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Elsayed HA, Mohamed AG, El-Sherbeeny AM, Aly AH, Abukhadra MR, Al Zoubi W, Mehaney A. Improved performance of temperature sensors based on the one-dimensional topological photonic crystals comprising hyperbolic metamaterials. Sci Rep 2024; 14:19733. [PMID: 39183352 PMCID: PMC11345424 DOI: 10.1038/s41598-024-69751-3] [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: 06/22/2024] [Accepted: 08/08/2024] [Indexed: 08/27/2024] Open
Abstract
This paper seeks to progress the field of topological photonic crystals (TPC) as a promising tool in face of construction flaws. In particular, the structure can be used as a novel temperature sensor. In this regard, the considered TPC structure comprising two different PC designs named PC1 and PC2. PC1 is designed from a stack of multilayers containing Silicon (Si) and Silicon dioxide (SiO2), while layers of SiO2 and composite layer named hyperbolic metamaterial (HMM) are considered in designing PC2. The HMM layer is engineered using subwavelength layers of Si and Bismuth Germinate, or BGO (Bi 4 Ge 3 O 12 ). The mainstay of our suggested temperature sensor is mainly based on the emergence of some resonant modes inside the transmittance spectrum that provide the stability in the presence of the geometrical changes. Meanwhile, our theoretical framework has been introduced in the vicinity of transfer matrix method (TMM), effective medium theory (EMT) and the thermo-optic characteristics of the considered materials. The numerical findings have extensively introduced the role of some topological parameters such as layers' thicknesses, filling ratio through HMM layers and the periodicity of HMM on the stability or the topological features of the introduced sensor. Meanwhile, the numerical results reveal that the considered design provides some topological edge states (TESs) of a promising robustness and stability against certain disturbances or geometrical changes in the constituent materials. In addition, our sensing tool offers a relatively high sensitivity of 0.27 nm/°C.
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Affiliation(s)
- Hussein A Elsayed
- TH-PPM Group, Physics Department, Faculty of Science, Beni-Suef University, Beni-Suef, 62512, Egypt
| | - Aliaa G Mohamed
- TH-PPM Group, Physics Department, Faculty of Science, Beni-Suef University, Beni-Suef, 62512, Egypt
| | - Ahmed M El-Sherbeeny
- Industrial Engineering Department, College of Engineering, King Saud University, P.O. Box 800, 11421, Riyadh, Saudi Arabia
| | - Arafa H Aly
- TH-PPM Group, Physics Department, Faculty of Science, Beni-Suef University, Beni-Suef, 62512, Egypt
- Department of Technical Sciences, Western Caspian University, Baku 1001, Azerbaijan
| | - Mostafa R Abukhadra
- Materials Technologies and Their Applications Lab, Faculty of Science, Beni-Suef University, Beni Suef City, Egypt
| | - Wail Al Zoubi
- Materials Electrochemistry Laboratory, School of Materials Science and Engineering, Yeungnam University, Gyeongsan, 38541, Republic of Korea.
| | - Ahmed Mehaney
- TH-PPM Group, Physics Department, Faculty of Science, Beni-Suef University, Beni-Suef, 62512, Egypt.
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2
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Wang H, Xu W, Zhu Z, Yang B. Photonic Weyl Waveguide and Saddle-Chips-like Modes. NANOMATERIALS (BASEL, SWITZERLAND) 2024; 14:620. [PMID: 38607154 PMCID: PMC11013772 DOI: 10.3390/nano14070620] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/17/2024] [Revised: 03/21/2024] [Accepted: 03/28/2024] [Indexed: 04/13/2024]
Abstract
Topological Weyl semimetals are characterized by open Fermi arcs on their terminal surfaces, these materials not only changed accepted concepts of the Fermi loop but also enabled many exotic phenomena, such as one-way propagation. The key prerequisite is that the two terminal surfaces have to be well separated, i.e., the Fermi arcs are not allowed to couple with each other. Thus, their interaction was overlooked before. Here, we consider coupled Fermi arcs and propose a Weyl planar waveguide, wherein we found a saddle-chips-like hybridized guiding mode. The hybridized modes consist of three components: surface waves from the top and bottom surfaces and bulk modes inside the Weyl semimetal. The contribution of these three components to the hybridized mode appears to be z-position-dependent rather than uniform. Beyond the conventional waveguide framework, those non-trivial surface states, with their arc-type band structures, exhibit strong selectivity in propagation direction, providing an excellent platform for waveguides. Compared with the conventional waveguide, the propagation direction of hybridized modes exhibits high z-position-dependency. For example, when the probe plane shifts from the top interface to the bottom interface, the component propagating horizontally becomes dimmer, while the component propagating vertically becomes brighter. Experimentally, we drilled periodic holes in metal plates to sandwich an ideal Weyl meta-crystal and characterize the topological guiding mode. Our study shows the intriguing behaviors of topological photonic waveguides, which could lead to beam manipulation, position sensing, and even 3D information processing on photonic chip. The Weyl waveguide also provides a platform for studying the coupling and the interaction between surface and bulk states.
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Affiliation(s)
- Hanyu Wang
- College of Advanced Interdisciplinary Studies, National University of Defense Technology, Changsha 410073, China; (H.W.); (W.X.)
- Hunan Provincial Key Laboratory of Novel Nano-Optoelectronic Information Materials and Devices, National University of Defense Technology, Changsha 410073, China
- Nanhu Laser Laboratory, National University of Defense Technology, Changsha 410073, China
| | - Wei Xu
- College of Advanced Interdisciplinary Studies, National University of Defense Technology, Changsha 410073, China; (H.W.); (W.X.)
- Hunan Provincial Key Laboratory of Novel Nano-Optoelectronic Information Materials and Devices, National University of Defense Technology, Changsha 410073, China
- Nanhu Laser Laboratory, National University of Defense Technology, Changsha 410073, China
| | - Zhihong Zhu
- College of Advanced Interdisciplinary Studies, National University of Defense Technology, Changsha 410073, China; (H.W.); (W.X.)
- Hunan Provincial Key Laboratory of Novel Nano-Optoelectronic Information Materials and Devices, National University of Defense Technology, Changsha 410073, China
- Nanhu Laser Laboratory, National University of Defense Technology, Changsha 410073, China
| | - Biao Yang
- College of Advanced Interdisciplinary Studies, National University of Defense Technology, Changsha 410073, China; (H.W.); (W.X.)
- Hunan Provincial Key Laboratory of Novel Nano-Optoelectronic Information Materials and Devices, National University of Defense Technology, Changsha 410073, China
- Nanhu Laser Laboratory, National University of Defense Technology, Changsha 410073, China
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3
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Pan Y, Cui C, Chen Q, Chen F, Zhang L, Ren Y, Han N, Li W, Li X, Yu ZM, Chen H, Yang Y. Real higher-order Weyl photonic crystal. Nat Commun 2023; 14:6636. [PMID: 37857622 PMCID: PMC10587095 DOI: 10.1038/s41467-023-42457-2] [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: 06/06/2023] [Accepted: 10/11/2023] [Indexed: 10/21/2023] Open
Abstract
Higher-order Weyl semimetals are a family of recently predicted topological phases simultaneously showcasing unconventional properties derived from Weyl points, such as chiral anomaly, and multidimensional topological phenomena originating from higher-order topology. The higher-order Weyl semimetal phases, with their higher-order topology arising from quantized dipole or quadrupole bulk polarizations, have been demonstrated in phononics and circuits. Here, we experimentally discover a class of higher-order Weyl semimetal phase in a three-dimensional photonic crystal (PhC), exhibiting the concurrence of the surface and hinge Fermi arcs from the nonzero Chern number and the nontrivial generalized real Chern number, respectively, coined a real higher-order Weyl PhC. Notably, the projected two-dimensional subsystem with kz = 0 is a real Chern insulator, belonging to the Stiefel-Whitney class with real Bloch wavefunctions, which is distinguished fundamentally from the Chern class with complex Bloch wavefunctions. Our work offers an ideal photonic platform for exploring potential applications and material properties associated with the higher-order Weyl points and the Stiefel-Whitney class of topological phases.
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Affiliation(s)
- Yuang Pan
- Interdisciplinary Center for Quantum Information, State Key Laboratory of Extreme Photonics and Instrumentation, ZJU-Hangzhou Global Scientific and Technological Innovation Center, Zhejiang University, Hangzhou, 310027, China
- International Joint Innovation Center, The Electromagnetics Academy at Zhejiang University, Zhejiang University, Haining, 314400, China
- Key Lab. of Advanced Micro/Nano Electronic Devices & Smart Systems of Zhejiang, Jinhua Institute of Zhejiang University, Zhejiang University, Jinhua, 321099, China
- Shaoxing Institute of Zhejiang University, Zhejiang University, Shaoxing, 312000, China
| | - Chaoxi Cui
- Centre for Quantum Physics, Key Laboratory of Advanced Optoelectronic Quantum Architecture and Measurement (MOE), School of Physics, Beijing Institute of Technology, Beijing, 100081, China
- Beijing Key Laboratory of Nanophotonics and Ultrafine Optoelectronic Systems, School of Physics, Beijing Institute of Technology, Beijing, 100081, China
| | - Qiaolu Chen
- Interdisciplinary Center for Quantum Information, State Key Laboratory of Extreme Photonics and Instrumentation, ZJU-Hangzhou Global Scientific and Technological Innovation Center, Zhejiang University, Hangzhou, 310027, China
- International Joint Innovation Center, The Electromagnetics Academy at Zhejiang University, Zhejiang University, Haining, 314400, China
- Key Lab. of Advanced Micro/Nano Electronic Devices & Smart Systems of Zhejiang, Jinhua Institute of Zhejiang University, Zhejiang University, Jinhua, 321099, China
- Shaoxing Institute of Zhejiang University, Zhejiang University, Shaoxing, 312000, China
| | - Fujia Chen
- Interdisciplinary Center for Quantum Information, State Key Laboratory of Extreme Photonics and Instrumentation, ZJU-Hangzhou Global Scientific and Technological Innovation Center, Zhejiang University, Hangzhou, 310027, China
- International Joint Innovation Center, The Electromagnetics Academy at Zhejiang University, Zhejiang University, Haining, 314400, China
- Key Lab. of Advanced Micro/Nano Electronic Devices & Smart Systems of Zhejiang, Jinhua Institute of Zhejiang University, Zhejiang University, Jinhua, 321099, China
- Shaoxing Institute of Zhejiang University, Zhejiang University, Shaoxing, 312000, China
| | - Li Zhang
- Interdisciplinary Center for Quantum Information, State Key Laboratory of Extreme Photonics and Instrumentation, ZJU-Hangzhou Global Scientific and Technological Innovation Center, Zhejiang University, Hangzhou, 310027, China
- International Joint Innovation Center, The Electromagnetics Academy at Zhejiang University, Zhejiang University, Haining, 314400, China
- Key Lab. of Advanced Micro/Nano Electronic Devices & Smart Systems of Zhejiang, Jinhua Institute of Zhejiang University, Zhejiang University, Jinhua, 321099, China
- Shaoxing Institute of Zhejiang University, Zhejiang University, Shaoxing, 312000, China
| | - Yudong Ren
- Interdisciplinary Center for Quantum Information, State Key Laboratory of Extreme Photonics and Instrumentation, ZJU-Hangzhou Global Scientific and Technological Innovation Center, Zhejiang University, Hangzhou, 310027, China
- International Joint Innovation Center, The Electromagnetics Academy at Zhejiang University, Zhejiang University, Haining, 314400, China
- Key Lab. of Advanced Micro/Nano Electronic Devices & Smart Systems of Zhejiang, Jinhua Institute of Zhejiang University, Zhejiang University, Jinhua, 321099, China
- Shaoxing Institute of Zhejiang University, Zhejiang University, Shaoxing, 312000, China
| | - Ning Han
- Interdisciplinary Center for Quantum Information, State Key Laboratory of Extreme Photonics and Instrumentation, ZJU-Hangzhou Global Scientific and Technological Innovation Center, Zhejiang University, Hangzhou, 310027, China
- International Joint Innovation Center, The Electromagnetics Academy at Zhejiang University, Zhejiang University, Haining, 314400, China
- Key Lab. of Advanced Micro/Nano Electronic Devices & Smart Systems of Zhejiang, Jinhua Institute of Zhejiang University, Zhejiang University, Jinhua, 321099, China
- Shaoxing Institute of Zhejiang University, Zhejiang University, Shaoxing, 312000, China
| | - Wenhao Li
- Interdisciplinary Center for Quantum Information, State Key Laboratory of Extreme Photonics and Instrumentation, ZJU-Hangzhou Global Scientific and Technological Innovation Center, Zhejiang University, Hangzhou, 310027, China
- International Joint Innovation Center, The Electromagnetics Academy at Zhejiang University, Zhejiang University, Haining, 314400, China
- Key Lab. of Advanced Micro/Nano Electronic Devices & Smart Systems of Zhejiang, Jinhua Institute of Zhejiang University, Zhejiang University, Jinhua, 321099, China
- Shaoxing Institute of Zhejiang University, Zhejiang University, Shaoxing, 312000, China
| | - Xinrui Li
- Interdisciplinary Center for Quantum Information, State Key Laboratory of Extreme Photonics and Instrumentation, ZJU-Hangzhou Global Scientific and Technological Innovation Center, Zhejiang University, Hangzhou, 310027, China
- International Joint Innovation Center, The Electromagnetics Academy at Zhejiang University, Zhejiang University, Haining, 314400, China
- Key Lab. of Advanced Micro/Nano Electronic Devices & Smart Systems of Zhejiang, Jinhua Institute of Zhejiang University, Zhejiang University, Jinhua, 321099, China
- Shaoxing Institute of Zhejiang University, Zhejiang University, Shaoxing, 312000, China
| | - Zhi-Ming Yu
- Centre for Quantum Physics, Key Laboratory of Advanced Optoelectronic Quantum Architecture and Measurement (MOE), School of Physics, Beijing Institute of Technology, Beijing, 100081, China.
- Beijing Key Laboratory of Nanophotonics and Ultrafine Optoelectronic Systems, School of Physics, Beijing Institute of Technology, Beijing, 100081, China.
| | - Hongsheng Chen
- Interdisciplinary Center for Quantum Information, State Key Laboratory of Extreme Photonics and Instrumentation, ZJU-Hangzhou Global Scientific and Technological Innovation Center, Zhejiang University, Hangzhou, 310027, China.
- International Joint Innovation Center, The Electromagnetics Academy at Zhejiang University, Zhejiang University, Haining, 314400, China.
- Key Lab. of Advanced Micro/Nano Electronic Devices & Smart Systems of Zhejiang, Jinhua Institute of Zhejiang University, Zhejiang University, Jinhua, 321099, China.
- Shaoxing Institute of Zhejiang University, Zhejiang University, Shaoxing, 312000, China.
| | - Yihao Yang
- Interdisciplinary Center for Quantum Information, State Key Laboratory of Extreme Photonics and Instrumentation, ZJU-Hangzhou Global Scientific and Technological Innovation Center, Zhejiang University, Hangzhou, 310027, China.
- International Joint Innovation Center, The Electromagnetics Academy at Zhejiang University, Zhejiang University, Haining, 314400, China.
- Key Lab. of Advanced Micro/Nano Electronic Devices & Smart Systems of Zhejiang, Jinhua Institute of Zhejiang University, Zhejiang University, Jinhua, 321099, China.
- Shaoxing Institute of Zhejiang University, Zhejiang University, Shaoxing, 312000, China.
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4
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Chern RL. Photonic helicoid-like surface states in chiral metamaterials. Sci Rep 2023; 13:13934. [PMID: 37626148 PMCID: PMC10457351 DOI: 10.1038/s41598-023-40926-8] [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: 05/31/2023] [Accepted: 08/18/2023] [Indexed: 08/27/2023] Open
Abstract
We investigate the photonic topological phases in chiral metamaterials characterized by the magnetoelectric tensors with diagonal chirality components. The underlying medium is considered a photonic analogue of the topological semimetal featured with a Weyl cone and a cylindrical surface in the frequency-wave vector space. As the 'spin'-degenerate condition is satisfied, the photonic system can be rearranged as two hybrid modes that are completely decoupled. By introducing the pseudospin states as the basis for the hybrid modes, the photonic system is described by two subsystems in the form of spin-orbit Hamiltonians of spin 1, which result in nonzero spin Chern numbers that determine the topological properties. Surface modes at the interface between vacuum and the chiral metamaterial exist in their common gap in the wave vector space, which are analytically formulated by algebraic equations. In particular, the surface modes form a pair of spiral surface sheets wrapping around the Weyl cone, resembling the helicoid surface states that occur in topological semimetals. At the Weyl frequency, the surface modes contain two Fermi arc-like states that concatenate to yield a straight line segment.
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Affiliation(s)
- Ruey-Lin Chern
- Institute of Applied Mechanics, National Taiwan University, Taipei, 106, Taiwan.
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5
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Abstract
The topological properties of an object, associated with an integer called the topological invariant, are global features that cannot change continuously but only through abrupt variations, hence granting them intrinsic robustness. Engineered metamaterials (MMs) can be tailored to support highly nontrivial topological properties of their band structure, relative to their electronic, electromagnetic, acoustic and mechanical response, representing one of the major breakthroughs in physics over the past decade. Here, we review the foundations and the latest advances of topological photonic and phononic MMs, whose nontrivial wave interactions have become of great interest to a broad range of science disciplines, such as classical and quantum chemistry. We first introduce the basic concepts, including the notion of topological charge and geometric phase. We then discuss the topology of natural electronic materials, before reviewing their photonic/phononic topological MM analogues, including 2D topological MMs with and without time-reversal symmetry, Floquet topological insulators, 3D, higher-order, non-Hermitian and nonlinear topological MMs. We also discuss the topological aspects of scattering anomalies, chemical reactions and polaritons. This work aims at connecting the recent advances of topological concepts throughout a broad range of scientific areas and it highlights opportunities offered by topological MMs for the chemistry community and beyond.
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Affiliation(s)
- Xiang Ni
- Photonics Initiative, Advanced Science Research Center, City University of New York, New York, New York 10031, United States
- School of Physics and Electronics, Central South University, Changsha, Hunan 410083, China
| | - Simon Yves
- Photonics Initiative, Advanced Science Research Center, City University of New York, New York, New York 10031, United States
| | - Alex Krasnok
- Department of Electrical and Computer Engineering, Florida International University, Miami, Florida 33174, USA
| | - Andrea Alù
- Photonics Initiative, Advanced Science Research Center, City University of New York, New York, New York 10031, United States
- Department of Electrical Engineering, City College, The City University of New York, 160 Convent Avenue, New York, New York 10031, United States
- Physics Program, The Graduate Center, The City University of New York, 365 Fifth Avenue, New York, New York 10016, United States
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6
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Wang D, Jia H, Yang Q, Hu J, Zhang ZQ, Chan CT. Intrinsic Triple Degeneracy Point Bounded by Nodal Surfaces in Chiral Photonic Crystal. PHYSICAL REVIEW LETTERS 2023; 130:203802. [PMID: 37267572 DOI: 10.1103/physrevlett.130.203802] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/26/2022] [Accepted: 04/24/2023] [Indexed: 06/04/2023]
Abstract
In periodic systems, band degeneracies are typically protected and classified by spatial symmetries. However, in photonic systems, the Γ point at zero frequency is an intrinsic degeneracy due to the polarization degree of freedom of electromagnetic waves. For chiral photonic crystals, such an intrinsic degeneracy carries ±2 chiral topological charge while having linear band dispersions, different from the general perception of charge-2 nodes being associated with quadratic dispersions. Here, we show that these topological characters originate from the spin-1 Weyl point at zero frequency node of triple degeneracy, due to the existence of an electrostatic flat band. Such a topological charge at zero frequency is usually buried in bulk band projections and has never been experimentally observed. To address this challenge, we introduce space-group screw symmetries in the design of chiral photonic crystal, which makes the Brillouin zone boundary an oppositely charged nodal surface enclosing the Γ point. As a result, the emergent Fermi arcs are forced to connect the projections of these topological singularities, enabling their experimental observation. The number of Fermi arcs then directly reveals the embedded topological charge at zero frequency.
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Affiliation(s)
- Dongyang Wang
- Department of Physics, Hong Kong University of Science and Technology, Hong Kong, China
| | - Hongwei Jia
- Department of Physics, Hong Kong University of Science and Technology, Hong Kong, China
- Institute for Advanced Study, Hong Kong University of Science and Technology, Hong Kong, China
| | - Quanlong Yang
- School of Physics and Electronics, Central South University, Changsha 410083, Hunan, China
| | - Jing Hu
- Department of Physics, Hong Kong University of Science and Technology, Hong Kong, China
| | - Z Q Zhang
- Department of Physics, Hong Kong University of Science and Technology, Hong Kong, China
| | - C T Chan
- Department of Physics, Hong Kong University of Science and Technology, Hong Kong, China
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7
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Fu Y, Dodin IY, Qin H. Spin Hall effect of radiofrequency waves in magnetized plasmas. Phys Rev E 2023; 107:055210. [PMID: 37329066 DOI: 10.1103/physreve.107.055210] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/28/2022] [Accepted: 05/03/2023] [Indexed: 06/18/2023]
Abstract
In inhomogeneous media, electromagnetic-wave rays deviate from the trajectories predicted by the leading-order geometrical optics. This effect, called the spin Hall effect of light, is typically neglected in ray-tracing codes used for modeling waves in plasmas. Here, we demonstrate that the spin Hall effect can be significant for radiofrequency waves in toroidal magnetized plasmas whose parameters are in the ballpark of those used in fusion experiments. For example, an electron-cyclotron wave beam can deviate by as large as 10 wavelengths (∼0.1 m) relative to the lowest-order ray trajectory in the poloidal direction. We calculate this displacement using gauge-invariant ray equations of extended geometrical optics, and we also compare our theoretical predictions with full-wave simulations.
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Affiliation(s)
- Yichen Fu
- Princeton Plasma Physics Laboratory, Princeton, New Jersey 08543, USA and Department of Astrophysical Sciences, Princeton University, Princeton, New Jersey 08544, USA
| | - I Y Dodin
- Princeton Plasma Physics Laboratory, Princeton, New Jersey 08543, USA and Department of Astrophysical Sciences, Princeton University, Princeton, New Jersey 08544, USA
| | - Hong Qin
- Princeton Plasma Physics Laboratory, Princeton, New Jersey 08543, USA and Department of Astrophysical Sciences, Princeton University, Princeton, New Jersey 08544, USA
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8
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Qin H, Fu Y. Topological Langmuir-cyclotron wave. SCIENCE ADVANCES 2023; 9:eadd8041. [PMID: 37000869 PMCID: PMC10065437 DOI: 10.1126/sciadv.add8041] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/05/2022] [Accepted: 02/27/2023] [Indexed: 06/18/2023]
Abstract
A theory is developed to describe the topological Langmuir-cyclotron wave (TLCW), a topological excitation in magnetized plasmas recently identified by numerical simulations. As a topological wave in a continuous medium, the TLCW propagates unidirectionally without scattering in complex boundaries and can be explored as an effective mechanism to energize particles. We show that, because momentum space in continuous media is contractible in general, the topology of the wave bundles is trivial over momentum space that contains no degeneracy points. This is in stark contrast to condensed matters with periodic lattice structures that impose nontrivial topology on momentum space. In continuous media without lattice structures, nontrivial topology of the eigenmode bundles manifests over phase space, and it is the nontrivial topology over phase space that underpins the topological excitations, such as the TLCW. It is shown that the TLCW can be faithfully modeled by a generic tilted Dirac cone in phase space, whose entire spectrum, including the spectral flow, is given.
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Affiliation(s)
- Hong Qin
- Corresponding author. (H.Q.); (Y.F.)
| | - Yichen Fu
- Corresponding author. (H.Q.); (Y.F.)
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9
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Zhongfu L, Chan HC, Xu S, Xiang Y. Asymmetry spin-polarization Fermi arc and topological chiral beam splitter with the triply degenerate point in metamaterial. OPTICS LETTERS 2023; 48:932-935. [PMID: 36790978 DOI: 10.1364/ol.482614] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/01/2022] [Accepted: 01/10/2023] [Indexed: 06/18/2023]
Abstract
Dirac points (DPs) and Weyl points (WPs) have received much attention in photonic crystals (PhCs) and three-dimensional (3D) metamaterials research due to the robust surface states and Fermi arcs. In this work, two pairs of triply degenerate points (TDPs) have been proposed in a 3D metamaterial by breaking the time reversal symmetry (T) with an external magnetic field. Based on these TDPs, two pairs of asymmetric surface states with spin-polarization are revealed, and a topological chiral beam splitter is demonstrated showing the different propagating directions of the right-handed polarization (RCP) and left-handed polarization (LCP) lights. Remarkably, we can achieve unidirectional propagation with RCP or LCP even excited by a linear source owing to the asymmetry surface state. Our work provides a new, to the best of our knowledge, platform to study spin-polarization surface states and the enhanced spin photonic Hall effect in the metamaterials.
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10
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Wang D, Yang B, Wang M, Zhang RY, Li X, Zhang ZQ, Zhang S, Chan CT. Observation of Non-Abelian Charged Nodes Linking Nonadjacent Gaps. PHYSICAL REVIEW LETTERS 2022; 129:263604. [PMID: 36608196 DOI: 10.1103/physrevlett.129.263604] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/09/2022] [Accepted: 11/22/2022] [Indexed: 06/17/2023]
Abstract
Nodal links are special configurations of band degeneracies in the momentum space, where nodal line branches encircle each other. In PT symmetric systems, nodal lines can be topologically characterized using the eigenvector frame rotations along an encircling loop and the linking structure can be described with non-Abelian frame charges involving adjacent bands. While the commutation rules between the frame charges are well established, the underlying relationship between distant band gap closing nodes remains to be explored. In this Letter, we present a photonic multiple nodal links system, where the nodal lines of nonadjacent bands are investigated with symmetry constraints on frame charges. Through an orthogonal nodal chain, the nodal line from the lower two bands predicts the existence of nodal lines formed between the higher bands. We designed and fabricated a metamaterial, with which the multiple nodal links and the topological connection between nonadjacent nodal lines are experimentally demonstrated.
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Affiliation(s)
- Dongyang Wang
- Department of Physics and Center for Metamaterials Research, Hong Kong University of Science and Technology, Hong Kong, China
| | - Biao Yang
- Department of Physics and Center for Metamaterials Research, Hong Kong University of Science and Technology, Hong Kong, China
- College of Advanced Interdisciplinary Studies, National University of Defense Technology, Changsha 410073, China
| | - Mudi Wang
- Department of Physics and Center for Metamaterials Research, Hong Kong University of Science and Technology, Hong Kong, China
| | - Ruo-Yang Zhang
- Department of Physics and Center for Metamaterials Research, Hong Kong University of Science and Technology, Hong Kong, China
| | - Xiao Li
- Department of Physics and Center for Metamaterials Research, Hong Kong University of Science and Technology, Hong Kong, China
| | - Z Q Zhang
- Department of Physics and Center for Metamaterials Research, Hong Kong University of Science and Technology, Hong Kong, China
| | - Shuang Zhang
- Department of Physics, The University of Hong Kong, Hong Kong, China
- Department of Electrical and Electronic Engineering, The University of Hong Kong, Hong Kong, China
| | - C T Chan
- Department of Physics and Center for Metamaterials Research, Hong Kong University of Science and Technology, Hong Kong, China
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11
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Chern RL, Chou YJ. Photonic topological phases in Tellegen metamaterials. OPTICS EXPRESS 2022; 30:47004-47016. [PMID: 36558638 DOI: 10.1364/oe.476682] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/07/2022] [Accepted: 11/28/2022] [Indexed: 06/17/2023]
Abstract
We investigate the photonic topological phases in Tellegen metamaterials characterized by the antisymmetric magnetoelectric tensors with real-valued quantities. The underlying medium is considered a photonic analogue of the topological semimetal featured with a displaced Weyl cone in the frequency-wave vector space. As the 'spin'-degenerate condition is satisfied, the photonic system consists of two hybrid modes that are completely decoupled. By introducing the pseudospin states as the basis for the hybrid modes, the photonic system is described by two subsystems in terms of the spin-orbit Hamiltonians with spin 1, which result in nonzero spin Chern numbers that determine the topological properties. Surface modes at the interface between two Tellegen metamaterials with opposite sign of the magnetoelectric parameter exist at their common gap in the wave vector space, which are analytically formulated by algebraic equations. In particular, two types of surface modes are tangent to or wrapping around the Weyl cones, which form a pair of bended and a pair of twisted surface sheets. At the Weyl frequency, the surface modes contain a typical and two open Fermi arc-like states that concatenate to yield an infinite straight line. Topological features of the Tellegen metamaterials are further illustrated with the robust transport of surface modes at an irregular boundary.
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12
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Photonic Weyl semimetals in pseudochiral metamaterials. Sci Rep 2022; 12:18847. [PMID: 36344624 PMCID: PMC9640650 DOI: 10.1038/s41598-022-23505-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/13/2022] [Accepted: 11/01/2022] [Indexed: 11/09/2022] Open
Abstract
We investigate the photonic topological phases in pseudochiral metamaterials characterized by the magnetoelectric tensors with symmetric off-diagonal chirality components. The underlying medium is considered a photonic analogue of the type-II Weyl semimetal featured with two pairs of tilted Weyl cones in the frequency-wave vector space. As the ’spin’-degenerate condition is satisfied, the photonic system consists of two hybrid modes that are completely decoupled. By introducing the pseudospin states as the basis for the hybrid modes, the photonic system is described by two subsystems in terms of the spin-orbit Hamiltonians with spin 1, which result in nonzero spin Chern numbers that determine the topological properties. Surface modes at the interface between vacuum and the pseudochiral metamaterial exist in their common gap in the wave vector space, which are analytically formulated by algebraic equations. In particular, the surface modes are tangent to both the vacuum light cone and the Weyl cones, which form two pairs of crossing surface sheets that are symmetric about the transverse axes. At the Weyl frequency, the surface modes that connect the Weyl points form four Fermi arc-like states as line segments. Topological features of the pseudochiral metamaterials are further illustrated with the robust transport of surface modes at an irregular boundary.
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Liu Y, Wang GP, Pendry JB, Zhang S. All-angle reflectionless negative refraction with ideal photonic Weyl metamaterials. LIGHT, SCIENCE & APPLICATIONS 2022; 11:276. [PMID: 36123359 PMCID: PMC9485223 DOI: 10.1038/s41377-022-00972-9] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/27/2022] [Revised: 08/17/2022] [Accepted: 08/29/2022] [Indexed: 06/02/2023]
Abstract
Negative refraction, an unnatural optical phenomenon in which the incident and the refracted waves reside on the same side of the surface normal, has been demonstrated with the invention of negative index media based on artificially engineered photonic structures called metamaterials. It has received wide attention due to its potential applications in imaging, nonlinear optics, and electromagnetic cloaking. However, it is highly challenging to realize negative refraction operating at all angles and with the perfect transmission. In this work, leveraging the recent development in topological photonics, we propose to realize reflectionless negative refraction for all incident angles with a topological metamaterial. The proposed metamaterial possesses two Weyl points of opposite topological charges. By interfacing the metamaterial with a perfect electric conductor (PEC) or a perfect magnetic conductor (PMC), the Fermi arc connecting the two Weyl points can take the form of a half-circle possessing a positive or a negative refractive index. Importantly, due to the topological protection, there is no reflection at the interface between the PEC and PMC covered areas, leading to the observation of all-angle negative refraction without reflection at the boundary. Our work provides a new platform for manipulating the propagation of surface waves, which may find applications in the construction of integrated photonic devices.
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Affiliation(s)
- Yachao Liu
- College of Electronics and Information Engineering, Shenzhen University, 518060, Shenzhen, China
- School of Physics & Astronomy, University of Birmingham, Birmingham, B15 2TT, UK
| | - Guo Ping Wang
- College of Electronics and Information Engineering, Shenzhen University, 518060, Shenzhen, China.
| | - John B Pendry
- The Blackett Laboratory, Department of Physics, Imperial College London, London, SW7 2AZ, UK.
| | - Shuang Zhang
- Department of Physics, University of Hong Kong, Hong Kong, China.
- Department of Electrical & Electronic Engineering, University of Hong Kong, Hong Kong, China.
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Wang HX, Chen Y, Guo GY, Kee HY, Jiang JH. Possible realization of optical Dirac points in woodpile photonic crystals. OPTICS EXPRESS 2022; 30:17204-17220. [PMID: 36221548 DOI: 10.1364/oe.456614] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/21/2022] [Accepted: 04/21/2022] [Indexed: 06/16/2023]
Abstract
The simulation of fermionic relativistic physics, e.g., Dirac and Weyl physics, has led to the discovery of many unprecedented phenomena in photonics, of which the optical-frequency realization is, however, still challenging. Here, surprisingly, we discover that the woodpile photonic crystals commonly used for optical frequency applications host exotic fermion-like relativistic degeneracies: a Dirac nodal line and a fourfold quadratic point, as protected by the nonsymmorphic crystalline symmetry. Deforming the woodpile photonic crystal leads to the emergence of type-II Dirac points from the fourfold quadratic point. Such type-II Dirac points can be detected by its anomalous refraction property which is manifested as a giant birefringence in a slab setup. Our findings provide a promising route towards 3D optical Dirac physics in all-dielectric photonic crystals.
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15
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Abstract
Thermal diffusion is dissipative and strongly related to non-Hermitian physics. At the same time, non-Hermitian Weyl systems have spurred tremendous interest across photonics and acoustics. This correlation has been long ignored and hence shed little light upon the question of whether the Weyl exceptional ring (WER) in thermal diffusion could exist. Intuitively, thermal diffusion provides no real parameter dimensions, thus prohibiting a topological nature and WER. This work breaks this perception by imitating synthetic dimensions via two spatiotemporal advection pairs. The WER is achieved in thermal diffusive systems. Both surface-like and bulk states are demonstrated by coupling two WERs with opposite topological charges. These findings extend topological notions to diffusions and motivate investigation of non-Hermitian diffusive and dissipative control. A non-Hermitian Weyl equation indispensably requires a three-dimensional (3D) real/synthetic space, and it is thereby perceived that a Weyl exceptional ring (WER) will not be present in thermal diffusion given its purely dissipative nature. Here, we report a recipe for establishing a 3D parameter space to imitate thermal spinor field. Two orthogonal pairs of spatiotemporally modulated advections are employed to serve as two synthetic parameter dimensions, in addition to the inherent dimension corresponding to heat exchanges. We first predict the existence of WER in our hybrid conduction–advection system and experimentally observe the WER thermal signatures verifying our theoretical prediction. When coupling two WERs of opposite topological charges, the system further exhibits surface-like and bulk topological states, manifested as stationary and continuously changing thermal processes, respectively, with good robustness. Our findings reveal the long-ignored topological nature in thermal diffusion and may empower distinct paradigms for general diffusion and dissipation controls.
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Chen Y, Wang HX, Bao Q, Jiang JH, Chen H. Ideal type-II Weyl points in twisted one-dimensional dielectric photonic crystals. OPTICS EXPRESS 2021; 29:40606-40616. [PMID: 34809396 DOI: 10.1364/oe.444780] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/01/2021] [Accepted: 11/10/2021] [Indexed: 06/13/2023]
Abstract
We proposed an one-dimensional layer-stacked photonic crystal using anisotropic materials to realize ideal type-II Weyl points. The topological transition from Dirac to Weyl points can be clearly observed by tuning the twist angle between layers. Also, on the interface between the photonic type-II Weyl material and air, gapless surface states have been demonstrated in an incomplete bulk bandgap. By breaking parameter symmetry, these ideal type-II Weyl points would transform into the non-ideal ones, exhibiting topological surface states with single group velocity. Our work may provide a new idea for the realization of photonic semimetal phases by utilizing naturally anisotropic materials.
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17
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Han N, Liu J, Gao Y, Zhou K, Liu S. Chiral and multiple one-way surface states on photonic gyroelectric metamaterials with small Chern number. OPTICS EXPRESS 2021; 29:33097-33108. [PMID: 34809128 DOI: 10.1364/oe.427068] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/08/2021] [Accepted: 09/09/2021] [Indexed: 06/13/2023]
Abstract
Topological one-way surface states allow light to pass through sharp corners without reflection. In order to enhance the capability of surface routing devices, multiple one-way surface modes are usually required. Different from previously reported multiple surface modes achieved with large Chern number photonic media, we realize multiple surface waves on a continuous medium with small Chern number, i.e., |C| = 1. The new topological phase is found when the hyperbolic and double semi-ellipsoid-like cone bands are simultaneously gapped by vacuum state. We also find the degeneracy of multiple one-way surface waves in the double semi-ellipsoid-like metamaterials. The propagation direction of the waves is determined by their own ellipticities. Our results may help to construct surface state devices with multiplexing capability and higher coupling efficiency.
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18
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Fu Y, Qin H. Topological phases and bulk-edge correspondence of magnetized cold plasmas. Nat Commun 2021; 12:3924. [PMID: 34168159 PMCID: PMC8225675 DOI: 10.1038/s41467-021-24189-3] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/26/2021] [Accepted: 06/07/2021] [Indexed: 12/01/2022] Open
Abstract
Plasmas have been recently studied as topological materials. However, a comprehensive picture of topological phases and topological phase transitions in cold magnetized plasmas is still missing. Here we systematically map out all the topological phases and establish the bulk-edge correspondence in cold magnetized plasmas. We find that for the linear eigenmodes, there are 10 topological phases in the parameter space of density n, magnetic field B, and parallel wavenumber kz, separated by the surfaces of Langmuir wave-L wave resonance, Langmuir wave-cyclotron wave resonance, and zero magnetic field. For fixed B and kz, only the phase transition at the Langmuir wave-cyclotron wave resonance corresponds to edge modes. A sufficient and necessary condition for the existence of this type of edge modes is given and verified by numerical solutions. We demonstrate that edge modes exist not only on a plasma-vacuum interface but also on more general plasma-plasma interfaces. This finding broadens the possible applications of these exotic excitations in space and laboratory plasmas. Magnetized plasma can be regarded as topological matter. Here the authors identify a necessary and sufficient condition for the existence of topological edge mode and find that cold magnetized plasma has ten topological phases in the plasma frequency, cyclotron frequency and wave-vector space.
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Affiliation(s)
- Yichen Fu
- Princeton Plasma Physics Laboratory, Princeton, NJ, USA. .,Department of Astrophysical Sciences, Princeton University, Princeton, NJ, USA.
| | - Hong Qin
- Princeton Plasma Physics Laboratory, Princeton, NJ, USA.,Department of Astrophysical Sciences, Princeton University, Princeton, NJ, USA
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19
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Abstract
Metals, semiconductors, metamaterials, and various two-dimensional materials with plasmonic dispersion exhibit numerous exotic physical effects in the presence of an external bias, for example an external static magnetic field or electric current. These physical phenomena range from Faraday rotation of light propagating in the bulk to strong confinement and directionality of guided modes on the surface and are a consequence of the breaking of Lorentz reciprocity in these systems. The recent introduction of relevant concepts of topological physics, translated from condensed-matter systems to photonics, has not only given a new perspective on some of these topics by relating certain bulk properties of plasmonic media to the surface phenomena, but has also led to the discovery of new regimes of truly unidirectional, backscattering-immune, surface-wave propagation. In this article, we briefly review the concepts of nonreciprocity and topology and describe their manifestation in plasmonic materials. Furthermore, we use these concepts to classify and discuss the different classes of guided surface modes existing on the interfaces of various plasmonic systems.
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Vaidya S, Noh J, Cerjan A, Jörg C, von Freymann G, Rechtsman MC. Observation of a Charge-2 Photonic Weyl Point in the Infrared. PHYSICAL REVIEW LETTERS 2020; 125:253902. [PMID: 33416372 DOI: 10.1103/physrevlett.125.253902] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/18/2020] [Revised: 10/27/2020] [Accepted: 11/09/2020] [Indexed: 06/12/2023]
Abstract
Weyl points are robust point degeneracies in the band structure of a periodic material, which act as monopoles of Berry curvature. They have been at the forefront of research in three-dimensional topological materials as they are associated with novel behavior both in the bulk and on the surface. Here, we present the experimental observation of a charge-2 photonic Weyl point in a low-index-contrast photonic crystal fabricated by two-photon polymerization. The reflection spectrum obtained via Fourier-transform infrared spectroscopy closely matches simulations and shows two bands with quadratic dispersion around a point degeneracy.
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Affiliation(s)
- Sachin Vaidya
- Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
| | - Jiho Noh
- Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
| | - Alexander Cerjan
- Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
| | - Christina Jörg
- Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
- Physics Department and Research Center OPTIMAS, Technische Universität Kaiserslautern, 67663 Kaiserslautern, Germany
| | - Georg von Freymann
- Physics Department and Research Center OPTIMAS, Technische Universität Kaiserslautern, 67663 Kaiserslautern, Germany
- Fraunhofer Institute for Industrial Mathematics ITWM, 67663 Kaiserslautern, Germany
| | - Mikael C Rechtsman
- Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
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22
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García-Elcano I, González-Tudela A, Bravo-Abad J. Tunable and Robust Long-Range Coherent Interactions between Quantum Emitters Mediated by Weyl Bound States. PHYSICAL REVIEW LETTERS 2020; 125:163602. [PMID: 33124853 DOI: 10.1103/physrevlett.125.163602] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/05/2019] [Accepted: 09/11/2020] [Indexed: 06/11/2023]
Abstract
Long-range coherent interactions between quantum emitters are instrumental for quantum information and simulation technologies, but they are generally difficult to isolate from dissipation. Here, we show how such interactions can be obtained in photonic Weyl environments due to the emergence of an exotic bound state whose wave function displays power-law spatial confinement. Using an exact formalism, we show how this bound state can mediate coherent transfer of excitations between emitters, with virtually no dissipation and with a transfer rate that follows the same scaling with distance as the bound state wave function. In addition, we show that the topological nature of Weyl points translates into two important features of the Weyl bound state, and, consequently, of the interactions it mediates: first, its range can be tuned without losing the power-law confinement, and, second, they are robust under energy disorder of the bath. To our knowledge, this is the first proposal of a photonic setup that combines simultaneously coherence, tunability, long range, and robustness to disorder. These findings could ultimately pave the way for the design of more robust long-distance entanglement protocols or quantum simulation implementations for studying long-range interacting systems.
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Affiliation(s)
- Iñaki García-Elcano
- Departamento de Física Teórica de la Materia Condensada and Condensed Matter Physics Center (IFIMAC), Universidad Autónoma de Madrid, E-28049 Madrid, Spain
| | | | - Jorge Bravo-Abad
- Departamento de Física Teórica de la Materia Condensada and Condensed Matter Physics Center (IFIMAC), Universidad Autónoma de Madrid, E-28049 Madrid, Spain
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23
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Cheng H, Gao W, Bi Y, Liu W, Li Z, Guo Q, Yang Y, You O, Feng J, Sun H, Tian J, Chen S, Zhang S. Vortical Reflection and Spiraling Fermi Arcs with Weyl Metamaterials. PHYSICAL REVIEW LETTERS 2020; 125:093904. [PMID: 32915597 DOI: 10.1103/physrevlett.125.093904] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/10/2020] [Accepted: 08/07/2020] [Indexed: 06/11/2023]
Abstract
Scatterings and transport in Weyl semimetals have caught growing attention in condensed matter physics, with observables including chiral zero modes and the associated magnetoresistance and chiral magnetic effects. Measurement of electrical conductance is usually performed in these studies, which, however, cannot resolve the momentum of electrons, preventing direct observation of the phase singularities in scattering matrix associated with Weyl point. Here we experimentally demonstrate a helical phase distribution in the angle (momentum) resolved scattering matrix of electromagnetic waves in a photonic Weyl metamaterial. It further leads to spiraling Fermi arcs in an air gap sandwiched between a Weyl metamaterial and a metal plate. Benefiting from the alignment-free feature of angular vortical reflection, our findings establish a new platform in manipulating optical angular momenta with photonic Weyl systems.
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Affiliation(s)
- Hua Cheng
- School of Physics & Astronomy, University of Birmingham, Birmingham B15 2TT, United Kingdom
- The Key Laboratory of Weak Light Nonlinear Photonics, Ministry of Education, School of Physics, TEDA Institute of Applied Physics, and Renewable Energy Conversion and Storage Center, Nankai University, Tianjin 300071, China
| | - Wenlong Gao
- School of Physics & Astronomy, University of Birmingham, Birmingham B15 2TT, United Kingdom
| | - Yangang Bi
- School of Physics & Astronomy, University of Birmingham, Birmingham B15 2TT, United Kingdom
- State Key Lab of Integrated Optoelectronics, College of Electronic Science and Engineering, Jilin University, Changchun 130012, China
| | - Wenwei Liu
- The Key Laboratory of Weak Light Nonlinear Photonics, Ministry of Education, School of Physics, TEDA Institute of Applied Physics, and Renewable Energy Conversion and Storage Center, Nankai University, Tianjin 300071, China
| | - Zhancheng Li
- The Key Laboratory of Weak Light Nonlinear Photonics, Ministry of Education, School of Physics, TEDA Institute of Applied Physics, and Renewable Energy Conversion and Storage Center, Nankai University, Tianjin 300071, China
| | - Qinghua Guo
- School of Physics & Astronomy, University of Birmingham, Birmingham B15 2TT, United Kingdom
| | - Yang Yang
- School of Physics & Astronomy, University of Birmingham, Birmingham B15 2TT, United Kingdom
| | - Oubo You
- School of Physics & Astronomy, University of Birmingham, Birmingham B15 2TT, United Kingdom
| | - Jing Feng
- State Key Lab of Integrated Optoelectronics, College of Electronic Science and Engineering, Jilin University, Changchun 130012, China
| | - Hongbo Sun
- State Key Lab of Integrated Optoelectronics, College of Electronic Science and Engineering, Jilin University, Changchun 130012, China
- State Key Laboratory of Precision Measurement Technology & Instruments, Department of Precision Instrument, Tsinghua University, Beijing 100084, China
| | - Jianguo Tian
- The Key Laboratory of Weak Light Nonlinear Photonics, Ministry of Education, School of Physics, TEDA Institute of Applied Physics, and Renewable Energy Conversion and Storage Center, Nankai University, Tianjin 300071, China
| | - Shuqi Chen
- The Key Laboratory of Weak Light Nonlinear Photonics, Ministry of Education, School of Physics, TEDA Institute of Applied Physics, and Renewable Energy Conversion and Storage Center, Nankai University, Tianjin 300071, China
| | - Shuang Zhang
- School of Physics & Astronomy, University of Birmingham, Birmingham B15 2TT, United Kingdom
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Kim M, Jacob Z, Rho J. Recent advances in 2D, 3D and higher-order topological photonics. LIGHT, SCIENCE & APPLICATIONS 2020; 9:130. [PMID: 32704363 PMCID: PMC7371865 DOI: 10.1038/s41377-020-0331-y] [Citation(s) in RCA: 70] [Impact Index Per Article: 17.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/27/2020] [Revised: 04/21/2020] [Accepted: 05/07/2020] [Indexed: 05/25/2023]
Abstract
Over the past decade, topology has emerged as a major branch in broad areas of physics, from atomic lattices to condensed matter. In particular, topology has received significant attention in photonics because light waves can serve as a platform to investigate nontrivial bulk and edge physics with the aid of carefully engineered photonic crystals and metamaterials. Simultaneously, photonics provides enriched physics that arises from spin-1 vectorial electromagnetic fields. Here, we review recent progress in the growing field of topological photonics in three parts. The first part is dedicated to the basics of topological band theory and introduces various two-dimensional topological phases. The second part reviews three-dimensional topological phases and numerous approaches to achieve them in photonics. Last, we present recently emerging fields in topological photonics that have not yet been reviewed. This part includes topological degeneracies in nonzero dimensions, unidirectional Maxwellian spin waves, higher-order photonic topological phases, and stacking of photonic crystals to attain layer pseudospin. In addition to the various approaches for realizing photonic topological phases, we also discuss the interaction between light and topological matter and the efforts towards practical applications of topological photonics.
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Affiliation(s)
- Minkyung Kim
- Department of Mechanical Engineering, Pohang University of Science and Technology (POSTECH), Pohang, 37673 Republic of Korea
| | - Zubin Jacob
- School of Electrical and Computer Engineering, Birck Nanotechnology Center, Purdue University, West Lafayette, IN 47906 USA
| | - Junsuk Rho
- Department of Mechanical Engineering, Pohang University of Science and Technology (POSTECH), Pohang, 37673 Republic of Korea
- Department of Chemical Engineering, Pohang University of Science and Technology (POSTECH), Pohang, 37673 Republic of Korea
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25
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Wang W, Gao W, Cao L, Xiang Y, Zhang S. Photonic topological fermi nodal disk in non-Hermitian magnetic plasma. LIGHT, SCIENCE & APPLICATIONS 2020; 9:40. [PMID: 32194954 PMCID: PMC7066160 DOI: 10.1038/s41377-020-0274-3] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 03/04/2019] [Revised: 01/13/2020] [Accepted: 02/26/2020] [Indexed: 06/10/2023]
Abstract
Topological physics mainly arises as a necessary link between properties of the bulk and the appearance of surface states, and has led to successful discoveries of novel topological surface states in Chern insulators, topological insulators, and topological Fermi arcs in Weyl, Dirac, and Nodal line semimetals owing to their nontrivial bulk topology. In particular, topological phases in non-Hermitian systems have attracted growing interests in recent years. In this work, we predict the emergence of the topologically stable nodal disks where the real part of the eigen frequency is degenerate between two bands in non-ideal magnetohydrodynamics plasma with collision and viscosity dissipations. Each nodal disk possesses continuously distributed topological surface charge density that integrates to unity. It is found that the lossy Fermi arcs at the interface connect to the middle of the projection of the nodal disks. We further show that the emergence, coalescence, and annihilation of the nodal disks can be controlled by plasma parameters and dissipation terms. Our findings contribute to understanding of the linear theory of bulk and surface wave dispersions of non-ideal warm magnetic plasmas from the perspective of topological physics.
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Affiliation(s)
- Wenhui Wang
- International Collaborative Laboratory of 2D Materials for Optoelectronic Science & Technology of Ministry of Education, Institute of Microscale Optoelectronics (IMO), Shenzhen University, 518060 Shenzhen, China
- School of Physics & Astronomy, University of Birmingham, Birmingham, B15 2TT UK
| | - Wenlong Gao
- School of Physics & Astronomy, University of Birmingham, Birmingham, B15 2TT UK
| | - Leifeng Cao
- National Key Laboratory for Laser Fusion, Research Centre of Laser Fusion, CAEP, 621900 Mianyang, China
| | - Yuanjiang Xiang
- School of Physics and Electronics, Hunan University, 410082 Changsha, China
| | - Shuang Zhang
- School of Physics & Astronomy, University of Birmingham, Birmingham, B15 2TT UK
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26
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Xiao M, Ye L, Qiu C, He H, Liu Z, Fan S. Experimental demonstration of acoustic semimetal with topologically charged nodal surface. SCIENCE ADVANCES 2020; 6:eaav2360. [PMID: 32128388 PMCID: PMC7034989 DOI: 10.1126/sciadv.aav2360] [Citation(s) in RCA: 17] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/27/2018] [Accepted: 12/04/2019] [Indexed: 05/31/2023]
Abstract
Weyl points are zero-dimensional band degeneracy in three-dimensional momentum space that has nonzero topological charges. The presence of the topological charges protects the degeneracy points against perturbations and enables a variety of fascinating phenomena. It is so far unclear whether such charged objects can occur in higher dimensions. Here, we introduce the concept of charged nodal surface, a two-dimensional band degeneracy surface in momentum space that is topologically charged. We provide an effective Hamiltonian for this charged nodal surface and show that such a Hamiltonian can be implemented in a tight-binding model. This is followed by an experimental realization in a phononic crystal. The measured topologically protected surface arc state of such an acoustic semimetal reproduces excellently the full-wave simulations. Creating high-dimensional charged geometric objects in momentum space promises a broad range of unexplored topological physics.
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Affiliation(s)
- Meng Xiao
- Department of Electrical Engineering, and Ginzton Laboratory, Stanford University, Stanford, CA 94305, USA
- Key Laboratory of Artificial Micro- and Nano-structures of Ministry of Education and School of Physics and Technology, Wuhan University, Wuhan 430072, China
| | - Liping Ye
- Key Laboratory of Artificial Micro- and Nano-structures of Ministry of Education and School of Physics and Technology, Wuhan University, Wuhan 430072, China
| | - Chunyin Qiu
- Key Laboratory of Artificial Micro- and Nano-structures of Ministry of Education and School of Physics and Technology, Wuhan University, Wuhan 430072, China
| | - Hailong He
- Key Laboratory of Artificial Micro- and Nano-structures of Ministry of Education and School of Physics and Technology, Wuhan University, Wuhan 430072, China
| | - Zhengyou Liu
- Key Laboratory of Artificial Micro- and Nano-structures of Ministry of Education and School of Physics and Technology, Wuhan University, Wuhan 430072, China
- Institute for Advanced Studies, Wuhan University, Wuhan 430072, China
| | - Shanhui Fan
- Department of Electrical Engineering, and Ginzton Laboratory, Stanford University, Stanford, CA 94305, USA
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27
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Photonic topological semimetals in bianisotropic metamaterials. Sci Rep 2019; 9:18312. [PMID: 31797947 PMCID: PMC6892789 DOI: 10.1038/s41598-019-54523-1] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/12/2019] [Accepted: 11/13/2019] [Indexed: 11/17/2022] Open
Abstract
We analyze the photonic topological phases in bianisotropic metamaterials characterized by a chirality tensor with zero trace. We found that the strength of chirality component determines the topological character of the metamaterial. The underlying medium can be considered as a topological semimetal with the nontrivial band gap in the momentum space. The topological properties are described by the spin-orbit Hamiltonians with spin 1 and characterized by the nonzero topological invariants. In particular, photonic quantum Hall states exist when the longitudinal chirality component exceeds the permittivity, whereas photonic quantum spin Hall states are present when the chiral nihility occurs. Considering the dispersion in the frequency domain, the bianisotropic metamaterial is regarded as a photonic Weyl system that supports the Weyl points and Fermi arcs. The topological features are further illustrated with the robust transport of edge states at an irregular boundary of the metamaterial.
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28
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Jin D, Xia Y, Christensen T, Freeman M, Wang S, Fong KY, Gardner GC, Fallahi S, Hu Q, Wang Y, Engel L, Xiao ZL, Manfra MJ, Fang NX, Zhang X. Topological kink plasmons on magnetic-domain boundaries. Nat Commun 2019; 10:4565. [PMID: 31594922 PMCID: PMC6783483 DOI: 10.1038/s41467-019-12092-x] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/11/2018] [Accepted: 07/31/2019] [Indexed: 11/09/2022] Open
Abstract
Two-dimensional topological materials bearing time reversal-breaking magnetic fields support protected one-way edge modes. Normally, these edge modes adhere to physical edges where material properties change abruptly. However, even in homogeneous materials, topology still permits a unique form of edge modes – kink modes – residing at the domain boundaries of magnetic fields within the materials. This scenario, despite being predicted in theory, has rarely been demonstrated experimentally. Here, we report our observation of topologically-protected high-frequency kink modes – kink magnetoplasmons (KMPs) – in a GaAs/AlGaAs two-dimensional electron gas (2DEG) system. These KMPs arise at a domain boundary projected from an externally-patterned magnetic field onto a uniform 2DEG. They propagate unidirectionally along the boundary, protected by a difference of gap Chern numbers (\documentclass[12pt]{minimal}
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\begin{document}$$\pm1$$\end{document}±1) in the two domains. They exhibit large tunability under an applied magnetic field or gate voltage, and clear signatures of nonreciprocity even under weak-coupling to evanescent photons. Topological kink modes are peculiar edge excitations that take place at domain boundaries of magnetic fields inside homogeneous materials. Here, the authors experimentally observe kink magnetoplasmons in a 2D electron gas using custom-shaped strong permanent magnets on top of a GaAs/AlGaAs heterojunction.
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Affiliation(s)
- Dafei Jin
- Nanoscale Science and Engineering Center, University of California, Berkeley, CA, 94706, USA.,Center for Nanoscale Materials, Argonne National Laboratory, Argonne, IL, 60439, USA
| | - Yang Xia
- Nanoscale Science and Engineering Center, University of California, Berkeley, CA, 94706, USA
| | - Thomas Christensen
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA
| | - Matthew Freeman
- National High Magnetic Field Laboratory, Tallahassee, FL, 32310, USA
| | - Siqi Wang
- Nanoscale Science and Engineering Center, University of California, Berkeley, CA, 94706, USA
| | - King Yan Fong
- Nanoscale Science and Engineering Center, University of California, Berkeley, CA, 94706, USA
| | - Geoffrey C Gardner
- Microsoft Quantum Purdue and Birck Nanotechnology Center, Purdue University, West Lafayette, IN, 47907, USA
| | - Saeed Fallahi
- Department of Physics and Astronomy and Birck Nanotechnology Center, Purdue University, West Lafayette, IN, 47907, USA
| | - Qing Hu
- Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA
| | - Yuan Wang
- Nanoscale Science and Engineering Center, University of California, Berkeley, CA, 94706, USA
| | - Lloyd Engel
- National High Magnetic Field Laboratory, Tallahassee, FL, 32310, USA
| | - Zhi-Li Xiao
- Material Science Division, Argonne National Laboratory, Argonne, IL, 60439, USA
| | - Michael J Manfra
- Microsoft Quantum Purdue, Department of Physics and Astronomy, Birck Nanotechnology Center, Schools of Electrical and Computer Engineering and Materials Engineering, Purdue University, West Lafayette, IN, 47907, USA
| | - Nicholas X Fang
- Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA
| | - Xiang Zhang
- Nanoscale Science and Engineering Center, University of California, Berkeley, CA, 94706, USA. .,Faculties of Sciences and Engineering University of Hong Kong, Hong Kong SAR, PR, China.
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29
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Ye W, Liu Y, Liu J, Horsley SAR, Wen S, Zhang S. Photonic Hall effect and helical Zitterbewegung in a synthetic Weyl system. LIGHT, SCIENCE & APPLICATIONS 2019; 8:49. [PMID: 31149334 PMCID: PMC6538614 DOI: 10.1038/s41377-019-0160-z] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/09/2018] [Revised: 04/09/2019] [Accepted: 05/06/2019] [Indexed: 05/31/2023]
Abstract
Systems supporting Weyl points have gained increasing attention in condensed physics, photonics and acoustics due to their rich physics, such as Fermi arcs and chiral anomalies. Acting as sources or drains of Berry curvature, Weyl points exhibit a singularity of the Berry curvature at their core. It is, therefore, expected that the induced effect of the Berry curvature can be dramatically enhanced in systems supporting Weyl points. In this work, we construct synthetic Weyl points in a photonic crystal that consists of a honeycomb array of coupled rods with slowly varying radii along the direction of propagation. The system possesses photonic Weyl points in the synthetic space of two momenta plus an additional physical parameter with an enhanced Hall effect resulting from the large Berry curvature in the vicinity of the Weyl point. Interestingly, a helical Zitterbewegung (ZB) is observed when the wave packet traverses very close to a Weyl point, which is attributed to the contribution of the non-Abelian Berry connection arising from the near degenerate eigenstates.
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Affiliation(s)
- Weimin Ye
- College of Advanced Interdisciplinary Studies, National University of Defense Technology, 410073 Changsha, China
| | - Yachao Liu
- Key Laboratory for Micro/Nano Optoelectronic Devices of Ministry of Education, School of Physics and Electronics, Hunan University, 410082 Changsha, China
- School of Physics & Astronomy, University of Birmingham, Birmingham, B15 2TT UK
| | - Jianlong Liu
- Department of Physics, Harbin Institute of Technology, 150001 Harbin, China
| | - Simon A. R. Horsley
- Department of Physics and Astronomy, University of Exeter, Exeter, EX4 4QL UK
| | - Shuangchun Wen
- Key Laboratory for Micro/Nano Optoelectronic Devices of Ministry of Education, School of Physics and Electronics, Hunan University, 410082 Changsha, China
| | - Shuang Zhang
- School of Physics & Astronomy, University of Birmingham, Birmingham, B15 2TT UK
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30
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Guo Q, You O, Yang B, Sellman JB, Blythe E, Liu H, Xiang Y, Li J, Fan D, Chen J, Chan CT, Zhang S. Observation of Three-Dimensional Photonic Dirac Points and Spin-Polarized Surface Arcs. PHYSICAL REVIEW LETTERS 2019; 122:203903. [PMID: 31172768 DOI: 10.1103/physrevlett.122.203903] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/27/2018] [Indexed: 05/28/2023]
Abstract
Three-dimensional (3D) Dirac points inheriting relativistic effects from high-energy physics appear as gapless excitations in the topological band theory. Hosting fourfold linear dispersion, they play the central role among various topological phases, such as representing the degeneracy of paired Weyl nodes carrying opposite chiralities. While they have been extensively investigated in solid state systems for electrons, 3D Dirac points have not yet been observed in any classical systems. Here, we experimentally demonstrate 3D photonic Dirac points in the microwave region with an elaborately designed metamaterial, where two symmetrically placed Dirac points are stabilized by electromagnetic duality symmetry. Furthermore, spin-polarized surface arcs (counterparts of Fermi arcs in electronic systems) are demonstrated, which opens the gate toward implementing spin-multiplexed topological surface wave propagation. Closely linked to other exotic states through topological phase transitions, our system offers an effective medium platform for topological photonics.
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Affiliation(s)
- Qinghua Guo
- School of Physics & Astronomy, University of Birmingham, Birmingham, B15 2TT, United Kingdom
- Department of Physics and Center for Metamaterials Research, The Hong Kong University of Science and Technology, Hong Kong, China
| | - Oubo You
- School of Physics & Astronomy, University of Birmingham, Birmingham, B15 2TT, United Kingdom
- International Collaborative Laboratory of 2D Materials for Optoelectronic Science and Technology of Ministry of Education, Shenzhen University, Shenzhen 518060, China
| | - Biao Yang
- School of Physics & Astronomy, University of Birmingham, Birmingham, B15 2TT, United Kingdom
- College of Advanced Interdisciplinary Studies, National University of Defense Technology, Changsha 410073, China
| | - James B Sellman
- School of Physics & Astronomy, University of Birmingham, Birmingham, B15 2TT, United Kingdom
| | - Edward Blythe
- School of Physics & Astronomy, University of Birmingham, Birmingham, B15 2TT, United Kingdom
| | - Hongchao Liu
- School of Physics & Astronomy, University of Birmingham, Birmingham, B15 2TT, United Kingdom
| | - Yuanjiang Xiang
- International Collaborative Laboratory of 2D Materials for Optoelectronic Science and Technology of Ministry of Education, Shenzhen University, Shenzhen 518060, China
| | - Jensen Li
- School of Physics & Astronomy, University of Birmingham, Birmingham, B15 2TT, United Kingdom
- Department of Physics and Center for Metamaterials Research, The Hong Kong University of Science and Technology, Hong Kong, China
| | - Dianyuan Fan
- International Collaborative Laboratory of 2D Materials for Optoelectronic Science and Technology of Ministry of Education, Shenzhen University, Shenzhen 518060, China
| | - Jing Chen
- School of Physics, Nankai University, Tianjin 300071, China
| | - C T Chan
- Department of Physics and Center for Metamaterials Research, The Hong Kong University of Science and Technology, Hong Kong, China
| | - Shuang Zhang
- School of Physics & Astronomy, University of Birmingham, Birmingham, B15 2TT, United Kingdom
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31
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Xia L, Guo Q, Yang B, Han J, Liu CX, Zhang W, Zhang S. Observation of Hourglass Nodal Lines in Photonics. PHYSICAL REVIEW LETTERS 2019; 122:103903. [PMID: 30932638 DOI: 10.1103/physrevlett.122.103903] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/18/2018] [Indexed: 06/09/2023]
Abstract
Nodal line semimetals exhibiting line degeneracies in three-dimensional momentum space have been demonstrated recently. In general, the presence of nodal line semimetals is protected by special symmetries, such as mirror symmetry. However, these symmetries are usually necessary but not sufficient conditions, as nodal lines can be annihilated even without breaking them. Very recently, nodal line semimetal possessing an hourglass-shaped band structure emerges as a more robust candidate, where line degeneracies cannot be annihilated while preserving all underlying spatial symmetries. Here, for the first time, we experimentally demonstrate the presence of an hourglass nodal line (HNL) in photonic metacrystal at microwave frequency. We observe the HNL through near-field scanning of the spatial fields, followed by subsequent Fourier transformations. The observed photonic HNL resides in a clean and large frequency interval and is immune to symmetry preserving perturbation, which provides an ideal robust platform for photonic applications, such as anomalous quantum oscillation, spontaneous emission and resonant scattering.
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Affiliation(s)
- Lingbo Xia
- School of Physics and Astronomy, University of Birmingham, Birmingham, B15 2TT, United Kingdom
- Center for Terahertz Waves and College of Precision Instrument and Optoelectronics Engineering, Tianjin University and the Key Laboratory of Optoelectronics Information and Technology (Ministry of Education), Tianjin 300072, China
| | - Qinghua Guo
- School of Physics and Astronomy, University of Birmingham, Birmingham, B15 2TT, United Kingdom
| | - Biao Yang
- School of Physics and Astronomy, University of Birmingham, Birmingham, B15 2TT, United Kingdom
- College of Advanced Interdisciplinary Studies, National University of Defense Technology, Changsha 410073, China
| | - Jiaguang Han
- Center for Terahertz Waves and College of Precision Instrument and Optoelectronics Engineering, Tianjin University and the Key Laboratory of Optoelectronics Information and Technology (Ministry of Education), Tianjin 300072, China
| | - Chao-Xing Liu
- Department of Physics, Pennsylvania State University, University Park, Pennsylvania 16802-6300, USA
| | - Weili Zhang
- Center for Terahertz Waves and College of Precision Instrument and Optoelectronics Engineering, Tianjin University and the Key Laboratory of Optoelectronics Information and Technology (Ministry of Education), Tianjin 300072, China
- School of Electrical and Computer Engineering, Oklahoma State University, Stillwater, Oklahoma 74078, USA
| | - Shuang Zhang
- School of Physics and Astronomy, University of Birmingham, Birmingham, B15 2TT, United Kingdom
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32
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Xie B, Liu H, Cheng H, Liu Z, Chen S, Tian J. Experimental Realization of Type-II Weyl Points and Fermi Arcs in Phononic Crystal. PHYSICAL REVIEW LETTERS 2019; 122:104302. [PMID: 30932672 DOI: 10.1103/physrevlett.122.104302] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/21/2018] [Indexed: 06/09/2023]
Abstract
Weyl points (WPs), as the doubly degenerate points in three-dimensional momentum band structures, carry quantized topological charges and give rise to a variety of extraordinary properties, such as robust surface wave and chiral anomaly. Type-II Weyl semimetals, which have conical dispersions in Fermi surfaces and a strongly tilted dispersion with respect to type I, have recently been proposed in condensed-matter systems and photonics. Although the type-II WPs have been theoretically predicted in acoustics, the experimental realization in phononic crystals has not been reported so far. Here, we experimentally realize a type-II Weyl phononic crystal. We demonstrate the topological transitions observed at the WP frequencies and the topological surface acoustic waves between the Weyl frequencies. The experiment results are in good accordance with our theoretical analyses. Due to the violation of the Lorentz symmetry, the type-II WPs only exist in low energy systems. As the analog counterpart in classical waves, the phononic crystal brings a platform for the research of type-II WPs in macroscopic systems.
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Affiliation(s)
- Boyang Xie
- The Key Laboratory of Weak Light Nonlinear Photonics, Ministry of Education, School of Physics and TEDA Institute of Applied Physics, Nankai University, Tianjin 300071, China
| | - Hui Liu
- The Key Laboratory of Weak Light Nonlinear Photonics, Ministry of Education, School of Physics and TEDA Institute of Applied Physics, Nankai University, Tianjin 300071, China
| | - Hua Cheng
- The Key Laboratory of Weak Light Nonlinear Photonics, Ministry of Education, School of Physics and TEDA Institute of Applied Physics, Nankai University, Tianjin 300071, China
- The collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China
| | - Zhengyou Liu
- Key Laboratory of Artificial Micro- and Nanostructures of Ministry of Education and School of Physics and Technology, Wuhan University, Wuhan 430072, China
| | - Shuqi Chen
- The Key Laboratory of Weak Light Nonlinear Photonics, Ministry of Education, School of Physics and TEDA Institute of Applied Physics, Nankai University, Tianjin 300071, China
- The collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China
- Renewable Energy Conversion and Storage Center, Nankai University, Tianjin 300071, China
| | - Jianguo Tian
- The Key Laboratory of Weak Light Nonlinear Photonics, Ministry of Education, School of Physics and TEDA Institute of Applied Physics, Nankai University, Tianjin 300071, China
- The collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China
- Renewable Energy Conversion and Storage Center, Nankai University, Tianjin 300071, China
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33
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Chattopadhyay U, Shi LK, Zhang B, Song JCW, Chong YD. Fermi-Arc-Induced Vortex Structure in Weyl Beam Shifts. PHYSICAL REVIEW LETTERS 2019; 122:066602. [PMID: 30822071 DOI: 10.1103/physrevlett.122.066602] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/17/2018] [Indexed: 06/09/2023]
Abstract
In periodic media, despite the close relationship between geometrical effects in the bulk and topological surface states, the two are typically probed separately. We show that when beams in a Weyl medium reflect off an interface with a gapped medium, the trajectory is influenced by both bulk geometrical effects and the Fermi arc surface states. The reflected beam experiences a displacement, analogous to the Goos-Hänchen or Imbert-Fedorov shifts, that forms a half-vortex in the two-dimensional surface momentum space. The half-vortex is centered where the Fermi arc of the reflecting surface touches the Weyl cone, with the magnitude of the shift scaling as an inverse square root away from the touching point, and diverging at the touching point. This striking feature provides a way to use bulk transport to probe the topological characteristics of a Weyl medium.
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Affiliation(s)
- Udvas Chattopadhyay
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore
| | - Li-Kun Shi
- Institute of High Performance Computing, A*STAR, Singapore 138632, Singapore
| | - Baile Zhang
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore
- Centre for Disruptive Photonic Technologies, Nanyang Technological University, Singapore 637371, Singapore
| | - Justin C W Song
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore
- Institute of High Performance Computing, A*STAR, Singapore 138632, Singapore
| | - Y D Chong
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore
- Centre for Disruptive Photonic Technologies, Nanyang Technological University, Singapore 637371, Singapore
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34
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Yin Z, Chen F, Guo K, Shen F, Zhou K, Gao J, Liu S, Guo Z. Tunable THz generalized Weyl points. OPTICS EXPRESS 2019; 27:512-522. [PMID: 30696136 DOI: 10.1364/oe.27.000512] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/07/2018] [Accepted: 12/30/2018] [Indexed: 06/09/2023]
Abstract
Weyl points, as linearly double degenerated point of band structures, have been extensively researched in electronic and classical wave systems. However, Weyl points' realization is always accompanied with delicate "lattice structures". In this work, frequency-tunable terahertz (THz) generalized Weyl points inside the parameter space have been investigated and displayed by a specially designed photonic crystal with polydimethylsiloxane (PDMS) immersed in 4-cyano'-pentylbipenyl (5CB) liquid crystals (LCs). The reflective phase vortices as a signature of the generalized Weyl points are observed through our numerically simulations. Besides, interface states between photonic crystals and any reflective substrates are fulfilled too. Meanwhile, we could also change the orientation of LC molecule by the external magnetic field so as to tune the frequency of the first two bands' Weyl point from 0.27698THz to 0.30013THz. This band lies in the short-range wireless communication. Thus, our proposal may be beneficial to the investigation and application of Weyl points' properties and strongly localized states.
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35
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Lu L, Gao H, Wang Z. Topological one-way fiber of second Chern number. Nat Commun 2018; 9:5384. [PMID: 30568189 PMCID: PMC6300610 DOI: 10.1038/s41467-018-07817-3] [Citation(s) in RCA: 29] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/11/2016] [Accepted: 11/26/2018] [Indexed: 11/14/2022] Open
Abstract
One-way waveguides have been discovered as topological edge states in two-dimensional (2D) photonic crystals. Here, we design one-way fiber modes in a 3D magnetic Weyl photonic crystal realizable at microwave frequencies. We first obtain a 3D Chern crystal with a non-zero first Chern number by annihilating the Weyl points through supercell modulation. When the modulation becomes helixes, one-way modes develop along the winding axis, with the number of modes determined by the spatial frequency of the helix. These single-polarization single-mode and multi-mode one-way fibers, having nearly identical group and phase velocities, are topologically-protected by the second Chern number in the 4D parameter space of the 3D wavevectors plus the winding angle of the helix. This work suggests a unique way to utilize high-dimensional topological physics using topological defects. Topological one-way fibers are promising candidates for novel fiber devices. Here, Lu et al. propose that one-way fiber modes are topologically protected by the second Chern number in a four-dimensional parameter space, which develop in a helically-modulated magnetic Weyl photonic crystal.
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Affiliation(s)
- Ling Lu
- Institute of Physics, Chinese Academy of Sciences/Beijing National Laboratory for Condensed Matter Physics, Beijing, 100190, China. .,Songshan Lake Materials Laboratory, Dongguan, Guangdong, 523808, China.
| | - Haozhe Gao
- Institute of Physics, Chinese Academy of Sciences/Beijing National Laboratory for Condensed Matter Physics, Beijing, 100190, China.,University of Chinese Academy of Sciences, Beijing, 100049, China
| | - Zhong Wang
- Institute for Advanced Study, Tsinghua University, Beijing, 100084, China. .,Collaborative Innovation Center of Quantum Matter, Beijing, 100871, China.
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36
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Fruchart M, Jeon SY, Hur K, Cheianov V, Wiesner U, Vitelli V. Soft self-assembly of Weyl materials for light and sound. Proc Natl Acad Sci U S A 2018; 115:E3655-E3664. [PMID: 29610349 PMCID: PMC5910856 DOI: 10.1073/pnas.1720828115] [Citation(s) in RCA: 37] [Impact Index Per Article: 6.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022] Open
Abstract
Soft materials can self-assemble into highly structured phases that replicate at the mesoscopic scale the symmetry of atomic crystals. As such, they offer an unparalleled platform to design mesostructured materials for light and sound. Here, we present a bottom-up approach based on self-assembly to engineer 3D photonic and phononic crystals with topologically protected Weyl points. In addition to angular and frequency selectivity of their bulk optical response, Weyl materials are endowed with topological surface states, which allow for the existence of one-way channels, even in the presence of time-reversal invariance. Using a combination of group-theoretical methods and numerical simulations, we identify the general symmetry constraints that a self-assembled structure has to satisfy to host Weyl points and describe how to achieve such constraints using a symmetry-driven pipeline for self-assembled material design and discovery. We illustrate our general approach using block copolymer self-assembly as a model system.
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Affiliation(s)
- Michel Fruchart
- Lorentz Institute, Leiden University, Leiden 2300 RA, The Netherlands;
| | - Seung-Yeol Jeon
- Center for Computational Science, Korea Institute of Science and Technology, Seoul 02792, Republic of Korea
| | - Kahyun Hur
- Center for Computational Science, Korea Institute of Science and Technology, Seoul 02792, Republic of Korea
| | - Vadim Cheianov
- Lorentz Institute, Leiden University, Leiden 2300 RA, The Netherlands
| | - Ulrich Wiesner
- Department of Materials Science and Engineering, Cornell University, Ithaca, NY 14850
| | - Vincenzo Vitelli
- Lorentz Institute, Leiden University, Leiden 2300 RA, The Netherlands;
- Department of Physics, The University of Chicago, Chicago, IL 60637
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37
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Hey D, Li E. Advances in synthetic gauge fields for light through dynamic modulation. ROYAL SOCIETY OPEN SCIENCE 2018; 5:172447. [PMID: 29765688 PMCID: PMC5936953 DOI: 10.1098/rsos.172447] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 12/31/2017] [Accepted: 03/13/2018] [Indexed: 06/08/2023]
Abstract
Photons are weak particles that do not directly couple to magnetic fields. However, it is possible to generate a photonic gauge field by breaking reciprocity such that the phase of light depends on its direction of propagation. This non-reciprocal phase indicates the presence of an effective magnetic field for the light itself. By suitable tailoring of this phase, it is possible to demonstrate quantum effects typically associated with electrons, and, as has been recently shown, non-trivial topological properties of light. This paper reviews dynamic modulation as a process for breaking the time-reversal symmetry of light and generating a synthetic gauge field, and discusses its role in topological photonics, as well as recent developments in exploring topological photonics in higher dimensions.
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Affiliation(s)
- Daniel Hey
- Author for correspondence: Daniel Hey e-mail:
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38
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Gao W, Yang B, Tremain B, Liu H, Guo Q, Xia L, Hibbins AP, Zhang S. Experimental observation of photonic nodal line degeneracies in metacrystals. Nat Commun 2018; 9:950. [PMID: 29507346 PMCID: PMC5838093 DOI: 10.1038/s41467-018-03407-5] [Citation(s) in RCA: 35] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/28/2017] [Accepted: 02/12/2018] [Indexed: 11/15/2022] Open
Abstract
Nodal line semimetals (NLS) are three-dimensional (3D) crystals that support band crossings in the form of one-dimensional rings in the Brillouin zone. In the presence of spin–orbit coupling or lowered crystal symmetry, NLS may transform into Dirac semimetals, Weyl semimetals, or 3D topological insulators. In the photonics context, despite the realization of topological phases, such as Chern insulators, topological insulators, Weyl, and Dirac degeneracies, no experimental demonstration of photonic nodal lines (NLs) has been reported so far. Here, we experimentally demonstrate NL degeneracies in microwave cut-wire metacrystals with engineered negative bulk plasma dispersion. Both the bulk and surface states of the NL metamaterial are observed through spatial Fourier transformations of the scanned near-field distributions. Furthermore, we theoretically show that the NL degeneracy can transform into two Weyl points when gyroelectric materials are incorporated into the metacrystal design. Our findings may inspire further advances in topological photonics. Nodal lines are 1D band crossings forming a ring in the Brillouin zone which can spawn Weyl points. Here, using a cut-wire metacrystal designed for gigahertz frequencies, Gao et al. observe photonic nodal line degeneracies as well as the photonic Weyl points arising from them.
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Affiliation(s)
- Wenlong Gao
- School of Physics and Astronomy, University of Birmingham, Birmingham, B15 2TT, UK
| | - Biao Yang
- School of Physics and Astronomy, University of Birmingham, Birmingham, B15 2TT, UK
| | - Ben Tremain
- Department of Physics and Astronomy, Electromagnetic and Acoustic Materials Group, University of Exeter, Stocker Road, Exeter, EX4 4QL, UK
| | - Hongchao Liu
- School of Physics and Astronomy, University of Birmingham, Birmingham, B15 2TT, UK
| | - Qinghua Guo
- School of Physics and Astronomy, University of Birmingham, Birmingham, B15 2TT, UK.,International Collaborative Laboratory of 2D Materials for Optoelectronics Science & Technology of Ministry of Education, Shenzhen University, Shenzhen, 518060, China
| | - Lingbo Xia
- School of Physics and Astronomy, University of Birmingham, Birmingham, B15 2TT, UK.,Center for Terahertz waves and College of Precision Instrument and Optoelectronics Engineering, Key Laboratory of Opto-electronics Information and Technical Science, Ministry of Education, Tianjin University, Tianjin, 300072, China
| | - Alastair P Hibbins
- International Collaborative Laboratory of 2D Materials for Optoelectronics Science & Technology of Ministry of Education, Shenzhen University, Shenzhen, 518060, China.
| | - Shuang Zhang
- School of Physics and Astronomy, University of Birmingham, Birmingham, B15 2TT, UK.
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39
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Guo Q, Yang B, Xia L, Gao W, Liu H, Chen J, Xiang Y, Zhang S. Three Dimensional Photonic Dirac Points in Metamaterials. PHYSICAL REVIEW LETTERS 2017; 119:213901. [PMID: 29219411 DOI: 10.1103/physrevlett.119.213901] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/23/2017] [Indexed: 06/07/2023]
Abstract
Topological semimetals, representing a new topological phase that lacks a full band gap in bulk states and exhibiting nontrivial topological orders, recently have been extended to photonic systems, predominantly in photonic crystals and to a lesser extent metamaterials. Photonic crystal realizations of Dirac degeneracies are protected by various space symmetries, where Bloch modes span the spin and orbital subspaces. Here, we theoretically show that Dirac points can also be realized in effective media through the intrinsic degrees of freedom in electromagnetism under electromagnetic duality. A pair of spin-polarized Fermi-arc-like surface states is observed at the interface between air and the Dirac metamaterials. Furthermore, eigenreflection fields show the decoupling process from a Dirac point to two Weyl points. We also find the topological correlation between a Dirac point and vortex or vector beams in classical photonics. The experimental feasibility of our scheme is demonstrated by designing a realistic metamaterial structure. The theoretical proposal of the photonic Dirac point lays the foundation for unveiling the connection between intrinsic physics and global topology in electromagnetism.
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Affiliation(s)
- Qinghua Guo
- Key Laboratory of Optoelectronic Devices and Systems of Ministry of Education and Guangdong Province, College of Optoelectronic Engineering, Shenzhen University, Shenzhen 518060, China
- School of Physics and Astronomy, University of Birmingham, Birmingham B15 2TT, United Kingdom
| | - Biao Yang
- School of Physics and Astronomy, University of Birmingham, Birmingham B15 2TT, United Kingdom
| | - Lingbo Xia
- School of Physics and Astronomy, University of Birmingham, Birmingham B15 2TT, United Kingdom
- Center for Terahertz Waves and College of Precision Instrument and Optoelectronics Engineering, Tianjin University, Tianjin 300072, China
| | - Wenlong Gao
- School of Physics and Astronomy, University of Birmingham, Birmingham B15 2TT, United Kingdom
| | - Hongchao Liu
- School of Physics and Astronomy, University of Birmingham, Birmingham B15 2TT, United Kingdom
| | - Jing Chen
- MOE Key Laboratory of Weak-Light Nonlinear Photonics, School of Physics, Nankai University, Tianjin 300071, China
| | - Yuanjiang Xiang
- Key Laboratory of Optoelectronic Devices and Systems of Ministry of Education and Guangdong Province, College of Optoelectronic Engineering, Shenzhen University, Shenzhen 518060, China
| | - Shuang Zhang
- School of Physics and Astronomy, University of Birmingham, Birmingham B15 2TT, United Kingdom
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40
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Zhou M, Ying L, Lu L, Shi L, Zi J, Yu Z. Electromagnetic scattering laws in Weyl systems. Nat Commun 2017; 8:1388. [PMID: 29123111 PMCID: PMC5680227 DOI: 10.1038/s41467-017-01533-0] [Citation(s) in RCA: 25] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/25/2017] [Accepted: 09/25/2017] [Indexed: 11/29/2022] Open
Abstract
Wavelength determines the length scale of the cross section when electromagnetic waves are scattered by an electrically small object. The cross section diverges for resonant scattering, and diminishes for non-resonant scattering, when wavelength approaches infinity. This scattering law explains the colour of the sky as well as the strength of a mobile phone signal. We show that such wavelength scaling comes from the conical dispersion of free space at zero frequency. Emerging Weyl systems, offering similar dispersion at non-zero frequencies, lead to new laws of electromagnetic scattering that allow cross sections to be decoupled from the wavelength limit. Diverging and diminishing cross sections can be realized at any target wavelength in a Weyl system, providing the ability to tailor the strength of wave–matter interactions for radiofrequency and optical applications. Scattering characteristics are important optical properties but they depend strongly on the relative electromagnetic size and environment of a particle. Here, the authors study the frequency-dependence of the scattering cross section for a scatterer located inside a photonic Weyl system.
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Affiliation(s)
- Ming Zhou
- Department of Electrical and Computer Engineering, University of Wisconsin, Madison, Madison, 53705, USA
| | - Lei Ying
- Department of Electrical and Computer Engineering, University of Wisconsin, Madison, Madison, 53705, USA
| | - Ling Lu
- Institute of Physics, Chinese Academy of Sciences and Beijing National Laboratory for Condensed Matter Physics, Beijing, 100190, China
| | - Lei Shi
- Department of Physics, Fudan University, Shanghai, 200433, China
| | - Jian Zi
- Department of Physics, Fudan University, Shanghai, 200433, China
| | - Zongfu Yu
- Department of Electrical and Computer Engineering, University of Wisconsin, Madison, Madison, 53705, USA.
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Yang B, Guo Q, Tremain B, Barr LE, Gao W, Liu H, Béri B, Xiang Y, Fan D, Hibbins AP, Zhang S. Direct observation of topological surface-state arcs in photonic metamaterials. Nat Commun 2017; 8:97. [PMID: 28733654 PMCID: PMC5522455 DOI: 10.1038/s41467-017-00134-1] [Citation(s) in RCA: 84] [Impact Index Per Article: 12.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/09/2017] [Revised: 05/28/2017] [Accepted: 06/05/2017] [Indexed: 11/09/2022] Open
Abstract
The discovery of topological phases has introduced new perspectives and platforms for various interesting physics originally investigated in quantum contexts and then, on an equal footing, in classic wave systems. As a characteristic feature, nontrivial Fermi arcs, connecting between topologically distinct Fermi surfaces, play vital roles in the classification of Dirac and Weyl semimetals, and have been observed in quantum materials very recently. However, in classical systems, no direct experimental observation of Fermi arcs in momentum space has been reported so far. Here, using near-field scanning measurements, we show the observation of photonic topological surface-state arcs connecting topologically distinct bulk states in a chiral hyperbolic metamaterial. To verify the topological nature of this system, we further observe backscattering-immune propagation of a nontrivial surface wave across a three-dimension physical step. Our results demonstrate a metamaterial approach towards topological photonics and offer a deeper understanding of topological phases in three-dimensional classical systems.Topological effects known from condensed matter physics have recently also been explored in photonic systems. Here, the authors directly observe topological surface-state arcs in momentum space by near-field scanning the surface of a chiral hyperbolic metamaterial.
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Affiliation(s)
- Biao Yang
- School of Physics and Astronomy, University of Birmingham, Birmingham, B15 2TT, UK
| | - Qinghua Guo
- School of Physics and Astronomy, University of Birmingham, Birmingham, B15 2TT, UK.,Key Laboratory of Optoelectronic Devices and Systems of Ministry of Education and Guangdong Province, College of Optoelectronic Engineering, Shenzhen University, Shenzhen, 518060, China
| | - Ben Tremain
- Electromagnetic and Acoustic Materials Group, Department of Physics and Astronomy, University of Exeter, Stocker Road, Exeter, EX4 4QL, UK
| | - Lauren E Barr
- Electromagnetic and Acoustic Materials Group, Department of Physics and Astronomy, University of Exeter, Stocker Road, Exeter, EX4 4QL, UK
| | - Wenlong Gao
- School of Physics and Astronomy, University of Birmingham, Birmingham, B15 2TT, UK
| | - Hongchao Liu
- School of Physics and Astronomy, University of Birmingham, Birmingham, B15 2TT, UK
| | - Benjamin Béri
- School of Physics and Astronomy, University of Birmingham, Birmingham, B15 2TT, UK
| | - Yuanjiang Xiang
- Key Laboratory of Optoelectronic Devices and Systems of Ministry of Education and Guangdong Province, College of Optoelectronic Engineering, Shenzhen University, Shenzhen, 518060, China
| | - Dianyuan Fan
- Key Laboratory of Optoelectronic Devices and Systems of Ministry of Education and Guangdong Province, College of Optoelectronic Engineering, Shenzhen University, Shenzhen, 518060, China
| | - Alastair P Hibbins
- Electromagnetic and Acoustic Materials Group, Department of Physics and Astronomy, University of Exeter, Stocker Road, Exeter, EX4 4QL, UK.
| | - Shuang Zhang
- School of Physics and Astronomy, University of Birmingham, Birmingham, B15 2TT, UK.
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Yang Z, Xiao M, Gao F, Lu L, Chong Y, Zhang B. Weyl points in a magnetic tetrahedral photonic crystal. OPTICS EXPRESS 2017; 25:15772-15777. [PMID: 28789089 DOI: 10.1364/oe.25.015772] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/29/2017] [Accepted: 06/19/2017] [Indexed: 06/07/2023]
Abstract
Weyl points have recently been predicted and experimentally observed in double-gyroid photonic crystals, as well as in other complex photonic structures such as stacked hexagonal-lattice slabs and helical waveguide arrays. In all above structures, the Weyl points are located between high frequency bands, and are difficult to probe experimentally. In this work, we show that a photonic crystal with a simple tetrahedral structure can host frequency-isolated Weyl points between the second and third bands. The minimal number of two Weyl points emerges from a threefold quadratic degeneracy at the Brillouin zone corner when time-reversal symmetry is broken. We verify theoretically that the Weyl points carry opposite topological charges, and are associated with Fermi arc-like surface states. This photonic crystal can be realized using ferromagnetic rods in the microwave frequency regime, providing a simple platform for studying the physics of Weyl points.
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Jin D, Christensen T, Soljačić M, Fang NX, Lu L, Zhang X. Infrared Topological Plasmons in Graphene. PHYSICAL REVIEW LETTERS 2017; 118:245301. [PMID: 28665651 DOI: 10.1103/physrevlett.118.245301] [Citation(s) in RCA: 21] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/23/2017] [Indexed: 06/07/2023]
Abstract
We propose a two-dimensional plasmonic platform-periodically patterned monolayer graphene-which hosts topological one-way edge states operable up to infrared frequencies. We classify the band topology of this plasmonic system under time-reversal-symmetry breaking induced by a static magnetic field. At finite doping, the system supports topologically nontrivial band gaps with mid-gap frequencies up to tens of terahertz. By the bulk-edge correspondence, these band gaps host topologically protected one-way edge plasmons, which are immune to backscattering from structural defects and subject only to intrinsic material and radiation loss. Our findings reveal a promising approach to engineer topologically robust chiral plasmonic devices and demonstrate a realistic example of high-frequency topological edge states.
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Affiliation(s)
- Dafei Jin
- Department of Mechanical Engineering, University of California, Berkeley, California 94720, USA
| | - Thomas Christensen
- Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Marin Soljačić
- Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Nicholas X Fang
- Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Ling Lu
- Institute of Physics, Chinese Academy of Sciences/Beijing National Laboratory for Condensed Matter Physics, Beijing 100190, China
| | - Xiang Zhang
- Department of Mechanical Engineering, University of California, Berkeley, California 94720, USA
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Photonic Weyl point in a two-dimensional resonator lattice with a synthetic frequency dimension. Nat Commun 2016; 7:13731. [PMID: 27976714 PMCID: PMC5172232 DOI: 10.1038/ncomms13731] [Citation(s) in RCA: 59] [Impact Index Per Article: 7.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/08/2016] [Accepted: 10/27/2016] [Indexed: 11/09/2022] Open
Abstract
Weyl points, as a signature of 3D topological states, have been extensively studied in condensed matter systems. Recently, the physics of Weyl points has also been explored in electromagnetic structures such as photonic crystals and metamaterials. These structures typically have complex three-dimensional geometries, which limits the potential for exploring Weyl point physics in on-chip integrated systems. Here we show that Weyl point physics emerges in a system of two-dimensional arrays of resonators undergoing dynamic modulation of refractive index. In addition, the phase of modulation can be controlled to explore Weyl points under different symmetries. Furthermore, unlike static structures, in this system the non-trivial topology of the Weyl point manifests in terms of surface state arcs in the synthetic space that exhibit one-way frequency conversion. Our system therefore provides a versatile platform to explore and exploit Weyl point physics on chip.
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45
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Jin D, Lu L, Wang Z, Fang C, Joannopoulos JD, Soljačić M, Fu L, Fang NX. Topological magnetoplasmon. Nat Commun 2016; 7:13486. [PMID: 27892453 PMCID: PMC5148233 DOI: 10.1038/ncomms13486] [Citation(s) in RCA: 79] [Impact Index Per Article: 9.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/30/2016] [Accepted: 10/03/2016] [Indexed: 11/09/2022] Open
Abstract
Classical wave fields are real-valued, ensuring the wave states at opposite frequencies and momenta to be inherently identical. Such a particle–hole symmetry can open up new possibilities for topological phenomena in classical systems. Here we show that the historically studied two-dimensional (2D) magnetoplasmon, which bears gapped bulk states and gapless one-way edge states near-zero frequency, is topologically analogous to the 2D topological p+ip superconductor with chiral Majorana edge states and zero modes. We further predict a new type of one-way edge magnetoplasmon at the interface of opposite magnetic domains, and demonstrate the existence of zero-frequency modes bounded at the peripheries of a hollow disk. These findings can be readily verified in experiment, and can greatly enrich the topological phases in bosonic and classical systems. The two dimensional magnetoplasmon edge state has been observed for a long time, but its nature is yet to be uncovered. Here, Jin et al. report that such a state is actually topological protected, analogous to the chiral Majorana edge state in a p-wave topological superconductor.
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Affiliation(s)
- Dafei Jin
- Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Ling Lu
- Institute of Physics, Chinese Academy of Sciences/Beijing National Laboratory for Condensed Matter Physics, Beijing 100190, China.,Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Zhong Wang
- Institute for Advanced Study, Tsinghua University, Beijing 100084, China.,Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
| | - Chen Fang
- Institute of Physics, Chinese Academy of Sciences/Beijing National Laboratory for Condensed Matter Physics, Beijing 100190, China.,Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - John D Joannopoulos
- Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Marin Soljačić
- Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Liang Fu
- Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Nicholas X Fang
- Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
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46
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One-way helical electromagnetic wave propagation supported by magnetized plasma. Sci Rep 2016; 6:21461. [PMID: 26883883 PMCID: PMC4756303 DOI: 10.1038/srep21461] [Citation(s) in RCA: 26] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/21/2015] [Accepted: 01/15/2016] [Indexed: 11/13/2022] Open
Abstract
In this paper we reveal the presence of photonic one-way helical surface states in a simple natural system- magnetized plasma. The application of an external magnetic field to a bulk plasma body not only breaks time-reversal-symmetry but also leads to separation of Equi-Frequency Contour surfaces (EFCs) to form topologically nontrivial gaps in k space. Interestingly, these EFCs support topologically protected surface states. We numerically investigate an interface between magnetized plasma, using a realistic model for parameter dispersion, and vacuum, to confirm the existence of one-way scatter-immune helical surface states. Unlike previous proposals for achieving photonic one-way propagation, our scheme does not require the use of artificial structures and should therefore be simple to implement experimentally.
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