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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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2
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Yang LP. Geometric phase for twisted light. OPTICS EXPRESS 2023; 31:10287-10296. [PMID: 37157579 DOI: 10.1364/oe.476989] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/10/2023]
Abstract
Polarization vectors of light traveling in a coiled optical fiber rotate around its propagating axis even in the absence of birefringence. This rotation was usually explained due to the Pancharatnam-Berry phase of spin-1 photons. Here, we use a purely geometric method to understand this rotation. We show that similar geometric rotations also exist for twisted light carrying orbital angular momentum (OAM). The corresponding geometric phase can be applied in photonic OAM-state-based quantum computation and quantum sensing.
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3
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Bliokh KY. Elastic Spin and Orbital Angular Momenta. PHYSICAL REVIEW LETTERS 2022; 129:204303. [PMID: 36462016 DOI: 10.1103/physrevlett.129.204303] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/01/2022] [Accepted: 10/20/2022] [Indexed: 06/17/2023]
Abstract
Motivated by recent theoretical and experimental interest in the spin and orbital angular momenta of elastic waves, we revisit canonical wave momentum, spin, and orbital angular momentum in isotropic elastic media. We show that these quantities are described by simple universal expressions, which differ from the results of Chaplain et al. [Phys. Rev. Lett. 128, 064301 (2022)PRLTAO0031-900710.1103/PhysRevLett.128.064301] and do not require separation of the longitudinal and transverse parts of the wave field. For cylindrical elastic modes, the normalized z component of the total (spin+orbital) angular momentum is quantized and equals the azimuthal quantum number of the mode, while the orbital and spin parts are not quantized due to the spin-orbit geometric-phase effects. In contrast to the claims of the above article, longitudinal, transverse, and "hybrid" contributions to the angular momenta are equally important in general and cannot be neglected. As another example, we calculate the transverse spin angular momentum of a surface Rayleigh wave.
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Affiliation(s)
- Konstantin Y Bliokh
- Theoretical Quantum Physics Laboratory, RIKEN Cluster for Pioneering Research, Wako-shi, Saitama 351-0198, Japan
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4
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Peng J, Zhang RY, Jia S, Liu W, Wang S. Topological near fields generated by topological structures. SCIENCE ADVANCES 2022; 8:eabq0910. [PMID: 36240266 PMCID: PMC9565808 DOI: 10.1126/sciadv.abq0910] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 03/17/2022] [Accepted: 08/31/2022] [Indexed: 06/16/2023]
Abstract
The central idea of metamaterials and metaoptics is that, besides their base materials, the geometry of structures offers a broad extra dimension to explore for exotic functionalities. Here, we discover that the topology of structures fundamentally dictates the topological properties of optical fields and offers a new dimension to exploit for optical functionalities that are irrelevant to specific material constituents or structural geometries. We find that the nontrivial topology of metal structures ensures the birth of polarization singularities (PSs) in the near field with rich morphologies and intriguing spatial evolutions including merging, bifurcation, and topological transition. By mapping the PSs to non-Hermitian exceptional points and using homotopy theory, we extract the core invariant that governs the topological classification of the PSs and the conservation law that regulates their spatial evolutions. The results bridge singular optics, topological photonics, and non-Hermitian physics, with potential applications in chiral sensing, chiral quantum optics, and beyond photonics in other wave systems.
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Affiliation(s)
- Jie Peng
- Department of Physics, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong, China
| | - Ruo-Yang Zhang
- Department of Physics, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China
| | - Shiqi Jia
- Department of Physics, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong, China
| | - Wei Liu
- College for Advanced Interdisciplinary Studies, National University of Defense Technology, Changsha, Hunan 410073, China
| | - Shubo Wang
- Department of Physics, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong, China
- City University of Hong Kong Shenzhen Research Institute, Shenzhen, Guangdong 518057, China
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5
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Ni J, Huang C, Zhou LM, Gu M, Song Q, Kivshar Y, Qiu CW. Multidimensional phase singularities in nanophotonics. Science 2021; 374:eabj0039. [PMID: 34672745 DOI: 10.1126/science.abj0039] [Citation(s) in RCA: 44] [Impact Index Per Article: 14.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022]
Abstract
[Figure: see text].
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Affiliation(s)
- Jincheng Ni
- Department of Electrical and Computer Engineering, National University of Singapore, Singapore 117583, Singapore
| | - Can Huang
- State Key Laboratory on Tunable Laser Technology, Ministry of Industry and Information Technology Key Laboratory of Micro-Nano Optoelectronic Information System, Shenzhen Graduate School, Harbin Institute of Technology, Shenzhen 518055, China
| | - Lei-Ming Zhou
- Department of Electrical and Computer Engineering, National University of Singapore, Singapore 117583, Singapore
| | - Min Gu
- Institute of Photonic Chips, University of Shanghai for Science and Technology, Shanghai, China.,Centre for Artificial-Intelligence Nanophotonics, School of Optical-Electrical and Computer Engineering, University of Shanghai for Science and Technology, Shanghai, China
| | - Qinghai Song
- State Key Laboratory on Tunable Laser Technology, Ministry of Industry and Information Technology Key Laboratory of Micro-Nano Optoelectronic Information System, Shenzhen Graduate School, Harbin Institute of Technology, Shenzhen 518055, China.,Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, 030006 Shanxi, China
| | - Yuri Kivshar
- Nonlinear Physics Centre, Research School of Physics, Australian National University, Canberra ACT 2601, Australia
| | - Cheng-Wei Qiu
- Department of Electrical and Computer Engineering, National University of Singapore, Singapore 117583, Singapore
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6
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Wang S, Zhang G, Wang X, Tong Q, Li J, Ma G. Spin-orbit interactions of transverse sound. Nat Commun 2021; 12:6125. [PMID: 34675212 PMCID: PMC8531336 DOI: 10.1038/s41467-021-26375-9] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/21/2021] [Accepted: 10/05/2021] [Indexed: 12/02/2022] Open
Abstract
Spin-orbit interactions (SOIs) endow light with intriguing properties and applications such as photonic spin-Hall effects and spin-dependent vortex generations. However, it is counterintuitive that SOIs can exist for sound, which is a longitudinal wave that carries no intrinsic spin. Here, we theoretically and experimentally demonstrate that airborne sound can possess artificial transversality in an acoustic micropolar metamaterial and thus carry both spin and orbital angular momentum. This enables the realization of acoustic SOIs with rich phenomena beyond those in conventional acoustic systems. We demonstrate that acoustic activity of the metamaterial can induce coupling between the spin and linear crystal momentum k, which leads to negative refraction of the transverse sound. In addition, we show that the scattering of the transverse sound by a dipole particle can generate spin-dependent acoustic vortices via the geometric phase effect. The acoustic SOIs can provide new perspectives and functionalities for sound manipulations beyond the conventional scalar degree of freedom and may open an avenue to the development of spin-orbit acoustics.
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Affiliation(s)
- Shubo Wang
- Department of Physics, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong, China.
| | - Guanqing Zhang
- Department of Physics, Hong Kong Baptist University, Kowloon Tong, Hong Kong, China
| | - Xulong Wang
- Department of Physics, Hong Kong Baptist University, Kowloon Tong, Hong Kong, China
| | - Qing Tong
- Department of Physics, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong, China
| | - Jensen Li
- Department of Physics, The Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong, China
| | - Guancong Ma
- Department of Physics, Hong Kong Baptist University, Kowloon Tong, Hong Kong, China.
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Fu Y, Shen C, Zhu X, Li J, Liu Y, Cummer SA, Xu Y. Sound vortex diffraction via topological charge in phase gradient metagratings. SCIENCE ADVANCES 2020; 6:eaba9876. [PMID: 33008907 PMCID: PMC7852395 DOI: 10.1126/sciadv.aba9876] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/21/2020] [Accepted: 08/21/2020] [Indexed: 05/31/2023]
Abstract
Wave fields with orbital angular momentum (OAM) have been widely investigated in metasurfaces. By engineering acoustic metasurfaces with phase gradient elements, phase twisting is commonly used to obtain acoustic OAM. However, it has limited ability to manipulate sound vortices, and a more powerful mechanism for sound vortex manipulation is strongly desired. Here, we propose the diffraction mechanism to manipulate sound vortices in a cylindrical waveguide with phase gradient metagratings (PGMs). A sound vortex diffraction law is theoretically revealed based on the generalized conservation principle of topological charge. This diffraction law can explain and predict the complicated diffraction phenomena of sound vortices, as confirmed by numerical simulations. To exemplify our findings, we designed and experimentally verified a PGM based on Helmholtz resonators that support asymmetric transmission of sound vortices. Our work provides previously unidentified opportunities for manipulating sound vortices, which can advance more versatile design for OAM-based devices.
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Affiliation(s)
- Yangyang Fu
- College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China.
| | - Chen Shen
- Department of Electrical and Computer Engineering, Duke University, Durham, NC 27708, USA
| | - Xiaohui Zhu
- Department of Electrical and Computer Engineering, Duke University, Durham, NC 27708, USA
| | - Junfei Li
- Department of Electrical and Computer Engineering, Duke University, Durham, NC 27708, USA
| | - Youwen Liu
- College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China
| | - Steven A Cummer
- Department of Electrical and Computer Engineering, Duke University, Durham, NC 27708, USA.
| | - Yadong Xu
- School of Physical Science and Technology, Soochow University, Suzhou 215006, China.
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8
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Long Y, Zhang D, Yang C, Ge J, Chen H, Ren J. Realization of acoustic spin transport in metasurface waveguides. Nat Commun 2020; 11:4716. [PMID: 32948761 PMCID: PMC7501247 DOI: 10.1038/s41467-020-18599-y] [Citation(s) in RCA: 19] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/22/2019] [Accepted: 08/25/2020] [Indexed: 11/08/2022] Open
Abstract
Spin angular momentum enables fundamental insights for topological matters, and practical implications for information devices. Exploiting the spin of carriers and waves is critical to achieving more controllable degrees of freedom and robust transport processes. Yet, due to the curl-free nature of longitudinal waves distinct from transverse electromagnetic waves, spin angular momenta of acoustic waves in solids and fluids have never been unveiled only until recently. Here, we demonstrate a metasurface waveguide for sound carrying non-zero acoustic spin with tight spin-momentum coupling, which can assist the suppression of backscattering when scatters fail to flip the acoustic spin. This is achieved by imposing a soft boundary of the π reflection phase, realized by comb-like metasurfaces. With the special-boundary-defined spin texture, the acoustic spin transports are experimentally manifested, such as the suppression of acoustic corner-scattering, the spin-selected acoustic router with spin-Hall-like effect, and the phase modulator with rotated acoustic spin.
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Affiliation(s)
- Yang Long
- Center for Phononics and Thermal Energy Science, China-EU Joint Center for Nanophononics, Shanghai Key Laboratory of Special Artificial Microstructure Materials and Technology, School of Physics Science and Engineering, Tongji University, Shanghai, 200092, China
| | - Danmei Zhang
- Center for Phononics and Thermal Energy Science, China-EU Joint Center for Nanophononics, Shanghai Key Laboratory of Special Artificial Microstructure Materials and Technology, School of Physics Science and Engineering, Tongji University, Shanghai, 200092, China
| | - Chenwen Yang
- Center for Phononics and Thermal Energy Science, China-EU Joint Center for Nanophononics, Shanghai Key Laboratory of Special Artificial Microstructure Materials and Technology, School of Physics Science and Engineering, Tongji University, Shanghai, 200092, China
| | - Jianmin Ge
- Institute of Acoustics, Shanghai Key Laboratory of Special Artificial Microstructure Materials and Technology, School of Physics Sciences and Engineering, Tongji University, Shanghai, 200092, China
| | - Hong Chen
- Center for Phononics and Thermal Energy Science, China-EU Joint Center for Nanophononics, Shanghai Key Laboratory of Special Artificial Microstructure Materials and Technology, School of Physics Science and Engineering, Tongji University, Shanghai, 200092, China
| | - Jie Ren
- Center for Phononics and Thermal Energy Science, China-EU Joint Center for Nanophononics, Shanghai Key Laboratory of Special Artificial Microstructure Materials and Technology, School of Physics Science and Engineering, Tongji University, Shanghai, 200092, China.
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9
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Tong L, Xiong Z, Shen YX, Peng YG, Huang XY, Ye L, Tang M, Cai FY, Zheng HR, Xu JB, Cheng GJ, Zhu XF. An Acoustic Meta-Skin Insulator. ADVANCED MATERIALS (DEERFIELD BEACH, FLA.) 2020; 32:e2002251. [PMID: 32696471 DOI: 10.1002/adma.202002251] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/01/2020] [Revised: 05/06/2020] [Indexed: 05/25/2023]
Abstract
Acoustic metamaterials with artificial microstructures are attractive to realize intriguing functions, including efficient waveguiding, which requires large impedance mismatches to realize total side reflection with negligible transmission and absorption. While large impedance mismatch can be readily realized in an air environment, acoustic waveguiding in an underwater environment remains elusive due to insufficient impedance mismatch of state-of-the-art metamaterials. Here, a superhydrophobic acoustic metasurface of microstructured poly(vinylidene fluoride) membrane, referred to as a "meta-skin" insulator, which is able to confine acoustic waves in an all-angle and wide spectrum range due to tremendous impedance mismatch at stable air/water interfaces, viz., the Cassie-Baxter state is demonstrated. By utilizing the meta-skin insulator with broadband and high throughput, orbital-angular-momentum multiplexing at a high spectral efficiency and binary coding along large-angle bending channels for bit-error-free acoustic data transmission in an underwater environment are demonstrated. Very different from optical and/or electrical cable communications, acoustic waves can be simply and effectively coupled into remote meta-skin acoustic fibers from free space, which is technologically significant for long-haul and anti-interference communication. This work can enlighten many fluidic applications based on efficient waveguiding, such as in vivo ultrasound medical treatment and imaging.
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Affiliation(s)
- Lei Tong
- School of Optical and Electronic Information and Wuhan National Laboratory for Optoelectronics, Huazhong University of Science and Technology, Wuhan, Hubei, 430074, P. R. China
| | - Zhu Xiong
- Institute of Environmental Research at Greater Bay, Key Laboratory for Water Quality and Conservation of the Pearl River Delta, Ministry of Education, Guangzhou University, Guangzhou, 510006, P. R. China
| | - Ya-Xi Shen
- School of Physics, Huazhong University of Science and Technology, Wuhan, Hubei, 430074, P. R. China
| | - Yu-Gui Peng
- School of Physics, Huazhong University of Science and Technology, Wuhan, Hubei, 430074, P. R. China
- Innovation Institute, Huazhong University of Science and Technology, Wuhan, Hubei, 430074, P. R. China
| | - Xin-Yu Huang
- School of Optical and Electronic Information and Wuhan National Laboratory for Optoelectronics, Huazhong University of Science and Technology, Wuhan, Hubei, 430074, P. R. China
| | - Lei Ye
- School of Optical and Electronic Information and Wuhan National Laboratory for Optoelectronics, Huazhong University of Science and Technology, Wuhan, Hubei, 430074, P. R. China
- Innovation Institute, Huazhong University of Science and Technology, Wuhan, Hubei, 430074, P. R. China
| | - Ming Tang
- School of Optical and Electronic Information and Wuhan National Laboratory for Optoelectronics, Huazhong University of Science and Technology, Wuhan, Hubei, 430074, P. R. China
| | - Fei-Yan Cai
- Institute of Biomedical and Health Engineering, Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, 1068 Xueyuan Avenue, Shenzhen, 518055, P. R. China
| | - Hai-Rong Zheng
- Institute of Biomedical and Health Engineering, Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, 1068 Xueyuan Avenue, Shenzhen, 518055, P. R. China
| | - Jian-Bin Xu
- Department of Electronic Engineering and Materials Science and Technology Research Center, The Chinese University of Hong Kong, Hong Kong SAR, P. R. China
| | - Gary J Cheng
- School of Industrial Engineering and Birck Nanotechnology Centre, Purdue University, West Lafayette, IN, 47907, USA
| | - Xue-Feng Zhu
- School of Physics, Huazhong University of Science and Technology, Wuhan, Hubei, 430074, P. R. China
- Innovation Institute, Huazhong University of Science and Technology, Wuhan, Hubei, 430074, P. R. China
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10
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Universal momentum-to-real-space mapping of topological singularities. Nat Commun 2020; 11:1586. [PMID: 32221307 PMCID: PMC7101314 DOI: 10.1038/s41467-020-15374-x] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/18/2019] [Accepted: 03/04/2020] [Indexed: 11/26/2022] Open
Abstract
Topological properties of materials are typically presented in momentum space. Here, we demonstrate a universal mapping of topological singularities from momentum to real space. By exciting Dirac-like cones in photonic honeycomb (pseudospin-1/2) and Lieb (pseudospin-1) lattices with vortex beams of topological charge l, optimally aligned with a given pseudospin state s, we directly observe topological charge conversion that follows the rule l → l + 2s. Although the mapping is observed in photonic lattices where pseudospin-orbit interaction takes place, we generalize the theory to show it is the nontrivial Berry phase winding that accounts for the conversion which persists even in systems where angular momentum is not conserved, unveiling its topological origin. Our results have direct impact on other branches of physics and material sciences beyond the 2D photonic platform: equivalent mapping occurs for 3D topological singularities such as Dirac-Weyl synthetic monopoles, achievable in mechanical, acoustic, or ultracold atomic systems, and even with electron beams. Topological properties of materials are typically presented in momentum space. Here, the authors show a universal mapping of topological singularities from momentum to real space, potentially applicable to a wide range of systems.
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11
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Rondón I, Leykam D. Acoustic vortex beams in synthetic magnetic fields. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2020; 32:104001. [PMID: 31711055 DOI: 10.1088/1361-648x/ab55f4] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
We analyze the propagation of acoustic vortex beams in longitudinal synthetic magnetic fields. We show how to generate two field configurations using a fluid contained in circulating cylinders: a uniform synthetic magnetic field hosting Laguerre-Gauss modes, and an Aharonov-Bohm flux tube hosting Bessel beams. For non-paraxial beams we find qualitative differences from the well-studied case of electron vortex beams in magnetic fields, arising due to the vectorial nature of the acoustic wave's velocity field. In particular, the pressure and velocity components of the acoustic wave can be individually sensitive to the relative sign of the beam orbital angular momentum and the magnetic field. Our findings illustrate how analogies between optical, electron, and acoustic vortex beams can break down in the presence of external vector potentials.
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Affiliation(s)
- Irving Rondón
- Center for Theoretical Physics of Complex Systems, Institute for Basic Science (IBS), Daejeon 34126, Republic of Korea
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12
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Affiliation(s)
- Huifeng Du
- Department of Mechanical Engineering, Massachusetts Institute of Technology, USA
| | - Chu Ma
- Department of Mechanical Engineering, Massachusetts Institute of Technology, USA
| | - Nicholas X Fang
- Department of Mechanical Engineering, Massachusetts Institute of Technology, USA
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13
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Shi H, Xiong Z, Chen W, Xu J, Wang S, Chen Y. Gauge-field description of Sagnac frequency shift and mode hybridization in a rotating cavity. OPTICS EXPRESS 2019; 27:28114-28122. [PMID: 31684569 DOI: 10.1364/oe.27.028114] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/14/2019] [Accepted: 08/16/2019] [Indexed: 06/10/2023]
Abstract
Active optical systems can give rise to intriguing phenomena and applications that are not available in conventional passive systems. Structural rotation has been widely employed to achieve non-reciprocity or time-reversal symmetry breaking. Here, we examine the quasi-normal modes and scattering properties of a dielectric disk under rotation. In addition to the familiar phenomenon of Sagnac frequency shift, we observe the the hybridization of the clockwise (CW) and counter-clockwise CCW) chiral modes of the cavity controlled by the rotation. The rotation tends to suppress one chiral mode while amplifying the other, and it leads to the variation of the far field. The phenomenon can be understood as the result of a synthetic gauge field induced by the rotation of the cavity. We explicitly derived this gauge field and the resulting Sagnac frequency shift. The analytical results are corroborated by finite element simulations. Our results can be applied in the measurement of rotating devices by probing the far field.
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14
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Hasan MA, Calderin L, Lucas P, Runge K, Deymier PA. Spectral analysis of amplitudes and phases of elastic waves: Application to topological elasticity. THE JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA 2019; 146:748. [PMID: 31370626 DOI: 10.1121/1.5114911] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/29/2018] [Accepted: 02/17/2019] [Indexed: 06/10/2023]
Abstract
The topological characteristics of waves in elastic structures are determined by the geometric phase of waves and, more specifically, by the Berry phase, as a characterization of the global vibrational behavior of the system. A computational procedure for the numerical determination of the geometrical phase characteristics of a general elastic structure is introduced: the spectral analysis of amplitudes and phases method. Molecular dynamics simulation is employed to computationally generate the band structure, traveling modes' amplitudes and phases, and subsequently the Berry phase associated with each band of periodic superlattices. In an innovative procedure, the phase information is used to selectively excite a particular mode in the band structure. It is shown analytically and numerically, in the case of one-dimensional elastic superlattices composed of various numbers of masses and spring stiffness, how the Berry phase varies as a function of the spatial arrangement of the springs. A symmetry condition on the arrangement of springs is established, which leads to bands with Berry phase taking the values of 0 or π. Finally, it is shown how the Berry phase may vary upon application of unitary operations that mathematically describe transformations of the structural arrangement of masses and springs within the unit cells.
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Affiliation(s)
- M Arif Hasan
- Department of Materials Science and Engineering, University of Arizona, Tucson, Arizona 85721, USA
| | - Lazaro Calderin
- Department of Materials Science and Engineering, University of Arizona, Tucson, Arizona 85721, USA
| | - Pierre Lucas
- Department of Materials Science and Engineering, University of Arizona, Tucson, Arizona 85721, USA
| | - Keith Runge
- Department of Materials Science and Engineering, University of Arizona, Tucson, Arizona 85721, USA
| | - Pierre A Deymier
- Department of Materials Science and Engineering, University of Arizona, Tucson, Arizona 85721, USA
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