Nonlinear control of photonic higher-order topological bound states in the continuum

Zhichan Hu; Domenico Bongiovanni; Dario Jukić; Ema Jajtić; Shiqi Xia; Daohong Song; Jingjun Xu; Roberto Morandotti; Hrvoje Buljan; Zhigang Chen

doi:10.1038/s41377-021-00607-5

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Nonlinear control of photonic higher-order topological bound states in the continuum

Articles

- Nonlinear control of photonic higher-order topological bound states in the continuum
- Light: Science & Applications Vol. 10, Issue 9, Pages: 1726-1735(2021)
- Affiliations：
  
  1.The MOE Key Laboratory of Weak-Light Nonlinear Photonics, TEDA Applied Physics Institute and School of Physics, Nankai University, 300457, Tianjin, China
  2.INRS-EMT, 1650 Boulevard Lionel-Boulet, Varennes, QC, J3X 1S2, Canada
  3.Faculty of Civil Engineering, University of Zagreb, A. Kačića Miošića 26, 10000, Zagreb, Croatia
  4.Department of Physics, Faculty of Science, University of Zagreb, Bijenička c. 32, 10000, Zagreb, Croatia
  5.Collaborative Innovation Center of Extreme Optics, Shanxi University, 030006, Taiyuan, Shanxi, China
  6.Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, 610054, Chengdu, Sichuan, China
  7.Department of Physics and Astronomy, San Francisco State University, San Francisco, CA, 94132, USA
- Author bio：
  
  Hrvoje Buljan (hbuljan@phy.hr)
  Zhigang Chen (zgchen@nankai.edu.cn)
- Funds：
- DOI：10.1038/s41377-021-00607-5
  CLC：
- Published：30 September 2021，
  
  Published Online：10 August 2021，
  
  Received：27 May 2021，
  
  Revised：26 July 2021，
  
  Accepted：26 July 2021
- Accepted：
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Hu, Z. C. et al. Nonlinear control of photonic higher-order topological bound states in the continuum. Light: Science & Applications, 10, 1726-1735 (2021).
DOI：

Hu, Z. C. et al. Nonlinear control of photonic higher-order topological bound states in the continuum. Light: Science & Applications, 10, 1726-1735 (2021). DOI： 10.1038/s41377-021-00607-5.

摘要

Abstract

Higher-order topological insulators (HOTIs) are recently discovered topological phases

possessing symmetry-protected corner states with fractional charges. An unexpected connection between these states and the seemingly unrelated phenomenon of bound states in the continuum (BICs) was recently unveiled. When nonlinearity is added to the HOTI system

a number of fundamentally important questions arise. For example

how does nonlinearity couple higher-order topological BICs with the rest of the system

including continuum states? In fact

thus far BICs in nonlinear HOTIs have remained unexplored. Here we unveil the interplay of nonlinearity

higher-order topology

and BICs in a photonic platform. We observe topological corner states that are also BICs in a laser-written second-order topological lattice and further demonstrate their nonlinear coupling with edge (but not bulk) modes under the proper action of both self-focusing and defocusing nonlinearities. Theoretically

we calculate the eigenvalue spectrum and analog of the Zak phase in the nonlinear regime

illustrating that a topological BIC can be actively tuned by nonlinearity in such a photonic HOTI. Our studies are applicable to other nonlinear HOTI systems

with promising applications in emerging topology-driven devices.

关键词

Keywords

references

Hasan, M. Z.&Kane, C. L. Colloquium: Topological insulators.Rev. Mod. Phys.82, 3045–3067 (2010)..

Cooper, N. R., Dalibard, J.&Spielman, I. B. Topological bands for ultracold atoms.Rev. Mod. Phys.91, 015005 (2019)..

Ozawa, T. et al. Topological photonics.Rev. Mod. Phys.91, 015006 (2019)..

Wang, Z. et al. Observation of unidirectional backscattering-immune topological electromagnetic states.Nature461, 772–775 (2009)..

Rechtsman, M. C. et al. Photonic Floquet topological insulators.Nature496, 196–200 (2013)..

Hafezi, M. et al. Imaging topological edge states in silicon photonics.Nat. Photonics7, 1001–1005 (2013)..

Benalcazar, W. A., Bernevig, B. A.&Hughes, T. L. Quantized electric multipole insulators.Science357, 61–66 (2017)..

Song, Z. D., Fang, Z.&Fang, C. (d-2)-Dimensional edge states of rotation symmetry protected topological states.Phys. Rev. Lett.119, 246402 (2017)..

Benalcazar, W. A., Bernevig, B. A.&Hughes, T. L. Electric multipole moments, topological multipole moment pumping, and chiral hinge states in crystalline insulators.Phys. Rev. B96, 245115 (2017)..

Langbehn, J. et al. Reflection-symmetric second-order topological insulators and superconductors.Phys. Rev. Lett.119, 246401 (2017)..

Schindler, F. et al. Higher-order topological insulators.Sci. Adv.4, eaat0346 (2018)..

Serra-Garcia, M. et al. Observation of a phononic quadrupole topological insulator.Nature555, 342–345 (2018)..

Peterson, C. W. et al. A quantized microwave quadrupole insulator with topologically protected corner states.Nature555, 346–350 (2018)..

Imhof, S. et al. Topolectrical-circuit realization of topological corner modes.Nat. Phys.14, 925–929 (2018)..

Kim, M.&Rho, J. Topological edge and corner states in a two-dimensional photonic Su-Schrieffer-Heeger lattice.Nanophotonics9, 3227–3234 (2020)..

Xie, B. Y. et al. Second-order photonic topological insulator with corner states.Phys. Rev. B98, 205147 (2018)..

Noh, J. et al. Topological protection of photonic mid-gap defect modes.Nat. Photonics12, 408–415 (2018)..

Chen, X. D. et al. Direct observation of corner states in second-order topological photonic crystal slabs.Phys. Rev. Lett.122, 233902 (2019)..

Xie, B. Y. et al. Visualization of higher-order topological insulating phases in two-dimensional dielectric photonic crystals.Phys. Rev. Lett.122, 233903 (2019)..

El Hassan, A. et al. Corner states of light in photonic waveguides.Nat. Photonics13, 697–700 (2019)..

Mittal, S. et al. Photonic quadrupole topological phases.Nat. Photonics13, 692–696 (2019)..

Chen, Z. G. et al. Corner states in a second-order acoustic topological insulator as bound states in the continuum.Phys. Rev. B100, 075120 (2019)..

Ni, X. et al. Observation of higher-order topological acoustic states protected by generalized chiral symmetry.Nat. Mater.18, 113–120 (2019)..

Xue, H. R. et al. Acoustic higher-order topological insulator on a kagome lattice.Nat. Mater.18, 108–112 (2019)..

Liu, T. et al. Second-order topological phases in non-Hermitian systems.Phys. Rev. Lett.122, 076801 (2019)..

Liu, S. et al. Octupole corner state in a three-dimensional topological circuit.Light. Sci. Appl.9, 145 (2020)..

Dutt, A. et al. Higher-order topological insulators in synthetic dimensions.Light. Sci. Appl.9, 131 (2020)..

Kim, M., Jacob, Z.&Rho, J. Recent advances in 2D, 3D and higher-order topological photonics.Light. Sci. Appl.9, 130 (2020)..

Kim, H. R. et al. Multipolar lasing modes from topological corner states.Nat. Commun.11, 5758 (2020)..

Noguchi, R. et al. Evidence for a higher-order topological insulator in a three-dimensional material built from van der Waals stacking of bismuth-halide chains.Nat. Mater.20, 473–479 (2021)..

Yang, Y. T. et al. Hybrid-order topological insulators in a phononic crystal.Phys. Rev. Lett.126, 156801 (2021)..

Zhang, W. X. et al. Experimental observation of higher-order topological Anderson insulators.Phys. Rev. Lett.126, 146802 (2021)..

Liu, B. et al. Higher-order band topology in twisted moiré superlattice.Phys. Rev. Lett.126, 066401 (2021)..

Liu, Y. et al. Bulk-disclination correspondence in topological crystalline insulators.Nature589, 381–385 (2021)..

Hsu, C. H. et al. Majorana Kramers pairs in higher-order topological insulators.Phys. Rev. Lett.121, 196801 (2018)..

Pahomi, T. E., Sigrist, M.&Soluyanov, A. A. Braiding majorana corner modes in a second-order topological superconductor.Phys. Rev. Res.2, 032068(R) (2020)..

Ota, Y. et al. Photonic crystal nanocavity based on a topological corner state.Optica6, 786–789 (2019)..

Zhang, W. X. et al. Low-threshold topological nanolasers based on the second-order corner state.Light. : Sci. Appl.9, 109 (2020)..

Smirnova, D. et al. Nonlinear topological photonics.Appl. Phys. Rev.7, 021306 (2020)..

Lumer, Y. et al. Self-localized states in photonic topological insulators.Phys. Rev. Lett.111, 243905 (2013)..

Leykam, D.&Chong, Y. D. Edge solitons in nonlinear-photonic topological insulators.Phys. Rev. Lett.117, 143901 (2016)..

Hadad, Y., Khanikaev, A. B.&Alù, A. Self-induced topological transitions and edge states supported by nonlinear staggered potentials.Phys. Rev. B93, 155112 (2016)..

Kruk, S. et al. Nonlinear light generation in topological nanostructures.Nat. Nanotechnol.14, 126–130 (2019)..

Xia, S. Q. et al. Nontrivial coupling of light into a defect: the interplay of nonlinearity and topology.Light. Sci. Appl.9, 147 (2020)..

Maczewsky, L. J. et al. Nonlinearity-induced photonic topological insulator.Science370, 701–704 (2020)..

Xia, S. Q. et al. Nonlinear tuning of PT symmetry and non-Hermitian topological states.Science372, 72–76 (2021)..

Mukherjee, S.&Rechtsman, M. C. Observation of Floquet solitons in a topological bandgap.Science368, 856–859 (2020)..

Zangeneh-Nejad, F.&Fleury, R. Nonlinear second-order topological insulators.Phys. Rev. Lett.123, 053902 (2019)..

Banerjee, R., Mandal, S.&Liew, T. C. H. Coupling between exciton-polariton corner modes through edge states.Phys. Rev. Lett.124, 063901 (2020)..

Zhang, Y. Q. et al. Nonlinear higher-order polariton topological insulator.Opt. Lett.45, 4710–4713 (2020)..

Kirsch, M. S. et al. Observation of nonlinear corner states in a higher-order photonic topological insulator. InConference on Lasers and Electro-Optics. Paper FTh4H. 2 (OSA, 2021).

Hu, Z. et al. Nonlinearity-induced transition of topological corner states. InConference on Lasers and Electro-Optics Optics. Paper FTh4H. 4 (OSA, 2021).

Kruk, S. et al. Nanoscale topological corner states in nonlinear optics.Nano Lett.21, 4592–4597 (2021)..

Benalcazar, W. A.&Cerjan, A. Bound states in the continuum of higher-order topological insulators.Phys. Rev. B101, 161116(R) (2020)..

Cerjan, A. et al. Observation of a higher-order topological bound state in the continuum.Phys. Rev. Lett.125, 213901 (2020)..

Zhen, B. et al. Topological nature of optical bound states in the continuum.Phys. Rev. Lett.113, 257401 (2014)..

Hsu, C. W. et al. Bound states in the continuum.Nat. Rev. Mater.1, 16048 (2016)..

Koshelev, K. et al. Nonradiating photonics with resonant dielectric nanostructures.Nanophotonics8, 725–745 (2019)..

Plotnik, Y. et al. Experimental observation of optical bound states in the continuum.Phys. Rev. Lett.107, 183901 (2011)..

Hsu, C. W. et al. Observation of trapped light within the radiation continuum.Nature499, 188–191 (2013)..

Liu, F.&Wakabayashi, K. Novel topological phase with a zero berry curvature.Phys. Rev. Lett.118, 076803 (2017)..

Li, M. Y. et al. Higher-order topological states in photonic kagome crystals with long-range interactions.Nat. Photonics14,89–94 (2020)..

Kirsch, M. S. et al. Nonlinear second-order photonic topological insulators.Nat. Phys.https://doi.org/10.1038/s41567-021-01275-3https://doi.org/10.1038/s41567-021-01275-3(2021)..

Efremidis, N. K., Sears, S., Christodoulides, D. N., Fleischer, J. W.&Segev, M. Discrete solitons in photorefractive optically induced photonic lattices.Phys. Rev. E66, 046602 (2002)..

Wang, X. et al. Observation of two-dimensional surface solitons.Phys. Rev. Lett.98, 123903 (2007)..

Su, W. P., Schrieffer, J. R.&Heeger, A. J. Solitons in polyacetylene.Phys. Rev. Lett.42, 1698–1701 (1979)..

Malkova, N. et al. Observation of optical Shockley-like surface states in photonic superlattices.Opt. Lett.34, 1633–1635 (2009)..

Szameit, A. et al. Observation of two-dimensional surface solitons in asymmetric waveguide arrays.Phys. Rev. Lett.98, 173903 (2007)..

Xia, S. Q. et al. Unconventional flatband line states in photonic Lieb lattices.Phys. Rev. Lett.121, 263902 (2018)..

Van Miert, G.&Ortix, C. On the topological immunity of corner states in two-dimensional crystalline insulators.npj Quantum Mater.5, 63 (2020)..

Jung, M., Yu, Y.&Shvets, G. Exact higher-order bulk-boundary correspondence of corner-localized states. Preprint athttps://arxiv.org/abs/2010.10299https://arxiv.org/abs/2010.10299(2021).

Chen, Z.&Segev, M. Highlighting photonics: looking into the next decade.eLight1, 2 (2021)..

Shih, M. F. et al. Waveguides induced by photorefractive screening solitons.J. Opt. Soc. Am. B14, 3091–3101 (1997)..

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