Topological laser on square lattice with gain-loss-induced higher-order corner modes

doi:10.1088/1674-1056/ad322a

中国物理B ›› 2024, Vol. 33 ›› Issue (6): 60305-060305.doi: 10.1088/1674-1056/ad322a

Topological laser on square lattice with gain-loss-induced higher-order corner modes

Ming-Jie Liao(廖明杰), Mei-Song Wei(韦梅松), Shuailing Wang(王帅领), Jingping Xu(许静平)†, and Yaping Yang(羊亚平)‡

MOE Key Laboratory of Advanced Micro-Structured Materials, School of Physics Science and Engineering, Tongji University, Shanghai 200092, China

收稿日期:2023-12-26 修回日期:2024-02-26 接受日期:2024-03-11 出版日期:2024-06-18 发布日期:2024-06-18
通讯作者: Jingping Xu, Yaping Yang E-mail:xx_jj_pp@tongji.edu.cn；yang_yaping@tongji.edu.cn
基金资助:
This work was supported by the National Natural Science Foundation of China (Grant Nos. 12274326 and 12174288) and the National Key R&D Program of China (Grant No. 2021YFA1400602).

Topological laser on square lattice with gain-loss-induced higher-order corner modes

Ming-Jie Liao(廖明杰), Mei-Song Wei(韦梅松), Shuailing Wang(王帅领), Jingping Xu(许静平)†, and Yaping Yang(羊亚平)‡

MOE Key Laboratory of Advanced Micro-Structured Materials, School of Physics Science and Engineering, Tongji University, Shanghai 200092, China

Received:2023-12-26 Revised:2024-02-26 Accepted:2024-03-11 Online:2024-06-18 Published:2024-06-18
Contact: Jingping Xu, Yaping Yang E-mail:xx_jj_pp@tongji.edu.cn；yang_yaping@tongji.edu.cn
Supported by:
This work was supported by the National Natural Science Foundation of China (Grant Nos. 12274326 and 12174288) and the National Key R&D Program of China (Grant No. 2021YFA1400602).

摘要/Abstract

摘要： We investigate the higher-order topological laser in the two-dimensional (2D) coupled-cavity array. By adding staggered on-site gain and loss to the 2D Hermitian array with a trivial phase, the system will emerge degenerate topological corner modes, which are protected by bulk band gap. For such a non-Hermitian model, by adjusting the parameters of the system and introducing the pumping into the cavity at the corner, a single-mode lasing with topological protection emerges. Furthermore, single-mode lasing exists over a wide range of pumping strengths. No matter where the cavity is initially stimulated, after enough time evolution, all the cavities belonging to the topological corner mode can emit a stable laser.

关键词: topological corner modes, nonlinear saturated gain, single-mode lasing

Abstract: We investigate the higher-order topological laser in the two-dimensional (2D) coupled-cavity array. By adding staggered on-site gain and loss to the 2D Hermitian array with a trivial phase, the system will emerge degenerate topological corner modes, which are protected by bulk band gap. For such a non-Hermitian model, by adjusting the parameters of the system and introducing the pumping into the cavity at the corner, a single-mode lasing with topological protection emerges. Furthermore, single-mode lasing exists over a wide range of pumping strengths. No matter where the cavity is initially stimulated, after enough time evolution, all the cavities belonging to the topological corner mode can emit a stable laser.

Key words: topological corner modes, nonlinear saturated gain, single-mode lasing

中图分类号: (Phases: geometric; dynamic or topological)

03.65.Vf

03.65.Vf (Phases: geometric; dynamic or topological) 42.60.By (Design of specific laser systems) 42.60.-v (Laser optical systems: design and operation)

Ming-Jie Liao(廖明杰), Mei-Song Wei(韦梅松), Shuailing Wang(王帅领), Jingping Xu(许静平), and Yaping Yang(羊亚平). Topological laser on square lattice with gain-loss-induced higher-order corner modes[J]. 中国物理B, 2024, 33(6): 60305-060305.

参考文献

[1] Qi X L and Zhang S C 2011 Rev. Mod. Phys. 83 1057
[2] Haldane F D M and Raghu S 2008 Phys. Rev. Lett. 100 013904
[3] Raghu S and Haldane F D M 2008 Phys. Rev. A 78 033834
[4] Khanikaev A B, Mousavi S H, Tse W K, Kargarian M, MacDonald A H and Shvets G 2013 Nat. Mater. 12 233
[5] Hafezi M, Mittal S, Fan J, Migdall A and Taylor J M 2013 Nat. Photon. 7 1001
[6] Rechtsman M C, Zeuner J M, Plotnik Y, Lumer Y, Podolsky D, Dreisow F, Nolte S, Segev M and Szameit A 2013 Nature 496 196
[7] Wu L H and Hu X 2015 Phys. Rev. Lett. 114 223901
[8] Leykam D and Chong Y D 2016 Phys. Rev. Lett. 117 143901
[9] Slobozhanyuk A P, Khanikaev A B, Filonov D S, Smirnova D A, Miroshnichenko A E and Kivshar Y S 2016 Sci. Rep. 6 22270
[10] Khanikaev A B and Shvets G 2017 Nat. Photon. 11 763
[11] Ota Y, Katsumi R, Watanabe K, Iwamoto S and Arakawa Y 2018 Commun. Phys. 1 86
[12] Ota Y, Liu F, Katsumi R, Watanabe K, Wakabayashi K, Arakawa Y and Iwamoto S 2019 Optica 6 786
[13] Hassan A E, Kunst F K, Moritz A, Andler G, Bergholtz E J and Bourennane M 2019 Nat. Photon. 13 697
[14] Yoshimi H, Yamaguchi T, Ota Y, Arakawa Y and Iwamoto S 2020 Opt. Lett. 45 2648
[15] Prodan E and Prodan C 2009 Phys. Rev. Lett. 103 248101
[16] Yang Z J, Gao F, Shi X H, Lin X, Gao Z, Chong Y Y and Zhang B L 2015 Phys. Rev. Lett. 114 114301
[17] Stenull O, Kane C L and Lubensky T C 2016 Phys. Rev. Lett. 117 068001
[18] Liu Y Z, Xu Y, Zhang S C and Duan W H 2017 Phys. Rev. B 96 064106
[19] Singh S, Wu Q S, Yue C M, Romero A H and Soluyanov A A 2018 Phys. Rev. Mater. 2 114204
[20] Saha K and Garate I 2014 Phys. Rev. B 89 205103
[21] Li J X, Wang L, Liu J X, Li R H, Zhang Z Y and Chen X Q 2020 Phys. Rev. B 101 081403
[22] Ren H J, Shah T, Pfeifer H, Brendel C, Peano V, Marquardt F and Painter O 2022 Nat. Commun. 13 3476
[23] Liu Y Z, Zou N L, Zhao S B, Chen X B, Xu Y and Duan W H 2022 Nano Lett. 22 2120
[24] Yang Y, Wang J H, Liu Y, Cui Y T, Ding G Q and Wang X T 2023 Phys. Rev. B 107 024304
[25] Amigo M G, Vergniory M G, Errea I and Manes J L 2023 Phys. Rev. B 107 144307
[26] Ningyuan J, Owens C, Sommer A, Schuster D and Simon J 2015 Phys. Rev. X 5 021031
[27] Albert V V, Glazman L I and Jiang L 2015 Phys. Rev. Lett. 114 173902
[28] Hadad Y, Soric J C, Khanikaev A B and Alù A 2018 Nat. Electron. 1 178
[29] Zhao E 2018 Ann Phys. 399 289
[30] Lee C H, Imhof S, Berger C, Bayer F, Brehm J, Molenkamp L W, Kiessling T and Thomale R 2018 Commun. Phys. 1 39
[31] Imhof S, Berger C, Bayer F, Brehm J, Molenkamp L W, Kiessling T, Schindler F, Lee C H, Greiter M, Neupert T and Thomale R 2018 Nat. Phys. 14 925
[32] Liu S, Ma S J, Zhang Q, Zhang L, Yang C H, You O, Gao W L, Xiang J Y, Cui T J and Zhang S 2020 Light Sci. Appl. 9 145
[33] Wang Y, Price H M, Zhang B L and Chong Y D 2020 Nat. Commun. 22 2356
[34] Olekhno N A, Kretov E I, Stepanenko A A, Ivanova P A, Yaroshenko V V, Puhtina E M, Filonov D S, Cappello B, Matekovits L and Gorlach M A 2022 Nat. Commun. 11 1436
[35] Zou D Y, Chen T, He W J, Bao J C, Lee CH H, Sun H J and Zhang X D 2021 Nat. Commun. 12 7201
[36] Shi A Q, Peng Y W, Jiang J P, Peng Y C, Peng P, Chen J Z, Chen H S, Wen S C, Lin X, Gao F and Liu J J 2024 Laser Photon. Rev. 2024 2300956
[37] Liu X Y, Lin Z Y, Song W E, Sun J C, Huang C Y, Wu S J, Xiao X J, Xin H R, Zhu S N and Li T 2024 Phys. Rev. Lett. 132 016601
[38] On M B, Ashtiani F, Sanchez-Jacome D, Perez-Lopez D, Yoo S J B and Blanco-Redondo A 2024 Nat. Commun. 15 629
[39] Xu Q X, Peng Y C, Shi A Q, Peng P and Liu J J 2024 J. Opt. Soc. Am. A 41 366
[40] Khanikaev A B and Alù A 2024 Nat. Commun. 15 931
[41] Fritzsche A, Biesenthal T, Maczewsky L J, Becker K, Ehrhardt M, Heinrich M, Thomale R, Joglekar Y N and Szameit A 2024 Nat. Mater. 23 377
[42] Guo H M and Franz M 2009 Phys. Rev. B 80 113102
[43] Xue H Y, Yang Y H, Gao F, Chong Y D and Zhang B L 2019 Nat. Mater. 18 108
[44] Lu X C, Chen Y and Chen H Y 2020 Phys. Rev. B 101 195143
[45] Shen K, Deng W M, Mo H C, Shi F L, Ma F, Chen X D and Dong J W 2023 Opt. Lett. 48 2825
[46] Ma H Y, Zhang Z, Fu P H, Wu J S and Yu X L 2022 Phys. Rev. B 106 245109
[47] Li C A, Choi S J, Zhang S B and Trauzettel B 2022 Phys. Rev. Res. 4 023193
[48] Li S, Yan X X, Gao J H and Hu Y 2022 Opt. Express 30 17054
[49] Zhang W H, Xie X, Hao H M, Dang J C, Xiao S, Shi S S, Ni H Q, Niu Z C, Wang C, Jin K J, Zhang X D, and Xu X L 2020 Light Sci. Appl. 9 109
[50] Wei M S, Liao M J, Wang C, Zhu C J, Yang Y P and Xu J P 2023 Opt. Express 31 3427
[51] Bahari B, Ndao A, Vallini F, Amili A E, Fainman Y and Kanté B 2017 Science 358 636
[52] Harari G, Bandres M A, Lumer Y, Rechtsman M C, Chong Y D, Khajavikhan M, Christodoulides D N and Segev M 2018 Science 359 eaar4003
[53] Bandres M A, Wittek S, Harari G, Parto M, Ren J H, Segev M, Christodoulides D N and Khajavikhan M 2018 Science 359 eaar4005
[54] Zeng Y Q, Chattopadhyay U, Zhu B F, Qiang B, Li J H, Jin Y H, Li L H, Davies A G, Linfield E H, Zhang B L, Chong Y D and Wang Q J 2020 Nature 578 246
[55] Amelio I and Carusotto I 2020 Phys. Rev. X 10 041060
[56] Shao Z K, Chen H Z, Wang S, Mao X R, Yang Z Q, Wang S L, Wang X X, Hu X and Ma R M 2020 Nat. Nanotechnol. 15 67
[57] Pelous A L, Amelio I, Seclĺ M and Carusotto I 2021 Phys. Rev. A 104 053516
[58] Zhong H, Kartashov Y V, Szameit A, Li Y D, Liu C L and Zhang Y Q 2021 APL Photon. 6 040802
[59] Ezawa M 2022 Phys. Rev. Res. 4 013195
[60] Gong Y K, Wong S, Bennett A J, Huffaker D L and Oh S S 2022 ACS Photon. 7 2089
[61] Tian J Y, Tan Q Y, Wang Y T, Yang Y H, Yuan G H, Adamo G and Soci C 2023 Nat. Commun. 14 1433
[62] Wu J Q, Ghosh S J, Gan Y S, Shi Y, Mandal S, Sun H D, Zhang B L, Liew T C H, Su R and Xiong Q H 2023 Sci. Adv. 9 eadg4322
[63] Han S, Cui J Y, Chua Y D, Zeng Y Q, Hu L X, Dai M J, Wang F K, Sun F Y, Zhu S, Li L H, Davies A G, Linfield E H, Tan C S, Kivshar Y and Wang Q J 2023 Light Sci. Appl. 12 145
[64] Longhi S, Gatti D and Valle G D 2015 Sci. Rep. 5 13376
[65] Mittal S, Orre V V, Zhu G Y, Gorlach M A, Poddubny A and Hafezi M 2019 Nat. Photon. 13 692
[66] Wheeler W A, Wagner L K and Hughes T L 2019 Phys. Rev. B 100 245135
[67] Luo X W and Zhang C W 2019 Phys. Rev. Lett. 123 073601
[68] Wei Y Z, Yan B, Peng Y C, Shi A Q, Zhao D Y, Peng R, Xiang Y J and Liu J J 2021 Opt. Lett. 46 3941
[69] Zhu B F, Wang Q, Zeng Y Q, Wang Q J and Chong Y D 2021 Phys. Rev. B 104 L140306
[70] Benalcazar W A, Bernevig B A and Hughes T L 2017 Phys. Rev. B 96 245115
[71] Zhu B F, Wang Q, Leykam D L, Xue H R, Wang Q J and Chong Y D 2022 Phys. Rev. Lett 129 013903

Topological laser on square lattice with gain-loss-induced higher-order corner modes

Topological laser on square lattice with gain-loss-induced higher-order corner modes

RichHTML

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

Metrics

本文评价

推荐阅读 0

[1]	Shi Huang(黄石) and Xi Luo(罗熙). Topological superconductors with spin-triplet pairings and Majorana Fermi arcs[J]. 中国物理B, 2024, 33(8): 87301-087301.
[2]	Wen-Chuang Shang(商文创), Yi-Ning Han(韩熠宁), Shimpei Endo, and Chao Gao(高超). Topological phases and edge modes of an uneven ladder[J]. 中国物理B, 2024, 33(8): 80202-080202.
[3]	Yu-Xiang Xu(徐宇翔), Wen-Jian Tang(唐文剑), Li-Wei Jiang(姜力炜), De-Xing Wu(吴德兴), Heng Wang(王恒), Bing-Cong Xu(许冰聪), and Lin Chen(陈林). Robust optical mode converter based on topological waveguide arrays[J]. 中国物理B, 2024, 33(6): 60306-060306.
[4]	Xin-Xin Xu(许欣欣), Zi-Ming Wang(王梓名), Dong-Hui Xu(许东辉), and Chui-Zhen Chen(陈垂针). Photoinduced Floquet higher-order Weyl semimetal in C₆ symmetric Dirac semimetals[J]. 中国物理B, 2024, 33(6): 67801-067801.
[5]	Sha Jin(金莎), Jian Li(李健), Qing-Xu Li(李清旭), and Jia-Ji Zhu(朱家骥). RKKY interaction in helical higher-order topological insulators[J]. 中国物理B, 2024, 33(7): 77503-077503.
[6]	Yun-Feng Shen(沈云峰), Xiao-Fang Xu(许孝芳), Ming Sun(孙铭), Wen-Ji Zhou(周文佶), and Ya-Jing Chang(常雅箐). Topological edge and corner states of valley photonic crystals with zipper-like boundary conditions[J]. 中国物理B, 2024, 33(4): 44203-044203.
[7]	Xiang-Long Zeng(曾相龙), Wen-Xi Lai(赖文喜), Yi-Wen Wei(魏祎雯), and Yu-Quan Ma(马余全). Quantum geometric tensor and the topological characterization of the extended Su-Schrieffer-Heeger model[J]. 中国物理B, 2024, 33(3): 30310-030310.
[8]	Qiu-Chen Yan(闫秋辰), Rui Ma(马睿), Xiao-Yong Hu(胡小永), and Qi-Huang Gong(龚旗煌). Progress and realization platforms of dynamic topological photonics[J]. 中国物理B, 2024, 33(1): 10301-10301.
[9]	Chao Zeng(曾超), Yue-Ran Shi(石悦然), Yi-Yi Mao(毛一屹), Fei-Fei Wu(武菲菲), Yan-Jun Xie(谢岩骏), Tao Yuan(苑涛), Han-Ning Dai(戴汉宁), and Yu-Ao Chen(陈宇翱). Observation of flat-band localized state in a one-dimensional diamond momentum lattice of ultracold atoms[J]. 中国物理B, 2024, 33(1): 10303-10303.
[10]	Huan Chen(陈焕), Zheng-Rong Liu(刘峥嵘), Rui Chen(陈锐), and Bin Zhou(周斌). Higher-order topological Anderson insulator on the Sierpiński lattice[J]. 中国物理B, 2024, 33(1): 17202-17202.
[11]	Jiu-Sheng Li(李九生) and Yi Chen(陈翊). Multi-channel terahertz focused beam generator based on shared-aperture metasurface[J]. 中国物理B, 2023, 32(12): 124204-124204.
[12]	Xin-Yue Kang(康鑫越), Jin-Yang Li(李金洋), and Si Li(李思). Straight and twisted Weyl nodal line phonons in Ho₂CF₂ material[J]. 中国物理B, 2023, 32(11): 116301-116301.
[13]	Xin Wan(万鑫), Chenyang Peng(彭晨阳), Gang Li(李港), Junhao Yang(杨俊豪), and Xinyuan Qi(齐新元). Topological resonators based on hexagonal-star valley photonic crystals[J]. 中国物理B, 2023, 32(11): 114208-114208.
[14]	Yu Lin(林宇), Yuandan Wang(王元旦), Junhao Yang(杨俊豪), Yixuan Fu(符艺萱), and Xinyuan Qi(齐新元). Topological states switching and group velocity control in two-dimensional non-reciprocal Hermitian photonic lattice[J]. 中国物理B, 2023, 32(11): 114213-114213.
[15]	Yi Qiao(乔艺), Junpeng Cao(曹俊鹏), Wen-Li Yang(杨文力), Kangjie Shi(石康杰), and Yupeng Wang(王玉鹏). Off-diagonal approach to the exact solution of quantum integrable systems[J]. 中国物理B, 2023, 32(11): 117504-117504.