1
|
Li YWY, Nie XF, Cao J, Cui WX, Wang HF. Topological phases and non-Hermitian topology in tunable nonreciprocal cyclic three-mode optical systems. OPTICS EXPRESS 2024; 32:13562-13573. [PMID: 38859323 DOI: 10.1364/oe.521228] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/08/2024] [Accepted: 03/13/2024] [Indexed: 06/12/2024]
Abstract
We propose a method for simulating a 1D non-Hermitian Su-Schrieffer-Heeger model with modulated nonreciprocal hopping using a cyclic three-mode optical system. The current system exhibits different localization of topologically nontrivial phases, which can be characterized by the winding number. We find that the eigenenergies of such a system undergo a real-complex transition as the nonreciprocal hopping changes, accompanied by a non-Bloch parity-time symmetry breaking. We explain this phase transition by considering the evolution of saddle points on the complex energy plan and the ratio of complex eigenenergies. Additionally, we demonstrate that the skin states resulting from the non-Hermitian skin effect possess higher-order exceptional points under the critical point of the non-Bloch parity-time phase transition. Furthermore, we investigate the non-Hermitian skin phase transition by the directional mean inverse participation ratio and the generalized Brillouin zone. This work provides an alternative way to investigate the novel topological and non-Hermitian effects in nonreciprocal optical systems.
Collapse
|
2
|
Ren B, Arkhipova AA, Zhang Y, Kartashov YV, Wang H, Zhuravitskii SA, Skryabin NN, Dyakonov IV, Kalinkin AA, Kulik SP, Kompanets VO, Chekalin SV, Zadkov VN. Observation of nonlinear disclination states. LIGHT, SCIENCE & APPLICATIONS 2023; 12:194. [PMID: 37558694 PMCID: PMC10412544 DOI: 10.1038/s41377-023-01235-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/24/2023] [Revised: 07/10/2023] [Accepted: 07/14/2023] [Indexed: 08/11/2023]
Abstract
Introduction of controllable deformations into periodic materials that lead to disclinations in their structure opens novel routes for construction of higher-order topological insulators hosting topological states at disclinations. Appearance of these topological states is consistent with the bulk-disclination correspondence principle, and is due to the filling anomaly that results in fractional charges to the boundary unit cells. So far, topological disclination states were observed only in the linear regime, while the interplay between nonlinearity and topology in the systems with disclinations has been never studied experimentally. We report here on the experimental observation of the nonlinear photonic disclination states in waveguide arrays with pentagonal or heptagonal disclination cores inscribed in transparent optical medium using the fs-laser writing technique. The transition between nontopological and topological phases in such structures is controlled by the Kekulé distortion coefficient r with topological phase hosting simultaneously disclination states at the inner disclination core and spatially separated from them corner-I, corner-II, and extended edge states at the outer edge of the structure. We show that the robust nonlinear disclination states bifurcate from their linear counterparts and that location of their propagation constants in the gap and, hence, their spatial localization can be controlled by their power. Nonlinear disclination states can be efficiently excited by Gaussian input beams, but only if they are focused into the waveguides belonging to the disclination core, where such topological states reside. Our results open new prospects for investigation of nonlinear effects in topological systems with disclinations and are relevant for different areas of science, including Bose-Einstein and polariton condensates, where potentials with the disclinations can be created.
Collapse
Affiliation(s)
- Boquan Ren
- Key Laboratory for Physical Electronics and Devices, Ministry of Education, School of Electronic Science and Engineering, Xi'an Jiaotong University, Xi'an, 710049, China
| | - Antonina A Arkhipova
- Institute of Spectroscopy, Russian Academy of Sciences, Troitsk, Moscow, 108840, Russia
- Faculty of Physics, Higher School of Economics, Moscow, 105066, Russia
| | - Yiqi Zhang
- Key Laboratory for Physical Electronics and Devices, Ministry of Education, School of Electronic Science and Engineering, Xi'an Jiaotong University, Xi'an, 710049, China.
| | - Yaroslav V Kartashov
- Institute of Spectroscopy, Russian Academy of Sciences, Troitsk, Moscow, 108840, Russia.
| | - Hongguang Wang
- Key Laboratory for Physical Electronics and Devices, Ministry of Education, School of Electronic Science and Engineering, Xi'an Jiaotong University, Xi'an, 710049, China
| | - Sergei A Zhuravitskii
- Institute of Spectroscopy, Russian Academy of Sciences, Troitsk, Moscow, 108840, Russia
- Quantum Technology Centre, Faculty of Physics, M. V. Lomonosov Moscow State University, Moscow, 119991, Russia
| | - Nikolay N Skryabin
- Institute of Spectroscopy, Russian Academy of Sciences, Troitsk, Moscow, 108840, Russia
- Quantum Technology Centre, Faculty of Physics, M. V. Lomonosov Moscow State University, Moscow, 119991, Russia
| | - Ivan V Dyakonov
- Quantum Technology Centre, Faculty of Physics, M. V. Lomonosov Moscow State University, Moscow, 119991, Russia
| | - Alexander A Kalinkin
- Institute of Spectroscopy, Russian Academy of Sciences, Troitsk, Moscow, 108840, Russia
- Quantum Technology Centre, Faculty of Physics, M. V. Lomonosov Moscow State University, Moscow, 119991, Russia
| | - Sergei P Kulik
- Quantum Technology Centre, Faculty of Physics, M. V. Lomonosov Moscow State University, Moscow, 119991, Russia
| | - Victor O Kompanets
- Institute of Spectroscopy, Russian Academy of Sciences, Troitsk, Moscow, 108840, Russia
| | - Sergey V Chekalin
- Institute of Spectroscopy, Russian Academy of Sciences, Troitsk, Moscow, 108840, Russia
| | - Victor N Zadkov
- Institute of Spectroscopy, Russian Academy of Sciences, Troitsk, Moscow, 108840, Russia
- Faculty of Physics, Higher School of Economics, Moscow, 105066, Russia
| |
Collapse
|
3
|
Yan W, Cheng W, Liu W, Liu Q, Chen F. Square-root higher-order topological insulators in a photonic decorated SSH lattice. OPTICS LETTERS 2023; 48:3765-3768. [PMID: 37450745 DOI: 10.1364/ol.498084] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/15/2023] [Accepted: 06/25/2023] [Indexed: 07/18/2023]
Abstract
Recently, there has been a surge of interest in square-root higher-order topological insulators (HOTIs) due to their unique topological properties inherited from their squared Hamiltonian. Different from conventional HOTIs, square-root HOTIs support paired corner states that exist in different bandgaps. In this work, we experimentally establish a series of two-dimensional photonic decorated Su-Schrieffer-Heeger (SSH) lattices by using the femtosecond-laser writing technique and thereby directly observe paired topological corner states. Interestingly, the higher-order topological properties of such square-root HOTIs are inherited from the parent Hamiltonian, which contains the celebrated 2D SSH lattice. The dynamic evolution of square-root corner states indicates that they exist in different bandgaps. This work not only provides a new platform to study higher-order topology in optics, it also brings about new possibilities for future studies of other novel HOTIs.
Collapse
|
4
|
Hu Z, Bongiovanni D, Jukić D, Jajtić E, Xia S, Song D, Xu J, Morandotti R, Buljan H, Chen Z. Nonlinear control of photonic higher-order topological bound states in the continuum. LIGHT, SCIENCE & APPLICATIONS 2021; 10:164. [PMID: 34376638 PMCID: PMC8355333 DOI: 10.1038/s41377-021-00607-5] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/27/2021] [Revised: 07/26/2021] [Accepted: 07/26/2021] [Indexed: 05/31/2023]
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.
Collapse
Affiliation(s)
- Zhichan Hu
- The MOE Key Laboratory of Weak-Light Nonlinear Photonics, TEDA Applied Physics Institute and School of Physics, Nankai University, 300457, Tianjin, China
| | - Domenico Bongiovanni
- The MOE Key Laboratory of Weak-Light Nonlinear Photonics, TEDA Applied Physics Institute and School of Physics, Nankai University, 300457, Tianjin, China
- INRS-EMT, 1650 Boulevard Lionel-Boulet, Varennes, QC, J3X 1S2, Canada
| | - Dario Jukić
- Faculty of Civil Engineering, University of Zagreb, A. Kačića Miošića 26, 10000, Zagreb, Croatia
| | - Ema Jajtić
- Department of Physics, Faculty of Science, University of Zagreb, Bijenička c. 32, 10000, Zagreb, Croatia
| | - Shiqi Xia
- The MOE Key Laboratory of Weak-Light Nonlinear Photonics, TEDA Applied Physics Institute and School of Physics, Nankai University, 300457, Tianjin, China
| | - Daohong Song
- The MOE Key Laboratory of Weak-Light Nonlinear Photonics, TEDA Applied Physics Institute and School of Physics, Nankai University, 300457, Tianjin, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, 030006, Taiyuan, Shanxi, China
| | - Jingjun Xu
- The MOE Key Laboratory of Weak-Light Nonlinear Photonics, TEDA Applied Physics Institute and School of Physics, Nankai University, 300457, Tianjin, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, 030006, Taiyuan, Shanxi, China
| | - Roberto Morandotti
- INRS-EMT, 1650 Boulevard Lionel-Boulet, Varennes, QC, J3X 1S2, Canada
- Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, 610054, Chengdu, Sichuan, China
| | - Hrvoje Buljan
- The MOE Key Laboratory of Weak-Light Nonlinear Photonics, TEDA Applied Physics Institute and School of Physics, Nankai University, 300457, Tianjin, China.
- Department of Physics, Faculty of Science, University of Zagreb, Bijenička c. 32, 10000, Zagreb, Croatia.
| | - Zhigang Chen
- The MOE Key Laboratory of Weak-Light Nonlinear Photonics, TEDA Applied Physics Institute and School of Physics, Nankai University, 300457, Tianjin, China.
- Collaborative Innovation Center of Extreme Optics, Shanxi University, 030006, Taiyuan, Shanxi, China.
- Department of Physics and Astronomy, San Francisco State University, San Francisco, CA, 94132, USA.
| |
Collapse
|