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Graphene is a one-atom-thick planar sheet of sp2-bonded carbon atoms that are densely packed in a honeycomb crystal lattice. Graphene has been found to support plasmons in a wide range from infrared to terahertz. The confinement of plasmons in graphene is stronger than that on metallic surface. Moreover, the plasmon properties can be dynamically adjusted by doping or grating graphene. In this study, a composite structure comprised of graphene and subwavelength grating is proposed. Highly confined plasmons in graphene are excited by using a diffraction grating with guided mode resonance effect. The wave vector of plasmonic wave in graphene is far larger than that of light in vacuum. To excite plasmons in graphene with a freespace optical wave, their large difference in wave vector must be overcome. Optical gratings are widely used to compensate for wave vector mismatches. A diffraction wave generated by the grating structure can overcome the large wave vector difference and excite surface plasmons. The guided-mode resonance can greatly enhance the intensity of the diffraction field and the coupling efficiency between graphene and incident light. When the phase matching between illuminating wave and a guide mode supported by grating is achieved, guided-mode resonance effect occurs. A nearly 100% diffraction efficiency peak in the reflection or transmission spectrum occurs at a certain wavelength. In this study, the influences of graphene and grating structure on the local characteristics (the surface electric field Ex/Ein, quality factor Q, and effective mode area Seff) of surface plasmons are investigated. The effects of the structural parameters (the thickness of the buffer layer T2, the grating period p, the carrier mobility , and the Fermi level EF) on localization properties are analyzed by the finite element method (COMSOL). The results reveal that the localizations of the surface plasmons in the graphene surface is significantly improved at the certain parameters. 1) The increase of T2 will reduce the intensity of electric field on graphene (Ex/Ein), but the quality factor will obtain a certain increase. The excition of highly confined SPPs needs to improve Q and keep the intensity of Ex/Ein, so in this study T2 = 10 nm. 2) By adjusting the quality factor of SPPs can be improved significantly without changing the resonance frequency ( = 0.7 m2(Vs), Qmax = 1793). 3) Small changes in p and EF will make the resonance peak shift obviously, and the electric field on graphene is greatly enhanced (p = 235 nm, Ex/Ein = 3154; EF = 0.72 eV, and Ex/Ein = 3968). Strong localization leads to strong light-matter interaction, and thus the proposed structure has the potential to be used as sensors with high sensitivity and high-efficiency nonlinear optical devices, greatly expanding the application of graphene in nano optics.
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Keywords:
- graphene /
- surface plasmon /
- subwavelength grating /
- guided mode
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[1] Xu H J 2013 M. S. Dissertation ( Nanjing: Southeast University) (in Chinese) [徐红菊 2013 硕士学位论文 (南京:东南大学)]
[2] Liu J L 2010 Ph. D. Dissertation (Harbin:Harbin Institute of Technology) (in Chinese) [刘建龙 2010 博士学位论文 (哈尔滨:哈尔滨工业大学)]
[3] Li S J, Gan S, Mu H R, Xu Q Y, Qiao H, Li P F, Xue Y Z, Bao Q L 2014 New Carbon Mater. 29 329 (in Chinese) [李绍娟, 甘胜, 沐浩然, 徐庆阳, 乔虹, 李鹏飞, 薛运周, 鲍桥梁 2014 新型炭材料 29 329]
[4] Wang B, Zhang X, Yuan X, Teng J 2012 Appl. Phys. Lett. 100 131111
[5] Liu Q Y, Zhang Y P, Zhang H Y, L H H, Li T T, Ren G J 2014 Acta Phys. Sin. 63 075201 (in Chinese) [刘亚青, 张玉萍, 张会云, 吕欢欢, 李彤彤, 任广军 2014 物理学报 63 075201]
[6] Liu P Q, Valmorra F, Maissen C, Faist J 2015 Optica 2 135
[7] Wang W, Leung K K, Fong W K, Wang S F, Hui Y Y Y, Lau S P P, Surya C 2012 Proc. SPIE 8470 84700E
[8] Nasari H, Abrishamian M S 2015 J. Lightwave Technol. 33 1
[9] Gerber J A, Samuel B, OCallahan B T, Raschke M B 2014 Phys. Rev. Lett. 113 055502
[10] Wu H Q, Linghu C Y, Lv H M, Qian H 2013 Chin. Phys. B 22 098106
[11] Jablan M, Buljan H, Soljacic M 2009 Phys. Rev. B 80 245435
[12] Chen P, Al A 2011 ACS Nano 5 5855
[13] Dubinov A A, Aleshkin V Y, Mitin V 2011 J. Phys. Conden. Matter 23 145302
[14] Vakil A, Engheta N 2011 Science 332 1291
[15] Chen J, Badioli M, AIonso-Gonzalez P, Thongrat-tanasiri S, Huth F, Osmond J, Spasenović M, Centeno A, Pesquera A, Godignon P, Elorza A Z, Camara N, Garca de Abajo F G, Hillenbrand R, Koppens F H L 2012 Nature 487 77
[16] Fei Z, Rodin A S, Andreev G O, Bao W, McLeod A S, Wagner M, Zhang L M, Zhao Z, Thiemens M, Dominguez G, Fogler M M, Castro Neto A H, Lau C N, Keilmann F, Basov D N 2012 Nature 487 82
[17] Zhang K B, Zhang H, Cheng X L 2016 Chin. Phys. B 25 037104
[18] Batke E, Heitmann D, Tu C W 1986 Phy. Rev. B 34 6951
[19] Wu S Q, Liu J S, Wang S L, Hu B 2013 Chin. Phys. B 22 104207
[20] Tae K J, Jaehyeon K, Hongkyw C, Choon-Gi C, Sung-Yool C 2012 Nanotechnology 23 132
[21] Long J, Baisong G, Jason H, Caglar G, Michael M, Zhao H, Hans A B, Xiaogan L, Alex Z, Shen Y R, Wang F 2011 Nat. Nanotechnol. 6 630
[22] Yan H, Li X, Chandra B, Tulevski G, Wu Y, Freitag M, Zhu W, Avouris P, Xia F 2012 Nat. Nanotechnol. 7 330
[23] Zheyu F, Sukosin T, Andrea S, Zheng L, Lulu M, Yumin W, Pulickel M A, Peter N, Naomi J H, Javier G D A 2013 ACS Nano 7 2388
[24] Fang Z, Wang Y, Schlather A E, Zhang L, Pulickel M A, Abajo F J G D, Peter N, Xing Z, Naomi J H 2014 Nano Lett. 14 299
[25] Priambodo P S 2003 Dissertation Abstracts International 26 203
[26] Zhao Y, Chen G, Tao Z, Zhang C, Zhu Y 2014 Rsc Adv. 4 26535
[27] Gao W, Shu J, Qiu C, Xu Q 2012 ACS Nano 6 7806
[28] Nikitin A Y, Guinea F, Garcia-Vidal F J, Martin-Moreno L 2011 Phys. Rev. B 84 3239
[29] Yang X X, Kong X Q, Dai Q 2015 Acta Phys. Sin. 64 106801 (in Chinese) [杨晓霞, 孔祥天, 戴庆 2015 物理学报 64 106801]
[30] Xu P P 2014 Ph. D. Dissertation (Hangzhou: Zhejiang University) (in Chinese) [许培鹏 2014 博士学位论文 (杭州: 浙江大学)]
[31] Zhu Y, Bai H, Huang Y 2015 Synthetic Met. 204 57
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