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In this paper, an improved hybrid surface plasmon nanolaser with a gain medium ridge and a layer of air gap is proposed. In order to achieve low propagation loss and sub-wavelength field confinement, a triangular air gap and a 50 nm microcavity end face silver mirror are adopted in this structure, and the combination of this particular triangular structure and silver mirror effectively improves the performance of nano-laser. In this paper, we numerically simulate the waveguide by using the finite-element method. The COMSOL multiphysics software is a superior numerical simulation software to simulate the real physical phenomena based on the finite element method. On the basic of the COMSOL multiphysics software, a two-dimensional cross-section model and a three-dimensional model are built, the transmission performance and microcavity performance of the improved structure are analyzed in detail at a working wavelength of 1550 nm. Some quantities including the electric field distribution, transmission length, normalized mode field area, average energy density, foundation modal volume, quality factor of the structure, threshold gain, quality factor, effective modal volume, and Purcell factor are considered here which are dependent on the dielectric constant and geometrical parameters. The results indicate that on a two-dimensional scale, the contradiction between transmission loss and transmission distance can be effectively solved by the guidance of Fom value, and the IHPM laser structure with optimal transmission characteristics is obtained under the guidance of quality factor and foundation modal volume. A deep sub-wavelength constraint on light is achieved:the propagation length of the electromagnetic mode reaches a millimeter level and the longest distance can reach 1.29 mm. When testing the microcavity performance of the laser separately on a two-dimensional scale and three-dimensional scale, the high quality factor, low gain threshold, ultra-small effective mode volume of 0.001092 μm3 and ultra-high Purcell factor of 8.29×105 are obtained by adjusting the structural parameters and plating a 50 nm-thick silver layer on the end face of the laser microcavity. Compared with the previous structure without air gaps, the designed structure has a low laser lasing threshold and strong micro-cavity local capability when these two structural parameters are unified. The designed hybrid surface plasmon nanolaser may serve as a fundamental building block for various functional photonic components and can have applications such as in sensing, nanofocusing, and nanolasing.
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Keywords:
- hybrid surface plasmons waveguide /
- nanolaser /
- finite-element method /
- micro-cavity
[1] Han Q Y, Tang J C, Zhang S, Wang C, Ma H Q, Yu L, Jiao R Z (in Chinese) [韩清瑶, 汤俊超, 张弨, 王川, 马海强, 于丽, 焦荣珍 2012 物理学报 61 135202]
[2] Zhang Y, Zhang Z 2016 Plasmonics 12 1
[3] Wang M S, Zhao C L, Miao X Y, Zhao Y H, Rufo J, Liu Y J, Huang T J, Zheng Y B 2015 Small (Germany:Weinheim an der Bergstrasse) 11 4422
[4] O'Dell D, Serey X, Erickson D 2014 Appl. Phys. Lett. 104 043112
[5] Maier S A, Kik P G, Atwater H A, Meltzer S, Harel E, Koel B E, Requicha A A G 2003 Nat. Mater. 2 229
[6] Berini P 2009 Adv. Opt. Photon. News 1 484
[7] Ly-Gagnon D S, Kocabas S E, Miller D A B 2008 IEEE J. Sel. Top. Quantum Electron. 14 1473
[8] Fu Y, Hu X, Lu C, Yue S, Yang H, Gong Q 2012 Nano Lett. 12 5784
[9] Bian Y, Zheng Z, Zhao X, Liu L, Liu J, Zhu J, Zhou T 2013 Opt. Commun. 287 245
[10] Avrutsky I, Soref R, Buchwald W 2010 Opt. Express 18 348
[11] Oulton R F, Sorger V J, Genov D A, Pile D F P, Zhang X 2008 Nat. Photon. 2 496.
[12] Chang S W, Chuang S L 2008 IEEE 2008 International Nano-Optoelectronics Workshop (i-Now) Japan, Tokyo, August 2-15, 2008 p195
[13] Zhang Z G 2015 M. S. Dissertation (Qinhuangdao:Yanshan University) (in Chinese) [张振国 2015 硕士学位论文 (秦皇岛:燕山大学)]
[14] Purcell E M 1995 Phys. Rev. 69 11
[15] Oulton R F, Sorger V J, Zentgraf T, Ma R M, Gladden C, Dai L, Bartal1 G, Zhang X 2009 Nature 461 629
[16] Wei W 2015 M. S. Dissertation (Beijing:Beijing University of Posts and Telecommunications) (in Chinese) [魏巍 2015 博士学位论文 (北京:北京邮电大学)]
[17] Li S X, Bai Z C, Huang Z, Zhang X, Qin S J, Mao W X 2012 Acta Phys. Sin. 61 115201 (in Chinese) [李世雄, 白忠臣, 黄政, 张欣, 秦水介, 毛文雪 2012 物理学报 61 115201]
[18] Li Q, Yu B Q, Li Z F, Wang X F, Zhang Z C, Pan L F 2017 Chin. Phys. B 26 085202
[19] Zou C L, Sun F W, Xiao Y F, Dong C H, Chen X D, Cui J M, Gong Q, Han Z F, Guo G C 2010 Appl. Phys. Lett. 97 183102
[20] Zhang B, Bian Y, Ren L, Guo F, Tang S Y, Mao Z, Liu X, Sun J J, Gong J Y, Guo X S, Huang T J 2017 Sci. Rep. 7 40479
[21] Huang H, Zhao Q, Hong K, Xu Q, Huang X 2014 Physica E 57 113
[22] Tian J, Sun M 2016 Eur. Phys. J. D 70 4
[23] Piao R Q 2016 M. S. Dissertation (Qinhuangdao:Yanshan University) (in Chinese) [朴瑞琦 2016 硕士学位论文 (秦皇岛:燕山大学)]
[24] Dai D, Shi Y, He S, Wosinski L, Thylen L 2011 Opt. Express 19 12925
[25] Gamzatov A G, Batdalov A B, Kamilov I K, Kaul A R, Babushkina N A 2013 Appl. Phys. Lett. 102 032404
[26] Chu H S, Bai P, Li E P, Hoefer W R J 2011 Plasmonics 6 591
[27] Zhu L, Zhao Y 2010 J. Opt. Soc. Am. B 27 1260
[28] Liu J T, Xu B Z, Zhang J, Cai L K, Song G F 2012 Chin. Phys. B 21 107303
[29] Cheng P J, Weng C Y, Chang S W, Lin T R, Tien C H 2013 Opt. Express 21 13479
[30] Wei B, Sheng X Z 2007 The Principle and Application of the Laser (Chongqing:Chongqing University Press) pp116-120 (in Chinese) [魏彪, 盛新志 2007激光原理(重庆:重庆大学出版社) 第116–120页]
[31] Sun W Z 2016 M. S. Dissertation (Haerbin:Harbin Institute of Technology) (in Chinese) [孙文钊 2016 硕士学位论文 (哈尔滨:哈尔滨工业大学)]
[32] Chou B T, Chou Y H, Chiang C K, Wu Y M 2015 IEEE J. Sel. Top. Quantum Electron. 21 6
[33] Wei W, Xin Y, Xia Z 2016 Sci. Rep. 6 33063
[34] Lu Q, Shu F J, Zou C L 2013 Opt. Lett. 38 5311
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[1] Han Q Y, Tang J C, Zhang S, Wang C, Ma H Q, Yu L, Jiao R Z (in Chinese) [韩清瑶, 汤俊超, 张弨, 王川, 马海强, 于丽, 焦荣珍 2012 物理学报 61 135202]
[2] Zhang Y, Zhang Z 2016 Plasmonics 12 1
[3] Wang M S, Zhao C L, Miao X Y, Zhao Y H, Rufo J, Liu Y J, Huang T J, Zheng Y B 2015 Small (Germany:Weinheim an der Bergstrasse) 11 4422
[4] O'Dell D, Serey X, Erickson D 2014 Appl. Phys. Lett. 104 043112
[5] Maier S A, Kik P G, Atwater H A, Meltzer S, Harel E, Koel B E, Requicha A A G 2003 Nat. Mater. 2 229
[6] Berini P 2009 Adv. Opt. Photon. News 1 484
[7] Ly-Gagnon D S, Kocabas S E, Miller D A B 2008 IEEE J. Sel. Top. Quantum Electron. 14 1473
[8] Fu Y, Hu X, Lu C, Yue S, Yang H, Gong Q 2012 Nano Lett. 12 5784
[9] Bian Y, Zheng Z, Zhao X, Liu L, Liu J, Zhu J, Zhou T 2013 Opt. Commun. 287 245
[10] Avrutsky I, Soref R, Buchwald W 2010 Opt. Express 18 348
[11] Oulton R F, Sorger V J, Genov D A, Pile D F P, Zhang X 2008 Nat. Photon. 2 496.
[12] Chang S W, Chuang S L 2008 IEEE 2008 International Nano-Optoelectronics Workshop (i-Now) Japan, Tokyo, August 2-15, 2008 p195
[13] Zhang Z G 2015 M. S. Dissertation (Qinhuangdao:Yanshan University) (in Chinese) [张振国 2015 硕士学位论文 (秦皇岛:燕山大学)]
[14] Purcell E M 1995 Phys. Rev. 69 11
[15] Oulton R F, Sorger V J, Zentgraf T, Ma R M, Gladden C, Dai L, Bartal1 G, Zhang X 2009 Nature 461 629
[16] Wei W 2015 M. S. Dissertation (Beijing:Beijing University of Posts and Telecommunications) (in Chinese) [魏巍 2015 博士学位论文 (北京:北京邮电大学)]
[17] Li S X, Bai Z C, Huang Z, Zhang X, Qin S J, Mao W X 2012 Acta Phys. Sin. 61 115201 (in Chinese) [李世雄, 白忠臣, 黄政, 张欣, 秦水介, 毛文雪 2012 物理学报 61 115201]
[18] Li Q, Yu B Q, Li Z F, Wang X F, Zhang Z C, Pan L F 2017 Chin. Phys. B 26 085202
[19] Zou C L, Sun F W, Xiao Y F, Dong C H, Chen X D, Cui J M, Gong Q, Han Z F, Guo G C 2010 Appl. Phys. Lett. 97 183102
[20] Zhang B, Bian Y, Ren L, Guo F, Tang S Y, Mao Z, Liu X, Sun J J, Gong J Y, Guo X S, Huang T J 2017 Sci. Rep. 7 40479
[21] Huang H, Zhao Q, Hong K, Xu Q, Huang X 2014 Physica E 57 113
[22] Tian J, Sun M 2016 Eur. Phys. J. D 70 4
[23] Piao R Q 2016 M. S. Dissertation (Qinhuangdao:Yanshan University) (in Chinese) [朴瑞琦 2016 硕士学位论文 (秦皇岛:燕山大学)]
[24] Dai D, Shi Y, He S, Wosinski L, Thylen L 2011 Opt. Express 19 12925
[25] Gamzatov A G, Batdalov A B, Kamilov I K, Kaul A R, Babushkina N A 2013 Appl. Phys. Lett. 102 032404
[26] Chu H S, Bai P, Li E P, Hoefer W R J 2011 Plasmonics 6 591
[27] Zhu L, Zhao Y 2010 J. Opt. Soc. Am. B 27 1260
[28] Liu J T, Xu B Z, Zhang J, Cai L K, Song G F 2012 Chin. Phys. B 21 107303
[29] Cheng P J, Weng C Y, Chang S W, Lin T R, Tien C H 2013 Opt. Express 21 13479
[30] Wei B, Sheng X Z 2007 The Principle and Application of the Laser (Chongqing:Chongqing University Press) pp116-120 (in Chinese) [魏彪, 盛新志 2007激光原理(重庆:重庆大学出版社) 第116–120页]
[31] Sun W Z 2016 M. S. Dissertation (Haerbin:Harbin Institute of Technology) (in Chinese) [孙文钊 2016 硕士学位论文 (哈尔滨:哈尔滨工业大学)]
[32] Chou B T, Chou Y H, Chiang C K, Wu Y M 2015 IEEE J. Sel. Top. Quantum Electron. 21 6
[33] Wei W, Xin Y, Xia Z 2016 Sci. Rep. 6 33063
[34] Lu Q, Shu F J, Zou C L 2013 Opt. Lett. 38 5311
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