1
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Hu SQ, Chen DQ, Du LL, Meng S. Solid-state high harmonic spectroscopy for all-optical band structure probing of high-pressure quantum states. Proc Natl Acad Sci U S A 2024; 121:e2316775121. [PMID: 38300874 PMCID: PMC10861900 DOI: 10.1073/pnas.2316775121] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/11/2023] [Accepted: 12/11/2023] [Indexed: 02/03/2024] Open
Abstract
High pressure has triggered various novel states/properties in condensed matter, as the most representative and dramatic example being near-room-temperature superconductivity in highly pressured hydrides (~200 GPa). However, the mechanism of superconductivity is not confirmed, due to the lacking of effective approach to probe the electronic band structure under such high pressures. Here, we theoretically propose that the band structure and electron-phonon coupling (EPC) of high-pressure quantum states can be probed by solid-state high harmonic generation (sHHG). This strategy is investigated in high-pressure Im-3m H3S by the state-of-the-art first-principles time-dependent density-functional theory simulations, where the sHHG is revealed to be strongly dependent on the electronic structures and EPC. The dispersion of multiple bands near the Fermi level is effectively retrieved along different momentum directions. Our study provides unique insights into the potential all-optical route for band structure and EPC probing of high-pressure quantum states, which is expected to be helpful for the experimental exploration of high-pressure superconductivity in the future.
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Affiliation(s)
- Shi-Qi Hu
- Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing100190, People’s Republic of China
| | - Da-Qiang Chen
- Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing100190, People’s Republic of China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing100049, People’s Republic of China
| | - Lan-Lin Du
- Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing100190, People’s Republic of China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing100049, People’s Republic of China
| | - Sheng Meng
- Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing100190, People’s Republic of China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing100049, People’s Republic of China
- Songshan Lake Materials Laboratory, Dongguan, Guangdong523808, People’s Republic of China
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2
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Li C, Guan M, Hong H, Chen K, Wang X, Ma H, Wang A, Li Z, Hu H, Xiao J, Dai J, Wan X, Liu K, Meng S, Dai Q. Coherent ultrafast photoemission from a single quantized state of a one-dimensional emitter. SCIENCE ADVANCES 2023; 9:eadf4170. [PMID: 37824625 PMCID: PMC10569710 DOI: 10.1126/sciadv.adf4170] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/21/2022] [Accepted: 09/08/2023] [Indexed: 10/14/2023]
Abstract
Femtosecond laser-driven photoemission source provides an unprecedented femtosecond-resolved electron probe not only for atomic-scale ultrafast characterization but also for free-electron radiation sources. However, for conventional metallic electron source, intense lasers may induce a considerable broadening of emitting energy level, which results in large energy spread (>600 milli-electron volts) and thus limits the spatiotemporal resolution of electron probe. Here, we demonstrate the coherent ultrafast photoemission from a single quantized energy level of a carbon nanotube. Its one-dimensional body can provide a sharp quantized electronic excited state, while its zero-dimensional tip can provide a quantized energy level act as a narrow photoemission channel. Coherent resonant tunneling electron emission is evidenced by a negative differential resistance effect and a field-driven Stark splitting effect. The estimated energy spread is ~57 milli-electron volts, which suggests that the proposed carbon nanotube electron source may promote electron probe simultaneously with subangstrom spatial resolution and femtosecond temporal resolution.
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Affiliation(s)
- Chi Li
- CAS Key Laboratory of Nanophotonic Materials and Devices, National Center for Nanoscience and Technology, Beijing 100190, China
| | - Mengxue Guan
- Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Science, Beijing 100190, China
- Centre for Quantum Physics, Key Laboratory of Advanced Optoelectronic Quantum Architecture and Measurement (Ministry of Education), School of Physics, Beijing Institute of Technology, Beijing 100081, China
| | - Hao Hong
- State Key Laboratory for Mesoscopic Physics, Frontiers Science Centre for Nano-optoelectronics, School of Physics, Peking University, Beijing 100871, China
| | - Ke Chen
- CAS Key Laboratory of Nanophotonic Materials and Devices, National Center for Nanoscience and Technology, Beijing 100190, China
| | - Xiaowei Wang
- Department of Physics, Hunan Key Laboratory of Extreme Matter and Applications, National University of Defense Technology, Changsha 410073, China
| | - He Ma
- State Key Laboratory for Mesoscopic Physics, Frontiers Science Centre for Nano-optoelectronics, School of Physics, Peking University, Beijing 100871, China
| | - Aiwei Wang
- CAS Key Laboratory of Nanophotonic Materials and Devices, National Center for Nanoscience and Technology, Beijing 100190, China
| | - Zhenjun Li
- CAS Key Laboratory of Nanophotonic Materials and Devices, National Center for Nanoscience and Technology, Beijing 100190, China
| | - Hai Hu
- CAS Key Laboratory of Nanophotonic Materials and Devices, National Center for Nanoscience and Technology, Beijing 100190, China
| | - Jianfeng Xiao
- CAS Key Laboratory of Nanophotonic Materials and Devices, National Center for Nanoscience and Technology, Beijing 100190, China
| | - Jiayu Dai
- Department of Physics, Hunan Key Laboratory of Extreme Matter and Applications, National University of Defense Technology, Changsha 410073, China
| | - Xiangang Wan
- National Laboratory of Solid State Microstructures and School of Physics, Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
| | - Kaihui Liu
- State Key Laboratory for Mesoscopic Physics, Frontiers Science Centre for Nano-optoelectronics, School of Physics, Peking University, Beijing 100871, China
| | - Sheng Meng
- Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Science, Beijing 100190, China
| | - Qing Dai
- CAS Key Laboratory of Nanophotonic Materials and Devices, National Center for Nanoscience and Technology, Beijing 100190, China
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3
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Ito S, Schüler M, Meierhofer M, Schlauderer S, Freudenstein J, Reimann J, Afanasiev D, Kokh KA, Tereshchenko OE, Güdde J, Sentef MA, Höfer U, Huber R. Build-up and dephasing of Floquet-Bloch bands on subcycle timescales. Nature 2023; 616:696-701. [PMID: 37046087 DOI: 10.1038/s41586-023-05850-x] [Citation(s) in RCA: 8] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/21/2022] [Accepted: 02/15/2023] [Indexed: 04/14/2023]
Abstract
Strong light fields have created opportunities to tailor novel functionalities of solids1-5. Floquet-Bloch states can form under periodic driving of electrons and enable exotic quantum phases6-15. On subcycle timescales, lightwaves can simultaneously drive intraband currents16-29 and interband transitions18,19,30,31, which enable high-harmonic generation16,18,19,21,22,25,28-30 and pave the way towards ultrafast electronics. Yet, the interplay of intraband and interband excitations and their relation to Floquet physics have been key open questions as dynamical aspects of Floquet states have remained elusive. Here we provide this link by visualizing the ultrafast build-up of Floquet-Bloch bands with time-resolved and angle-resolved photoemission spectroscopy. We drive surface states on a topological insulator32,33 with mid-infrared fields-strong enough for high-harmonic generation-and directly monitor the transient band structure with subcycle time resolution. Starting with strong intraband currents, we observe how Floquet sidebands emerge within a single optical cycle; intraband acceleration simultaneously proceeds in multiple sidebands until high-energy electrons scatter into bulk states and dissipation destroys the Floquet bands. Quantum non-equilibrium calculations explain the simultaneous occurrence of Floquet states with intraband and interband dynamics. Our joint experiment and theory study provides a direct time-domain view of Floquet physics and explores the fundamental frontiers of ultrafast band-structure engineering.
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Affiliation(s)
- S Ito
- Department of Physics, Philipps-University of Marburg, Marburg, Germany
| | - M Schüler
- Laboratory for Materials Simulations, Paul Scherrer Institute, Villigen PSI, Switzerland
- Department of Physics, University of Fribourg, Fribourg, Switzerland
| | - M Meierhofer
- Department of Physics, University of Regensburg, Regensburg, Germany
| | - S Schlauderer
- Department of Physics, University of Regensburg, Regensburg, Germany
| | - J Freudenstein
- Department of Physics, University of Regensburg, Regensburg, Germany
| | - J Reimann
- Department of Physics, Philipps-University of Marburg, Marburg, Germany
| | - D Afanasiev
- Department of Physics, University of Regensburg, Regensburg, Germany
| | - K A Kokh
- A.V. Rzhanov Institute of Semiconductor Physics and V.S. Sobolev Institute of Geology and Mineralogy SB RAS, Novosibirsk, Russian Federation
| | - O E Tereshchenko
- A.V. Rzhanov Institute of Semiconductor Physics and V.S. Sobolev Institute of Geology and Mineralogy SB RAS, Novosibirsk, Russian Federation
| | - J Güdde
- Department of Physics, Philipps-University of Marburg, Marburg, Germany
| | - M A Sentef
- Max Planck Institute for the Structure and Dynamics of Matter, Hamburg, Germany.
| | - U Höfer
- Department of Physics, Philipps-University of Marburg, Marburg, Germany.
- Department of Physics, University of Regensburg, Regensburg, Germany.
| | - R Huber
- Department of Physics, University of Regensburg, Regensburg, Germany.
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4
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Controlling Floquet states on ultrashort time scales. Nat Commun 2022; 13:7103. [DOI: 10.1038/s41467-022-34973-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/06/2022] [Accepted: 11/14/2022] [Indexed: 11/21/2022] Open
Abstract
AbstractThe advent of ultrafast laser science offers the unique opportunity to combine Floquet engineering with extreme time resolution, further pushing the optical control of matter into the petahertz domain. However, what is the shortest driving pulse for which Floquet states can be realised remains an unsolved matter, thus limiting the application of Floquet theory to pulses composed by many optical cycles. Here we ionized Ne atoms with few-femtosecond pulses of selected time duration and show that a Floquet state can be observed already with a driving field that lasts for only 10 cycles. For shorter pulses, down to 2 cycles, the finite lifetime of the driven state can still be explained using an analytical model based on Floquet theory. By demonstrating that the amplitude and number of Floquet-like sidebands in the photoelectron spectrum can be controlled not only with the driving laser pulse intensity and frequency, but also by its duration, our results add a new lever to the toolbox of Floquet engineering.
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5
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Düvel M, Merboldt M, Bange JP, Strauch H, Stellbrink M, Pierz K, Schumacher HW, Momeni D, Steil D, Jansen GSM, Steil S, Novko D, Mathias S, Reutzel M. Far-from-Equilibrium Electron-Phonon Interactions in Optically Excited Graphene. NANO LETTERS 2022; 22:4897-4904. [PMID: 35649249 DOI: 10.1021/acs.nanolett.2c01325] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
Comprehending far-from-equilibrium many-body interactions is one of the major goals of current ultrafast condensed matter physics research. Here, a particularly interesting but barely understood situation occurs during a strong optical excitation, where the electron and phonon systems can be significantly perturbed and the quasiparticle distributions cannot be described with equilibrium functions. In this work, we use time- and angle-resolved photoelectron spectroscopy to study such far-from-equilibrium many-body interactions for the prototypical material graphene. In accordance with theoretical simulations, we find remarkable transient renormalizations of the quasiparticle self-energy caused by the photoinduced nonequilibrium conditions. These observations can be understood by ultrafast scatterings between nonequilibrium electrons and strongly coupled optical phonons, which signify the crucial role of ultrafast nonequilibrium dynamics on many-body interactions. Our results advance the understanding of many-body physics in extreme conditions, which is important for any endeavor to optically manipulate or create non-equilibrium states of matter.
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Affiliation(s)
- Marten Düvel
- I. Physikalisches Institut, Georg-August-Universität Göttingen, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany
| | - Marco Merboldt
- I. Physikalisches Institut, Georg-August-Universität Göttingen, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany
| | - Jan Philipp Bange
- I. Physikalisches Institut, Georg-August-Universität Göttingen, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany
| | - Hannah Strauch
- I. Physikalisches Institut, Georg-August-Universität Göttingen, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany
| | - Michael Stellbrink
- I. Physikalisches Institut, Georg-August-Universität Göttingen, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany
| | - Klaus Pierz
- Physikalisch-Technische Bundesanstalt, Bundesallee 100, 38116 Braunschweig, Germany
| | | | - Davood Momeni
- Physikalisch-Technische Bundesanstalt, Bundesallee 100, 38116 Braunschweig, Germany
| | - Daniel Steil
- I. Physikalisches Institut, Georg-August-Universität Göttingen, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany
| | - G S Matthijs Jansen
- I. Physikalisches Institut, Georg-August-Universität Göttingen, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany
| | - Sabine Steil
- I. Physikalisches Institut, Georg-August-Universität Göttingen, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany
| | - Dino Novko
- Institute of Physics, HR-10000 Zagreb, Croatia
| | - Stefan Mathias
- I. Physikalisches Institut, Georg-August-Universität Göttingen, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany
- International Center for Advanced Studies of Energy Conversion (ICASEC), University of Göttingen, 37077 Göttingen, Germany
| | - Marcel Reutzel
- I. Physikalisches Institut, Georg-August-Universität Göttingen, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany
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6
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Feizollah P, Berg MJ. Electromagnetically induced modification of gold optical properties. OPTICS EXPRESS 2022; 30:18374-18391. [PMID: 36221640 DOI: 10.1364/oe.459728] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/01/2022] [Accepted: 05/02/2022] [Indexed: 06/16/2023]
Abstract
The reflection of light from a metal film, i.e., a mirror, is among the most fundamental and well-understood effects in optics. If the film thickness is greater than the wavelength, reflection is strong and is explained in simple terms by the Fresnel equations. For film thickness much less than the wavelength, reflection is far weaker and more exotic effects become possible. This is especially so if the light illuminating the film is pulsed at the femtosecond time scale. In this work, a phenomenon is proposed where few-femtosecond laser pulses temporarily modify a thin metal film's optical properties via processes that appear linear and classical in nature. By casting a pulsed standing-wave pattern across the metal surface, we consider the possibility that conduction electrons are redistributed to create temporary regions of partly enhanced or reduced density without the excitation of inter-band transitions. The process would constitute a temporary change to the conductivity of the metal, and thus, may be observable as changes to the metal's transmittance and reflectance. In regions where the density is enhanced (reduced), the transmittance is decreased (increased). The concept is termed Electromagnetically Induced Modification (EIM) and is premised on the fact that the pulse length is shorter than the relaxation time of the conduction electrons. An experiment is conducted to test the concept by measuring the change in reflectance and transmittance of gold films with thickness ranging from 20-300 Angstrom. The results show that the film's transmittance decreases only when the standing-wave pattern is present. As the pulse length is increased, or as the film thickness is increased, the changes disappear. The changes show little dependence on the pulse intensity as it is varied by a factor of two. To gain further insight, the Drude theory is used to develop a simplified model for EIM, which qualitatively agrees with the observations. However, neither the experiment nor the model can prove the validity of the EIM concept. As such, an assessment is made for the potential of alternative well-known processes to explain the observations.
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7
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Heide C, Eckstein T, Boolakee T, Gerner C, Weber HB, Franco I, Hommelhoff P. Electronic Coherence and Coherent Dephasing in the Optical Control of Electrons in Graphene. NANO LETTERS 2021; 21:9403-9409. [PMID: 34735774 DOI: 10.1021/acs.nanolett.1c02538] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
Electronic coherence is of utmost importance for the access and control of quantum-mechanical solid-state properties. Using a purely electronic observable, the photocurrent, we measure a lower bound of the electronic coherence time of 22 ± 4 fs in graphene. The photocurrent is ideally suited to measure electronic coherence, as it is a direct result of coherent quantum-path interference, controlled by the delay between two ultrashort two-color laser pulses. The maximum delay for which interference between the population amplitude injected by the first pulse interferes with that generated by the second pulse determines the electronic coherence time. In particular, numerical simulations reveal that the experimental data yields a lower bound on the electronic coherence time, masked by coherent dephasing due to the broadband absorption in graphene. We expect that our results will significantly advance the understanding of coherent quantum control in solid-state systems ranging from excitation with weak fields to strongly driven systems.
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Affiliation(s)
- Christian Heide
- Department of Physics, Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Staudtstrasse 1, D-91058 Erlangen, Germany
- Stanford PULSE Institute, SLAC National Accelerator Laboratory, Menlo Park, California 94025, United States
| | - Timo Eckstein
- Department of Physics, Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Staudtstrasse 1, D-91058 Erlangen, Germany
| | - Tobias Boolakee
- Department of Physics, Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Staudtstrasse 1, D-91058 Erlangen, Germany
| | - Constanze Gerner
- Department of Physics, Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Staudtstrasse 1, D-91058 Erlangen, Germany
| | - Heiko B Weber
- Department of Physics, Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Staudtstrasse 1, D-91058 Erlangen, Germany
| | - Ignacio Franco
- Departments of Chemistry and Physics, University of Rochester, Rochester, New York 14627, United States
| | - Peter Hommelhoff
- Department of Physics, Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Staudtstrasse 1, D-91058 Erlangen, Germany
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8
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Dai Y, Zhou Z, Ghosh A, Mong RSK, Kubo A, Huang CB, Petek H. Plasmonic topological quasiparticle on the nanometre and femtosecond scales. Nature 2020; 588:616-619. [PMID: 33361792 DOI: 10.1038/s41586-020-3030-1] [Citation(s) in RCA: 40] [Impact Index Per Article: 10.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/11/2019] [Accepted: 10/02/2020] [Indexed: 11/09/2022]
Abstract
At the interface of classical and quantum physics, the Maxwell and Schrödinger equations describe how optical fields drive and control electronic phenomena to enable lightwave electronics at terahertz or petahertz frequencies and on ultrasmall scales1-5. The electric field of light striking a metal interacts with electrons and generates light-matter quasiparticles, such as excitons6 or plasmons7, on an attosecond timescale. Here we create and image a quasiparticle of topological plasmonic spin texture in a structured silver film. The spin angular momentum components of linearly polarized light interacting with an Archimedean coupling structure with a designed geometric phase generate plasmonic waves with different orbital angular momenta. These plasmonic fields undergo spin-orbit interaction and their superposition generates an array of plasmonic vortices. Three of these vortices can form spin textures that carry non-trivial topological charge8 resembling magnetic meron quasiparticles9. These spin textures are localized within a half-wavelength of light, and exist on the timescale of the plasmonic field. We use ultrafast nonlinear coherent photoelectron microscopy to generate attosecond videos of the spatial evolution of the vortex fields; electromagnetic simulations and analytic theory confirm the presence of plasmonic meron quasiparticles. The quasiparticles form a chiral field, which breaks the time-reversal symmetry on a nanometre spatial scale and a 20-femtosecond timescale (the 'nano-femto scale'). This transient creation of non-trivial spin angular momentum topology pertains to cosmological structure creation and topological phase transitions in quantum matter10-12, and may transduce quantum information on the nano-femto scale13,14.
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Affiliation(s)
- Yanan Dai
- Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, PA, USA. .,Pittsburgh Quantum Institute, University of Pittsburgh, Pittsburgh, PA, USA.
| | - Zhikang Zhou
- Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, PA, USA.,Pittsburgh Quantum Institute, University of Pittsburgh, Pittsburgh, PA, USA
| | - Atreyie Ghosh
- Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, PA, USA.,Pittsburgh Quantum Institute, University of Pittsburgh, Pittsburgh, PA, USA
| | - Roger S K Mong
- Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, PA, USA.,Pittsburgh Quantum Institute, University of Pittsburgh, Pittsburgh, PA, USA
| | - Atsushi Kubo
- Division of Physics, Faculty of Pure and Applied Sciences, University of Tsukuba, Tsukuba-shi, Japan
| | - Chen-Bin Huang
- Institute of Photonics Technologies, National Tsing Hua University, Hsinchu, Taiwan
| | - Hrvoje Petek
- Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, PA, USA. .,Pittsburgh Quantum Institute, University of Pittsburgh, Pittsburgh, PA, USA.
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9
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Da Browski M, Dai Y, Petek H. Ultrafast Photoemission Electron Microscopy: Imaging Plasmons in Space and Time. Chem Rev 2020; 120:6247-6287. [PMID: 32530607 DOI: 10.1021/acs.chemrev.0c00146] [Citation(s) in RCA: 26] [Impact Index Per Article: 6.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/30/2022]
Abstract
Plasmonics is a rapidly growing field spanning research and applications across chemistry, physics, optics, energy harvesting, and medicine. Ultrafast photoemission electron microscopy (PEEM) has demonstrated unprecedented power in the characterization of surface plasmons and other electronic excitations, as it uniquely combines the requisite spatial and temporal resolution, making it ideally suited for 3D space and time coherent imaging of the dynamical plasmonic phenomena on the nanofemto scale. The ability to visualize plasmonic fields evolving at the local speed of light on subwavelength scale with optical phase resolution illuminates old phenomena and opens new directions for growth of plasmonics research. In this review, we guide the reader thorough experimental description of PEEM as a characterization tool for both surface plasmon polaritons and localized plasmons and summarize the exciting progress it has opened by the ultrafast imaging of plasmonic phenomena on the nanofemto scale.
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Affiliation(s)
- Maciej Da Browski
- Department of Physics and Astronomy and Pittsburgh Quantum Institute, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, United States.,Department of Physics and Astronomy, University of Exeter, Stocker Road, Exeter, Devon EX4 4QL, U.K
| | - Yanan Dai
- Department of Physics and Astronomy and Pittsburgh Quantum Institute, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, United States
| | - Hrvoje Petek
- Department of Physics and Astronomy and Pittsburgh Quantum Institute, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, United States
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