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Coen S, Garbin B, Xu G, Quinn L, Goldman N, Oppo GL, Erkintalo M, Murdoch SG, Fatome J. Nonlinear topological symmetry protection in a dissipative system. Nat Commun 2024; 15:1398. [PMID: 38360729 PMCID: PMC10869785 DOI: 10.1038/s41467-023-44640-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/19/2023] [Accepted: 12/21/2023] [Indexed: 02/17/2024] Open
Abstract
We investigate experimentally and theoretically a system ruled by an intricate interplay between topology, nonlinearity, and spontaneous symmetry breaking. The experiment is based on a two-mode coherently-driven optical resonator where photons interact through the Kerr nonlinearity. In presence of a phase defect, the modal structure acquires a synthetic Möbius topology enabling the realization of spontaneous symmetry breaking in inherently bias-free conditions without fine tuning of parameters. Rigorous statistical tests confirm the robustness of the underlying symmetry protection, which manifests itself by a periodic alternation of the modes reminiscent of period-doubling. This dynamic also confers long term stability to various localized structures including domain walls, solitons, and breathers. Our findings are supported by an effective Hamiltonian model and have relevance to other systems of interacting bosons and to the Floquet engineering of quantum matter. They could also be beneficial to the implementation of coherent Ising machines.
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Affiliation(s)
- Stéphane Coen
- Physics Department, The University of Auckland, Private Bag 92019, Auckland, 1142, New Zealand.
- The Dodd-Walls Centre for Photonic and Quantum Technologies, Dunedin, New Zealand.
| | - Bruno Garbin
- Physics Department, The University of Auckland, Private Bag 92019, Auckland, 1142, New Zealand
- The Dodd-Walls Centre for Photonic and Quantum Technologies, Dunedin, New Zealand
- NcodiN SAS, 10 Boulevard Thomas Gobert, F-91120, Palaiseau, France
| | - Gang Xu
- Physics Department, The University of Auckland, Private Bag 92019, Auckland, 1142, New Zealand
- The Dodd-Walls Centre for Photonic and Quantum Technologies, Dunedin, New Zealand
- School of Optical and Electronic Information, Huazhong University of Science and Technology, 1037 Luoyu Road, Wuhan, China
| | - Liam Quinn
- Physics Department, The University of Auckland, Private Bag 92019, Auckland, 1142, New Zealand
- The Dodd-Walls Centre for Photonic and Quantum Technologies, Dunedin, New Zealand
| | - Nathan Goldman
- Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles, CP 231, B-1050, Brussels, Belgium
- Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-Université PSL, Sorbonne Université, 11 Place Marcelin Berthelot, 75005, Paris, France
| | - Gian-Luca Oppo
- SUPA and Department of Physics, University of Strathclyde, Glasgow, G4 0NG, Scotland
| | - Miro Erkintalo
- Physics Department, The University of Auckland, Private Bag 92019, Auckland, 1142, New Zealand
- The Dodd-Walls Centre for Photonic and Quantum Technologies, Dunedin, New Zealand
| | - Stuart G Murdoch
- Physics Department, The University of Auckland, Private Bag 92019, Auckland, 1142, New Zealand
- The Dodd-Walls Centre for Photonic and Quantum Technologies, Dunedin, New Zealand
| | - Julien Fatome
- Physics Department, The University of Auckland, Private Bag 92019, Auckland, 1142, New Zealand
- The Dodd-Walls Centre for Photonic and Quantum Technologies, Dunedin, New Zealand
- Laboratoire Interdisciplinaire Carnot de Bourgogne (ICB), UMR 6303 CNRS, Université de Bourgogne, 9 Avenue Alain Savary, BP 47870, F-21078, Dijon, France
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Zhu X, Zhang B, Zhao D, Yang L, Liu S, Hou J. Pulse evolution and multi-pulse state of coherently coupled polarization domain walls in a fiber ring laser. OPTICS EXPRESS 2021; 29:30558-30566. [PMID: 34614778 DOI: 10.1364/oe.436030] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/06/2021] [Accepted: 08/25/2021] [Indexed: 06/13/2023]
Abstract
Pulse evolution and multi-pulse state of coherently coupled polarization domain walls (PDW) is experimentally demonstrated in a novel fiber ring laser. Versatile pulse shapes benefit by wide range moving of PDW in the weakly birefringent fiber. The 8.6 m short-cavity structure is more compact and accessible based on a 976 nm pump with nearly zero negative dispersion (-0.0002 ps2). Besides, multi-pulse patterns such as PDW splitting, harmonic mode-locking, and periodic soliton collision are also observed under larger net negative dispersion (-3.09 ps2) and 151m-longer cavity. This is the first demonstration of coherently coupled PDW in a fiber laser using a bandpass filter and the formation of coherently coupled PDW is ascribed to the BPF's force filtering.
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Abstract
We formulate and experimentally validate a set of spin–momentum equations which are analogous to the Maxwell’s equations and govern spin–orbit coupling in electromagnetic guided waves. The Maxwell-like spin–momentum equations reveal the spin–momentum locking, the chiral spin texture of the field, Berry phase, and the spin–orbit interaction in the optical near field. The observed spin–momentum behavior can be extended to other classical waves, such as acoustic, fluid, gas, and gravitational waves. Spin–momentum locking, a manifestation of topological properties that governs the behavior of surface states, was studied intensively in condensed-matter physics and optics, resulting in the discovery of topological insulators and related effects and their photonic counterparts. In addition to spin, optical waves may have complex structure of vector fields associated with orbital angular momentum or nonuniform intensity variations. Here, we derive a set of spin–momentum equations which describes the relationship between the spin and orbital properties of arbitrary complex electromagnetic guided modes. The predicted photonic spin dynamics is experimentally verified with four kinds of nondiffracting surface structured waves. In contrast to the one-dimensional uniform spin of a guided plane wave, a two-dimensional chiral spin swirl is observed for structured guided modes. The proposed framework opens up opportunities for designing the spin structure and topological properties of electromagnetic waves with practical importance in spin optics, topological photonics, metrology and quantum technologies and may be used to extend the spin-dynamics concepts to fluid, acoustic, and gravitational waves.
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Garbin B, Fatome J, Oppo GL, Erkintalo M, Murdoch SG, Coen S. Dissipative Polarization Domain Walls in a Passive Coherently Driven Kerr Resonator. PHYSICAL REVIEW LETTERS 2021; 126:023904. [PMID: 33512212 DOI: 10.1103/physrevlett.126.023904] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/18/2020] [Accepted: 12/07/2020] [Indexed: 06/12/2023]
Abstract
Using a passive, coherently driven nonlinear optical fiber ring resonator, we report the experimental realization of dissipative polarization domain walls. The domain walls arise through a symmetry breaking bifurcation and consist of temporally localized structures where the amplitudes of the two polarization modes of the resonator interchange, segregating domains of orthogonal polarization states. We show that dissipative polarization domain walls can persist in the resonator without changing shape. We also demonstrate on-demand excitation, as well as pinning of domain walls at specific positions for arbitrary long times. Our results could prove useful for the analog simulation of ubiquitous domain-wall related phenomena, and pave the way to an all-optical buffer adapted to the transmission of topological bits.
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Affiliation(s)
- Bruno Garbin
- Dodd-Walls Centre, Physics Department, The University of Auckland, Private Bag 92019, Auckland 1142, New Zealand
- Université Paris-Saclay, CNRS, Centre de Nanosciences et de Nanotechnologies, 91120 Palaiseau, France
| | - Julien Fatome
- Dodd-Walls Centre, Physics Department, The University of Auckland, Private Bag 92019, Auckland 1142, New Zealand
- Laboratoire Interdisciplinaire Carnot de Bourgogne (ICB), UMR 6303 CNRS, Université de Bourgogne Franche-Comté, 9 Avenue Alain Savary, BP 47870, F-21078 Dijon, France
| | - Gian-Luca Oppo
- SUPA and Department of Physics, University of Strathclyde, Glasgow G4 0NG, Scotland, European Union
| | - Miro Erkintalo
- Dodd-Walls Centre, Physics Department, The University of Auckland, Private Bag 92019, Auckland 1142, New Zealand
| | - Stuart G Murdoch
- Dodd-Walls Centre, Physics Department, The University of Auckland, Private Bag 92019, Auckland 1142, New Zealand
| | - Stéphane Coen
- Dodd-Walls Centre, Physics Department, The University of Auckland, Private Bag 92019, Auckland 1142, New Zealand
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Cui L, Liu X, Guo C, Zhang Z, Zhao N, Vasilyev M, Li X. Measurement of effective nonlinear coefficients in few-mode fibers. OPTICS LETTERS 2019; 44:5768-5771. [PMID: 31774775 DOI: 10.1364/ol.44.005768] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/26/2019] [Accepted: 11/01/2019] [Indexed: 06/10/2023]
Abstract
Because of random mode coupling, the nonlinear coefficient in few-mode fibers (FMFs) is averaged to an effective value, which can be theoretically modeled and calculated by using the multi-mode Manakov equations. In this Letter, we experimentally measure the effective nonlinear coefficients in a 530-m-long FMF supporting two mode groups, namely, the $ {\rm LP}_{01} $LP01 and $ {\rm LP}_{11} $LP11 mode groups, by exploiting the self-phase and cross-phase modulations of pulsed fields. By using the nonlinear coefficient of the $ {\rm LP}_{01} $LP01 mode as a reference and comparing the spectral broadening of the pulsed fields, we obtain the intra-modal effective nonlinear coefficient of the $ {\rm LP}_{11} $LP11 mode and the inter-modal effective nonlinear coefficient between the $ {\rm LP}_{01} $LP01 and $ {\rm LP}_{11} $LP11 modes. The experimental results are in good agreement with the theoretical predictions of the multi-mode Manakov equations.
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Zhang W, Zhan L, Xian T, Gao L. Bidirectional dark-soliton fiber lasers for high-sensitivity gyroscopic application. OPTICS LETTERS 2019; 44:4008-4011. [PMID: 31415534 DOI: 10.1364/ol.44.004008] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/16/2019] [Accepted: 07/15/2019] [Indexed: 06/10/2023]
Abstract
Bidirectional mode-locked lasers are very useful in laser sensing and optical communications. Here we report a bidirectional domain wall soliton (DWS) fiber laser with an anomalous dispersion cavity. Two mode-locked dark pulse trains propagating in the opposite directions have been generated. Moreover, the specific application as a gyroscopic effect has been demonstrated by mounting this DWS laser on a rotating platform. The beat frequency of the two dark pulse DWS beams is measured as a linear function of the rotation velocity. The rotation sensitivity reaches 3.31 kHz/(deg/s), which are comparable with the one in a bright pulse laser gyroscope. Without the limit of using tunable delay lines, the DWS laser gyroscope has the advantages of simple structure, high sensitivity, and low cost, while possessing the entire superiority of a mode-locked laser gyroscope. It is more promising for the applications in modern inertia navigation systems.
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Tsesses S, Ostrovsky E, Cohen K, Gjonaj B, Lindner NH, Bartal G. Optical skyrmion lattice in evanescent electromagnetic fields. Science 2018; 361:993-996. [PMID: 30026318 DOI: 10.1126/science.aau0227] [Citation(s) in RCA: 70] [Impact Index Per Article: 11.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/29/2018] [Accepted: 07/03/2018] [Indexed: 01/21/2023]
Abstract
Topological defects play a key role in a variety of physical systems, ranging from high-energy to solid-state physics. A skyrmion is a type of topological defect that has shown promise for applications in the fields of magnetic storage and spintronics. We show that optical skyrmion lattices can be generated using evanescent electromagnetic fields and demonstrate this using surface plasmon polaritons, imaged by phase-resolved near-field optical microscopy. We show how the optical skyrmion lattice exhibits robustness to imperfections while the topological domain walls in the lattice can be continuously tuned, changing the spatial structure of the skyrmions from bubble type to Néel type. Extending the generation of skyrmions to photonic systems provides various possibilities for applications in optical information processing, transfer, and storage.
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Affiliation(s)
- S Tsesses
- Andrew and Erna Viterbi Department of Electrical Engineering, Technion-Israel Institute of Technology, 3200003 Haifa, Israel
| | - E Ostrovsky
- Andrew and Erna Viterbi Department of Electrical Engineering, Technion-Israel Institute of Technology, 3200003 Haifa, Israel
| | - K Cohen
- Andrew and Erna Viterbi Department of Electrical Engineering, Technion-Israel Institute of Technology, 3200003 Haifa, Israel
| | - B Gjonaj
- Faculty of Medical Sciences, Albanian University, Durrës Street, Tirana 1000, Albania
| | - N H Lindner
- Physics Department, Technion-Israel Institute of Technology, 3200003 Haifa, Israel
| | - G Bartal
- Andrew and Erna Viterbi Department of Electrical Engineering, Technion-Israel Institute of Technology, 3200003 Haifa, Israel.
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Tsitoura F, Gietz U, Chabchoub A, Hoffmann N. Phase Domain Walls in Weakly Nonlinear Deep Water Surface Gravity Waves. PHYSICAL REVIEW LETTERS 2018; 120:224102. [PMID: 29906183 DOI: 10.1103/physrevlett.120.224102] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/22/2017] [Indexed: 06/08/2023]
Abstract
We report a theoretical derivation, an experimental observation and a numerical validation of nonlinear phase domain walls in weakly nonlinear deep water surface gravity waves. The domain walls presented are connecting homogeneous zones of weakly nonlinear plane Stokes waves of identical amplitude and wave vector but differences in phase. By exploiting symmetry transformations within the framework of the nonlinear Schrödinger equation we demonstrate the existence of exact analytical solutions representing such domain walls in the weakly nonlinear limit. The walls are in general oblique to the direction of the wave vector and stationary in moving reference frames. Experimental and numerical studies confirm and visualize the findings. Our present results demonstrate that nonlinear domain walls do exist in the weakly nonlinear regime of general systems exhibiting dispersive waves.
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Affiliation(s)
- F Tsitoura
- Dynamics Group, Hamburg University of Technology, Hamburg 21073, Germany
| | - U Gietz
- Department of Fluid Dynamics and Ship Theory, Hamburg University of Technology, Hamburg 21073, Germany
| | - A Chabchoub
- School of Civil Engineering, The University of Sydney, Sydney, NSW 2006, Australia
| | - N Hoffmann
- Dynamics Group, Hamburg University of Technology, Hamburg 21073, Germany
- Department of Mechanical Engineering, Imperial College London, London SW7 2AZ, United Kingdom
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