1900054 Google Scholar
[18]	Genet C, van Exter M P, Woerdman J 2003 Opt. Commun. 225 331 Google Scholar
[19]	Connerade J P, Lane A 1988 Rep. Prog. Phys. 51 1439 Google Scholar
[20]	Gu L, Fang L, Fang H, Li J, Zheng J, Zhao J, Zhao Q, Gan X 2020 APL Photonics 5 016108 Google Scholar
[21]	Fan S 2002 Appl. Phys. Lett. 80 908 Google Scholar
[22]	Liu X, Yu Y, Zhang X 2019 Opt. Lett. 44 251 Google Scholar
[23]	Smith D D, Chang H, Fuller K A, Rosenberger A, Boyd R W 2004 Phys. Rev. A 69 063804 Google Scholar
[24]	Mahan G D 2013 Many-particle Physics (Boston: Springer) pp205−218
[25]	Miroshnichenko A E, Mingaleev S F, Flach S, Kivshar Y S 2005 Phys. Rev. E 71 036626 Google Scholar
[26]	Manolatou C, Khan M, Fan S, Villeneuve P R, Haus H, Joannopoulos J 1999 IEEE J. Quantum Electron. 35 1322 Google Scholar
[27]	Fan S, Suh W, Joannopoulos J D 2003 J. Opt. Soc. Am. A 20 569 Google Scholar
[28]	Li Q, Wang T, Su Y, Yan M, Qiu M 2010 Opt. Express 18 8367 Google Scholar
[29]	Du H, Zhang X, Chen G, Deng J, Chau F S, Zhou G 2016 Sci. Rep. 6 24766 Google Scholar
[30]	Du H, Zhang W, Littlejohns C, Stankovic S, Yan X, Tran D, Sharp G, Gardes F, Thomson D, Sorel M 2019 Opt. Express 27 7365 Google Scholar
[31]	Zhu B, Zhang W, Pan S, Yao J 2018 J. Lightwave Technol. 37 2527 Google Scholar
[32]	Xu Z, Wu Z, Chen Y, Zhang S, Liu L, Zhou L, Yang C, Zhang Y, Yu S 2019 Asia Communications and Photonics Conference Chengdu, China, November 2–5, 2019 p294
[33]	Dong G, Wang Y, Zhang X 2018 Opt. Lett. 43 5977 Google Scholar
[34]	Gu L, Fang H, Li J, Fang L, Chua S J, Zhao J, Gan X 2019 Nanophotonics 8 841 Google Scholar
[35]	Li A, Bogaerts W 2020 Optica 7 7 Google Scholar
[36]	Tu X, Mario L Y, Mei T 2010 Opt. Express 18 18820 Google Scholar
[37]	Lin T, Chau F S, Deng J, Zhou G 2015 Appl. Phys. Lett. 107 223105 Google Scholar
[38]	Mehta K K, Orcutt J S, Ram R J 2013 Appl. Phys. Lett. 102 081109 Google Scholar
[39]	Yu P, Hu T, Qiu H, Ge F, Yu H, Jiang X, Yang J 2013 Appl. Phys. Lett. 103 091104 Google Scholar
[40]	Meng Z M, Liang A, Li Z Y 2017 J. Appl. Phys. 121 193102 Google Scholar
[41]	Meng Z M, Li Z Y 2018 J. Phys. D-Appl. Phys. 51 095106 Google Scholar
[42]	Meng Z M, Chen C B, Qin F 2020 J. Phys. D-Appl. Phys. 53 205105 Google Scholar
[43]	Burr J R, Wood M G, Reano R M 2016 IEEE Photonics J. 8 1 Google Scholar
[44]	Chang C M, Solgaard O 2013 Opt. Express 21 27209 Google Scholar
[45]	Cheng Z, Dong J, Zhang X 2020 Opt. Lett. 45 2363 Google Scholar
[46]	Chao C Y, Guo L J 2003 Appl. Phys. Lett. 83 1527 Google Scholar
[47]	Ruege A C, Reano R M 2010 J. Lightwave Technol. 28 2964 Google Scholar
[48]	Yi H, Citrin D, Zhou Z 2010 Opt. Express 18 2967 Google Scholar
[49]	Lu Y, Fu X, Chu D, Wen W, Yao J 2011 Opt. Commun. 284 476 Google Scholar
[50]	Zhao G, Zhao T, Xiao H, Liu Z, Liu G, Yang J, Ren Z, Bai J, Tian Y 2016 Opt. Express 24 20187 Google Scholar
[51]	Huang Q, Ma K, He S 2015 IEEE Photonics Technol. Lett. 27 1402 Google Scholar
[52]	Zhang W, Li W, Yao J 2016 Opt. Lett. 41 2474 Google Scholar
[53]	Zhang Z, Ng G I, Hu T, Qiu H, Guo X, Wang W, Rouifed M S, Liu C, Wang H 2017 Appl. Phys. Lett. 111 081105 Google Scholar
[54]	Tu Z, Gao D, Zhang M, Zhang D 2017 Opt. Express 25 20911 Google Scholar
[55]	Zhao C Y, Zhang L, Zhang C M 2018 Opt. Commun. 414 212 Google Scholar
[56]	Peng F, Wang Z, Yuan G, Guan L, Peng Z 2018 IEEE Photonics J. 10 1 Google Scholar
[57]	Xiao Y F, Li M, Liu Y C, Li Y, Sun X, Gong Q 2010 Phys. Rev. A 82 065804 Google Scholar
[58]	Zhou J, Han W, Meng Y, Song H, Mu D, Park W 2014 J. Lightwave Technol. 32 4104 Google Scholar
[59]	Qiu C, Yu P, Hu T, Wang F, Jiang X, Yang J 2012 Appl. Phys. Lett. 101 021110 Google Scholar
[60]	Wang G, Dai T, Jiang J, Yu H, Hao Y, Wang Y, Li Y, Jiang X, Yang J 2017 J. Opt. 19 025803 Google Scholar
[61]	Wang G, Shen A, Zhao C, Yang L, Dai T, Wang Y, Li Y, Jiang X, Yang J 2016 Opt. Lett. 41 544 Google Scholar
[62]	Zhou X, Zhang L, Armani A M, Beausoleil R G, Willner A E, Pang W 2013 Opt. Express 21 20179 Google Scholar
[63]	Zhou X Y, Zhang L, Armani A M, Zhang D, Duan X, Liu J, Zhang H, Pang W 2013 IEEE J. Sel. Top. Quantum Electron. 20 35 Google Scholar
[64]	Zhou X Y, Zhang L, Armani A M, Liu J, Duan X, Zhang D, Zhang H, Pang W 2015 J. Lightwave Technol. 33 4521 Google Scholar
[65]	Dotan I E, Scheuer J 2012 Opt. Commun. 285 3475 Google Scholar
[66]	Yu C, Tian H, Qian Z, Bai R, Zhu L, Zhang Y 2017 Appl. Phys. Express 10 122202 Google Scholar
[67]	Xiao H, Wu X, Liu Z, Zhao G, Guo X, Meng Y, Deng L, Chen W, Tian Y, Yang J 2017 Appl. Phys. Lett. 111 091901 Google Scholar
[68]	Wen Y, Sun Y, Deng C, Huang L, Hu G, Yun B, Zhang R, Cui Y 2019 Opt. Commun. 446 141 Google Scholar
[69]	Zhao T, Xiao H, Li Y, Yang J, Jia H, Ren G, Mitchell A, Tian Y 2019 Opt. Lett. 44 3154 Google Scholar
[70]	Chaudhry M R, Zakwan M, Onbasli M C, Serpengüzel A 2019 IEEE J. Sel. Top. Quantum Electron. 26 1 Google Scholar
[71]	Thomas R, Makri E, Kottos T, Shapiro B, Vitebskiy I 2018 Phys. Rev. A 98 053806 Google Scholar
[72]	Whitlock M C, Phillips P C, Moore F B G, Tonsor S J 1995 Annu. Rev. Ecol. Syst. 26 601 Google Scholar
[73]	Li J, Yu R, Ding C, Wu Y 2016 Phys. Rev. A 93 023814 Google Scholar
[74]	Lu Y, Xu L, Yu Y, Wang P, Yao J 2006 J. Opt. Soc. Am. A 23 1718 Google Scholar
[75]	Zheng S, Ruan Z, Gao S, Long Y, Li S, He M, Zhou N, Du J, Shen L, Cai X, Wang J 2017 Opt. Express 25 25655 Google Scholar
[76]	Li A, Bogaerts W 2017 APL Photonics 2 096101 Google Scholar
[77]	Li A, Bogaerts W 2017 Opt. Express 25 31688 Google Scholar
[78]	Li A, Bogaerts W 2019 Laser Photon. Rev. 13 1800244 Google Scholar
[79]	Yang J, Wang F, Jiang X, Qu H, Wang M, Wang Y 2004 Opt. Express 12 4178 Google Scholar
[80]	Chen S, Zhou G, Zhou L, Lu L, Chen J 2020 J. Lightwave Technol. 18 3395 Google Scholar
[81]	Troia B, Penades J S, Qu Z, Khokhar A Z, Osman A, Wu Y, Stirling C, Nedeljkovic M, Passaro V M, Mashanovich G Z 2017 Appl. Optics 56 8769 Google Scholar
[82]	Zheng S, Cao X, Wang J 2020 Opt. Lett. 45 1035 Google Scholar
[83]	Zhou L, Poon A W 2007 Opt. Lett. 32 781 Google Scholar
[84]	Lu Y, Xu L, Shu M, Wang P, Yao J 2008 IEEE Photonics Technol. Lett. 20 529 Google Scholar
[85]	Le T T, Cahill L 2013 Opt. Commun. 301 100 Google Scholar
[86]	Wang F, Wang X, Zhou H, Zhou Q, Hao Y, Jiang X, Wang M, Yang J 2009 Opt. Express 17 7708 Google Scholar
[87]	Hu T, Yu P, Qiu C, Qiu H, Wang F, Yang M, Jiang X, Yu H, Yang J 2013 Appl. Phys. Lett. 102 011112 Google Scholar
[88]	Guo X, Dai T, Chen B, Yu H, Wang Y, Yang J 2019 Opt. Lett. 44 4527 Google Scholar
[89]	Zhang W, Yao J 2018 Opt. Lett. 43 5415 Google Scholar
[90]	Zhou L, Ye T, Chen J 2011 Opt. Lett. 36 13 Google Scholar
[91]	Tang H, Zhou L, Xie J, Lu L, Chen J 2018 J. Lightwave Technol. 36 2188 Google Scholar
[92]	Bera A, Kuittinen M, Honkanen S, Roussey M 2018 Opt. Lett. 43 3489 Google Scholar
[93]	Yu Y, Heuck M, Hu H, Xue W, Peucheret C, Chen Y, Oxenløwe L K, Yvind K, Mork J 2014 Appl. Phys. Lett. 105 061117 Google Scholar
[94]	Poulton C V, Zeng X, Wade M T, Popović M A 2015 Opt. Lett. 40 4206 Google Scholar
[95]	Xie X, Khurgin J, Kang J, Chow F S 2003 IEEE Photonics Technol. Lett. 15 531 Google Scholar
[96]	Tazawa H, Steier W H 2005 IEEE Photonics Technol. Lett. 17 1851 Google Scholar
[97]	Cardenas J, Morton P A, Khurgin J B, Griffith A, Poitras C B, Preston K, Lipson M 2013 Opt. Express 21 22549 Google Scholar
[98]	Zhang J, Leroux X, Duraán-Valdeiglesias E, Alonso-Ramos C, Marris-Morini D, Vivien L, He S, Cassan E 2018 ACS Photonics 5 4229 Google Scholar
[99]	Terrel M, Digonnet M J, Fan S 2009 Appl. Optics 48 4874 Google Scholar
[100]	Yu Y, Chen Y, Hu H, Xue W, Yvind K, Mork J 2015 Laser Photon. Rev. 9 241 Google Scholar
[101]	Yang K Y, Skarda J, Cotrufo M, Dutt A, Ahn G H, Sawaby M, Vercruysse D, Arbabian A, Fan S, Alù A J 2019 Conference on Lasers and Electro-Optics (CLEO) San Jose, USA, May 1–5, 2019 pSW4J.3
[102]	Kivshar Y, Rybin M 2017 Nat. Photonics 11 212 Google Scholar
[103]	An Y, Fu T, Liu Q, Ouyang Z 2020 Appl. Phys. Express 13 032006 Google Scholar
[104]	Zangeneh-Nejad F, Fleury R 2019 Phys. Rev. Lett. 122 014301 Google Scholar

[1]	陈召, 马昕新, 李童, 王艺霖. 耦合谐振系统中基于Fano共振的光学压力传感器. 物理学报, 2024, 73(8): 084205. doi: 10.7498/aps.73.20232025
[2]	刘宁, 刘肯, 朱志宏. 集成二维材料非线性光学特性研究进展. 物理学报, 2023, 72(17): 174202. doi: 10.7498/aps.72.20230729
[3]	杨其利, 张兴坊, 刘凤收, 闫昕, 梁兰菊. 劈裂环-盘二聚体结构的多重Fano共振. 物理学报, 2022, 71(2): 027802. doi: 10.7498/aps.71.20210855
[4]	杨其利, 张兴坊. 劈裂环-盘二聚体结构的多重Fano共振研究. 物理学报, 2021, (): . doi: 10.7498/aps.70.20210855
[5]	朱一帆, 耿滔. 谐振腔内的高质量圆对称艾里光束的产生方法. 物理学报, 2020, 69(1): 014205. doi: 10.7498/aps.69.20191088
[6]	张兴坊, 刘凤收, 闫昕, 梁兰菊, 韦德全. 同心椭圆柱-纳米管结构的双重Fano共振研究. 物理学报, 2019, 68(6): 067301. doi: 10.7498/aps.68.20182249
[7]	李爱云, 张兴坊, 刘凤收, 闫昕, 梁兰菊. 对称纳米棒三聚体结构的Fano共振特性研究. 物理学报, 2019, 68(19): 197801. doi: 10.7498/aps.68.20190978
[8]	陈颖, 曹景刚, 谢进朝, 高新贝, 许扬眉, 李少华. 含双挡板金属-电介质-金属波导耦合方形腔的独立调谐双重Fano共振特性. 物理学报, 2019, 68(10): 107302. doi: 10.7498/aps.68.20181985
[9]	涂鑫, 陈震旻, 付红岩. 硅基光波导开关技术综述. 物理学报, 2019, 68(10): 104210. doi: 10.7498/aps.68.20190011
[10]	梁振江, 刘海霞, 牛燕雄, 刘凯铭, 尹贻恒. THz谐振腔型石墨烯光电探测器的设计. 物理学报, 2016, 65(16): 168101. doi: 10.7498/aps.65.168101
[11]	李培, 王辅忠, 张丽珠, 张光璐. 左手介质对谐振腔谐振频率的影响. 物理学报, 2015, 64(12): 124103. doi: 10.7498/aps.64.124103
[12]	庄煜阳, 周雯, 季珂, 陈鹤鸣. 一种双反射壁型二维光子晶体窄带滤波器. 物理学报, 2015, 64(22): 224202. doi: 10.7498/aps.64.224202
[13]	肖金标, 罗辉, 徐银, 孙小菡. 硅基槽式微环谐振腔型偏振解复用器全矢量分析. 物理学报, 2015, 64(19): 194207. doi: 10.7498/aps.64.194207
[14]	周培基, 李智勇, 俞育德, 余金中. 硅基光子集成研究进展. 物理学报, 2014, 63(10): 104218. doi: 10.7498/aps.63.104218
[15]	杨彪, 李智勇, 肖希, Nemkova Anastasia, 余金中, 俞育德. 硅基光栅耦合器的研究进展. 物理学报, 2013, 62(18): 184214. doi: 10.7498/aps.62.184214
[16]	雷朝军, 喻胜, 李宏福, 牛新建, 刘迎辉, 候慎勇, 张天钟. 缓变回旋管谐振腔研究. 物理学报, 2012, 61(18): 180202. doi: 10.7498/aps.61.180202
[17]	方进勇, 黄惠军, 张治强, 黄文华, 江伟华. 基于圆柱谐振腔的高功率微波脉冲压缩系统. 物理学报, 2011, 60(4): 048404. doi: 10.7498/aps.60.048404
[18]	柏宁丰, 洪玮, 孙小菡. 复合缺陷型电磁帯隙谐振腔. 物理学报, 2011, 60(1): 018401. doi: 10.7498/aps.60.018401
[19]	刘畅, 罗尧天, 唐昌建, 刘濮鲲. 回旋管光子带隙谐振腔冷腔电磁模式分析. 物理学报, 2009, 58(12): 8174-8179. doi: 10.7498/aps.58.8174
[20]	刘漾, 巩华荣, 魏彦玉, 宫玉彬, 王文祥, 廖复疆. 有效抑制光子晶体加载矩形谐振腔中模式竞争的方法. 物理学报, 2009, 58(11): 7845-7851. doi: 10.7498/aps.58.7845

计量

文章访问数: 17524
PDF下载量: 987
被引次数: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

搜索

留言板