Topological multipolar corner state in a supercell metasurface and its interplay with two-dimensional materials

Zhaojian Zhang; Junbo Yang; Te Du; Xinpeng Jiang

doi:10.1364/PRJ.443025

[1] M. Z. Hasan, C. L. Kane. Colloquium: topological insulators. Rev. Mod. Phys., 82, 3045-3067(2010).

[2] X. L. Qi, S. C. Zhang. Topological insulators and superconductors. Rev. Mod. Phys., 83, 1057-1110(2011).

[3] M. J. Gilbert. Topological electronics. Commun. Phys., 4, 70(2021).

[4] S. D. Huber. Topological mechanics. Nat. Phys., 12, 621-623(2016).

[5] X. Zhang, M. Xiao, Y. Cheng, M. H. Lu, J. Christensen. Topological sound. Commun. Phys., 1, 97(2018).

[6] L. Lu, J. D. Joannopoulos, M. Soljacic. Topological photonics. Nat. Photonics, 8, 821-829(2014).

[7] T. Ozawa, H. M. Price, A. Amo, N. Goldman, M. Hafezi, L. Lu, M. C. Rechtsman, D. Schuster, J. Simon, O. Zilberberg, I. Carusotto. Topological photonics. Rev. Mod. Phys., 91, 015006(2019).

[8] Z. Chen, M. Segev. Highlighting photonics: looking into the next decade. eLight, 1, 2(2021).

[9] X. T. He, E. T. Liang, J. J. Yuan, H. Y. Qiu, X. D. Chen, F. L. Zhao, J. W. Dong. A silicon-on-insulator slab for topological valley transport. Nat. Commun., 10, 872(2019).

[10] M. I. Shalaev, W. Walasik, A. Xu, Y. Tsukernik, N. M. Litchinitser. Robust topologically protected transport in photonic crystals at telecommunication wavelengths. Nat. Nanotechnol., 14, 31-34(2019).

[11] M. Serra-Garcia, V. Peri, R. Süsstrunk, O. R. Bilal, T. Larsen, L. G. Villanueva, S. D. Huber. Observation of a phononic quadrupole topological insulator. Nature, 555, 342-345(2018).

[12] C. W. Peterson, W. A. Benalcazar, T. L. Hughes, G. Bahl. A quantized microwave quadrupole insulator with topologically protected corner states. Nature, 555, 346-350(2018).

[13] S. Imhof, C. Berger, F. Bayer, J. Brehm, L. W. Molenkamp, T. Kiessling, R. Thomale. Topolectrical-circuit realization of topological corner modes. Nat. Phys., 14, 925-929(2018).

[14] B. Y. Xie, H. F. Wang, H. X. Wang, X. Y. Zhu, J. H. Jiang, M. H. Lu, Y. F. Chen. Second-order photonic topological insulator with corner states. Phys. Rev. B, 98, 205147(2018).

[15] B. Y. Xie, G. X. Su, H. F. Wang, H. Su, X. P. Shen, P. Zhan, M. H. Lu, Z. L. Wang, Y. F. Chen. Visualization of higher-order topological insulating phases in two-dimensional dielectric photonic crystals. Phys. Rev. Lett., 122, 233903(2019).

[16] Y. Ota, F. Liu, R. Katsumi, K. Watanabe, K. Wakabayashi, Y. Arakawa, S. Iwamoto. Photonic crystal nanocavity based on a topological corner state. Optica, 6, 786-789(2019).

[17] X. Xie, W. Zhang, X. He, S. Wu, J. Dang, K. Peng, X. Xu. Cavity quantum electrodynamics with second-order topological corner state. Laser Photon. Rev., 14, 1900425(2020).

[18] W. Zhang, X. Xie, H. Hao, J. Dang, S. Xiao, S. Shi, H. Ni, Z. Niu, C. Wang, K. Jin, X. Zhang, X. Xu. Low-threshold topological nanolasers based on the second-order corner state. Light Sci. Appl., 9, 109(2020).

[19] H. R. Kim, M. S. Hwang, D. Smirnova, K. Y. Jeong, Y. Kivshar, H. G. Park. Multipolar lasing modes from topological corner states. Nat. Commun., 11, 5758(2020).

[20] P. Törmä, W. L. Barnes. Strong coupling between surface plasmon polaritons and emitters: a review. Rep. Prog. Phys., 78, 013901(2014).

[21] D. G. Baranov, M. Wersall, J. Cuadra, T. J. Antosiewicz, T. Shegai. Novel nanostructures and materials for strong light–matter interactions. ACS Photon., 5, 24-42(2018).

[22] D. N. Basov, M. M. Fogler, F. J. García de Abajo. Polaritons in van der Waals materials. Science, 354, aag1992(2016).

[23] N. Rivera, I. Kaminer. Light–matter interactions with photonic quasiparticles. Nat. Rev. Phys., 2, 538-561(2020).

[24] A. Amo, T. C. H. Liew, C. Adrados, R. Houdré, E. Giacobino, A. V. Kavokin, A. Bramati. Exciton–polariton spin switches. Nat. Photonics, 4, 361-366(2010).

[25] E. Orgiu, J. George, J. A. Hutchison, E. Devaux, J. F. Dayen, B. Doudin, F. Stellacci, C. Genet, J. Schachenmayer, C. Genes, G. Pupillo, P. Samorì, T. W. Ebbesen. Conductivity in organic semiconductors hybridized with the vacuum field. Nat. Mater., 14, 1123-1129(2015).

[26] A. Thomas, L. Lethuillier-Karl, K. Nagarajan, M. A. Vergauwe, J. George, T. Chervy, A. Shalabney, E. Devaux, C. Genet, J. Moran, T. W. Ebbesen. Tilting a ground-state reactivity landscape by vibrational strong coupling. Science, 363, 615-619(2019).

[27] T. Karzig, C. E. Bardyn, N. H. Lindner, G. Refael. Topological polaritons. Phys. Rev. X, 5, 031001(2015).

[28] D. D. Solnyshkov, G. Malpuech, P. St-Jean, S. Ravets, J. Bloch, A. Amo. Microcavity polaritons for topological photonics. Opt. Mater. Express, 11, 1119-1142(2021).

[29] S. Klembt, T. H. Harder, O. A. Egorov, K. Winkler, R. Ge, M. A. Bandres, M. Emmerling, L. Worschech, T. C. H. Liew, M. Segev, C. Schneider, S. Höfling. Exciton-polariton topological insulator. Nature, 562, 552-556(2018).

[30] P. St-Jean, V. Goblot, E. Galopin, A. Lemaître, T. Ozawa, L. le Gratiet, I. Sagnes, J. Bloch, A. Amo. Lasing in topological edge states of a one-dimensional lattice. Nat. Photonics, 11, 651-656(2017).

[31] W. Liu, Z. Ji, Y. Wang, G. Modi, M. Hwang, B. Zheng, V. J. Sorger, A. Pan, R. Agarwal. Generation of helical topological exciton-polaritons. Science, 370, 600-604(2020).

[32] M. Li, I. Sinev, F. Benimetskiy, T. Ivanova, E. Khestanova, S. Kiriushechkina, A. Vakulenko, S. Guddala, M. Skolnick, V. Menon, D. Krizhanovskii, A. Alù, A. Samusev, A. B. Khanikaev. Experimental observation of topological Z₂ exciton-polaritons in transition metal dichalcogenide monolayers. Nat. Commun., 12, 4425(2021).

[33] Q. He, S. Sun, L. Zhou. Tunable/reconfigurable metasurfaces: physics and applications. Research, 2019, 1849272(2019).

[34] X. Cheng, C. Jouvaud, X. Ni, S. H. Mousavi, A. Z. Genack, A. B. Khanikaev. Robust reconfigurable electromagnetic pathways within a photonic topological insulator. Nat. Mater., 15, 542-548(2016).

[35] M. Goryachev, M. E. Tobar. Reconfigurable microwave photonic topological insulator. Phys. Rev. Appl., 6, 064006(2016).

[36] M. I. Shalaev, S. Desnavi, W. Walasik, N. M. Litchinitser. Reconfigurable topological photonic crystal. New J. Phys., 20, 023040(2018).

[37] Y. Wang, W. Zhang, X. Zhang. Tunable topological valley transport in two-dimensional photonic crystals. New J. Phys., 21, 093020(2019).

[38] T. Cao, L. Fang, Y. Cao, N. Li, Z. Fan, Z. Tao. Dynamically reconfigurable topological edge state in phase change photonic crystals. Sci. Bull., 64, 814-822(2019).

[39] M. I. Shalaev, W. Walasik, N. M. Litchinitser. Optically tunable topological photonic crystal. Optica, 6, 839-844(2019).

[40] J. Wang, Y. Liu, D. Yang, Z. Hu, X. Zhang, S. Xia, J. Xu. Tunable terahertz topological edge and corner states in designer surface plasmon crystals. Opt. Express, 29, 19531-19539(2021).

[41] F. Bonaccorso, Z. Sun, T. Hasan, A. C. Ferrari. Graphene photonics and optoelectronics. Nat. Photonics, 4, 611-622(2010).

[42] Z. Song, H. Liu, N. Huang, Z. Wang. Electrically tunable robust edge states in graphene-based topological photonic crystal slabs. J. Phys. D, 51, 095108(2018).

[43] M. A. Gorlach, X. Ni, D. A. Smirnova, D. Korobkin, D. Zhirihin, A. P. Slobozhanyuk, P. A. Belov, A. Alù, A. B. Khanikaev. Far-field probing of leaky topological states in all-dielectric metasurfaces. Nat. Commun., 9, 909(2018).

[44] D. Smirnova, S. Kruk, D. Leykam, E. Melik-Gaykazyan, D. Y. Choi, Y. Kivshar. Third-harmonic generation in photonic topological metasurfaces. Phys. Rev. Lett., 123, 103901(2019).

[45] W. L. Barnes, A. Dereux, T. W. Ebbesen. Surface plasmon subwavelength optics. Nature, 424, 824-830(2003).

[46] S. Jahani, Z. Jacob. All-dielectric metamaterials. Nat. Nanotechnol., 11, 23-36(2016).

[47] K. Ohtani, B. Meng, M. Franckié, L. Bosco, C. Ndebeka-Bandou, M. Beck, J. Faist. An electrically pumped phonon-polariton laser. Sci. Adv., 5, eaau1632(2019).

[48] X. Song, S. A. Dereshgi, E. Palacios, Y. Xiang, K. Aydin. Enhanced interaction of optical phonons in h-BN with plasmonic lattice and cavity modes. ACS Appl. Mater. Interfaces, 13, 25224-25233(2021).

[49] M. Barra-Burillo, U. Muniain, S. Catalano, F. Casanova, L. E. Hueso, J. Aizpurua, R. Esteban, R. Hillenbrand. Microcavity phonon polaritons from weak to ultrastrong phonon-photon coupling(2021).

[50] J. D. Caldwell, L. Lindsay, V. Giannini, I. Vurgaftman, T. L. Reinecke, S. A. Maier, O. J. Glembocki. Low-loss, infrared and terahertz nanophotonics using surface phonon polaritons. Nanophotonics, 4, 44-68(2015).

[51] D. Sanvitto, S. Kéna-Cohen. The road towards polaritonic devices. Nat. Mater., 15, 1061-1073(2016).

[52] S. Guddala, F. Komissarenko, S. Kiriushechkina, A. Vakulenko, M. Li, V. M. Menon, A. B. Khanikaev. Topological phonon-polariton funneling in midinfrared metasurfaces. Science, 374, 225-227(2021).

[53] E. D. Palik. Handbook of Optical Constants of Solids, 3(1998).

[54] J. D. Joannopoulos, S. G. Johnson, J. N. Winn, R. D. Meade. Molding the Flow of Light(2008).

[55] S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, L. A. Kolodziejski. Guided modes in photonic crystal slabs. Phys. Rev. B, 60, 5751-5758(1999).

[56] R. Gansch, S. Kalchmair, H. Detz, A. M. Andrews, P. Klang, W. Schrenk, G. Strasser. Higher order modes in photonic crystal slabs. Opt. Express, 19, 15990-15995(2011).

[57] H. Y. Ryu, J. K. Hwang, Y. H. Lee. Conditions of single guided mode in two-dimensional triangular photonic crystal slab waveguides. J. Appl. Phys., 88, 4941-4946(2000).

[58] L. C. Andreani, M. Agio. Photonic bands and gap maps in a photonic crystal slab. IEEE J. Quantum Electron., 38, 891-898(2002).

[59] Z. Zhang, J. W. You, Z. Lan, N. C. Panoiu. Lattice topological edge and corner modes of photonic crystal slabs. J. Opt., 23, 095102(2021).

[60] M. F. Limonov, M. V. Rybin, A. N. Poddubny, Y. S. Kivshar. Fano resonances in photonics. Nat. Photonics, 11, 543-554(2017).

[61] N. Papasimakis, V. A. Fedotov, Y. H. Fu, D. P. Tsai, N. I. Zheludev. Coherent and incoherent metamaterials and order-disorder transitions. Phys. Rev. B, 80, 041102(2009).

[62] V. A. Fedotov, N. Papasimakis, E. Plum, A. Bitzer, M. Walther, P. Kuo, N. I. Zheludev. Spectral collapse in ensembles of metamolecules. Phys. Rev. Lett., 104, 223901(2010).

[63] F. Xie, W. Wu, M. Ren, W. Cai, J. Xu. Lattice collective interaction engineered optical activity in metamaterials. Adv. Opt. Mater., 8, 1901435(2020).

[64] N. I. Zheludev, S. L. Prosvirnin, N. Papasimakis, V. A. Fedotov. Lasing spaser. Nat. Photonics, 2, 351-354(2008).

[65] N. Rivera, T. Christensen, P. Narang. Phonon polaritonics in two-dimensional materials. Nano Lett., 19, 2653-2660(2019).

[66] N. Li, X. Guo, X. Yang, R. Qi, T. Qiao, Y. Li, R. Shi, Y. Li, K. Liu, Z. Xu, L. Liu, F. Javier García de Abajo, Q. Dai, E. G. Wang, P. Gao. Direct observation of highly confined phonon polaritons in suspended monolayer hexagonal boron nitride. Nat. Mater., 20, 43-48(2021).

[67] A. J. Giles, S. Dai, I. Vurgaftman, T. Hoffman, S. Liu, L. Lindsay, C. T. Ellis, N. Assefa, I. Chatzakis, T. L. Reinecke, J. G. Tischler, M. M. Fogler, J. H. Edgar, D. N. Basov, J. D. Caldwell. Ultralow-loss polaritons in isotopically pure boron nitride. Nat. Mater., 17, 134-139(2018).

[68] E. S. H. Kang, S. Chen, S. Sardar, D. Tordera, N. Armakavicius, V. Darakchieva, T. Shegai, M. P. Jonsson. Strong plasmon–exciton coupling with directional absorption features in optically thin hybrid nanohole metasurfaces. ACS Photon., 5, 4046-4055(2018).

[69] L. Novotny. Strong coupling, energy splitting, and level crossings: a classical perspective. Am. J. Phys., 78, 1199-1202(2020).

[70] M. Autore, P. Li, I. Dolado, F. J. Alfaro-Mozaz, R. Esteban, A. Atxabal, F. Casanova, L. E. Hueso, P. Alonso-González, J. Aizpurua, A. Y. Nikitin, S. Vélez, R. Hillenbrand. Boron nitride nanoresonators for phonon-enhanced molecular vibrational spectroscopy at the strong coupling limit. Light Sci. Appl., 7, 17172(2018).

[71] A. Bylinkin, M. Schnell, M. Autore, F. Calavalle, P. Li, J. Taboada-Gutièrrez, S. Liu, J. H. Edgar, F. Casanova, L. E. Hueso, P. Alonso-Gonzalez, A. Y. Nikitin, R. Hillenbrand. Real-space observation of vibrational strong coupling between propagating phonon polaritons and organic molecules. Nat. Photonics, 15, 197-202(2021).

[72] M. Qin, S. Xiao, W. Liu, M. Ouyang, T. Yu, T. Wang, Q. Liao. Strong coupling between excitons and magnetic dipole quasi-bound states in the continuum in WS₂-TiO₂ hybrid metasurfaces. Opt. Express, 29, 18026-18036(2021).

[73] T. Low, P. Avouris. Graphene plasmonics for terahertz to mid-infrared applications. ACS Nano, 8, 1086-1101(2014).

[74] A. Andryieuski, A. V. Lavrinenko. Graphene metamaterials based tunable terahertz absorber: effective surface conductivity approach. Opt. Express, 21, 9144-9155(2013).

[75] C. Zhang, L. Liang, L. Ding, B. Jin, Y. Hou, C. Li, P. Wu. Label-free measurements on cell apoptosis using a terahertz metamaterial-based biosensor. Appl. Phys. Lett., 108, 241105(2016).

[76] S. X. Xia, X. Zhai, L. L. Wang, S. C. Wen. Plasmonically induced transparency in double-layered graphene nanoribbons. Photon. Res., 6, 692-702(2018).

[77] M. J. Heck, J. F. Bauters, M. L. Davenport, J. K. Doylend, S. Jain, G. Kurczveil, J. E. Bowers. Hybrid silicon photonic integrated circuit technology. IEEE J. Sel. Top. Quantum Electron., 19, 6100117(2012).

[78] C. V. Poulton, M. J. Byrd, P. Russo, E. Timurdogan, M. Khandaker, D. Vermeulen, M. R. Watts. Long-range LiDAR and free-space data communication with high-performance optical phased arrays. IEEE J. Sel. Top. Quantum Electron., 25, 7700108(2019).

[79] Y. Lee, S. J. Kim, H. Park, B. Lee. Metamaterials and metasurfaces for sensor applications. Sensors, 17, 1726(2017).

[80] T. Huang, X. Zhao, S. Zeng, A. Crunteanu, P. P. Shum, N. Yu. Planar nonlinear metasurface optics and their applications. Rep. Prog. Phys., 83, 126101(2020).

[81] A. Cerjan, M. Jürgensen, W. A. Benalcazar, S. Mukherjee, M. C. Rechtsman. Observation of a higher-order topological bound state in the continuum. Phys. Rev. Lett., 125, 213901(2020).

[82] Z. Hu, D. Bongiovanni, D. Jukić, E. Jajtić, S. Xia, D. Song, J. Xu, R. Morandotti, H. Buljan, Z. Chen. Nonlinear control of photonic higher-order topological bound states in the continuum. Light Sci. Appl., 10, 164(2021).

[83] J. Zak. Berry’s phase for energy bands in solids. Phys. Rev. Lett., 62, 2747-2750(1989).

[84] H. X. Wang, G. Y. Guo, J. H. Jiang. Band topology in classical waves: Wilson-loop approach to topological numbers and fragile topology. New J. Phys., 21, 093029(2019).