Reducing thermal noise in the mirrors of gravitational wave detectors. A short review and some new results

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Optical coatings play a crucial role in interferometric detectors of gravitational waves. A short up-to-date review of related research lines and results is proposed, including new methods and results from the Author’s resarch group.

gravitational wave detectors \ optical coatings \ thermal noise

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References Reducing thermal noise in the mirrors of gravitational wave detectors. A short review and some new results

  • J. Aasi et al., Advanced LIGO, Class. Quantum Grav. 32 (2015) 074001
  • F. Acernese et al., Advanced Virgo: a 2nd Generation GW Detector, Class. Quantum Grav. 32 (2015) 024001
  • T. Akutsu et al., Overview of KAGRA: Detector Design and Construction History, Progr. Th. Experim. Phys. 2021 (2021) 05A101
  • LSC, Instrument Science White Paper, LIGO Document T2200384 (2022) https://dcc.ligo.org/LIGO-T2200384
  • S. Gossler et al., Coating-Free Mirrors for High Precision Interferometric Experiments, Phys. Rev. A76 (2007) 053810
  • A.G. Gurkovsky et al., Reducing Thermal Noise in Future Gravitational Wave Detectors by Employing Khalili Etalons, Phys. Lett. A. 375 (2011) 4147
  • D. Heinert et al., Calculation of Thermal Noise in Grating Reflectors, Phys. Rev. D. 88 (2013) 042001
  • I.M. Pinto, M. Principe, R. DeSalvo, Reflectivity and Thickness Optimization, Ch. 12 in Optical Coatings and Thermal Noise in Precision Measurements, G. Harry et al., Eds., Cambridge Univ. Press, Cambridge (UK), 2012, ISBN 978-1-107-00338-5.
  • D.R.M. Crookes et al., Experimental Measurements of Mechanical Dissipation Associated with Dielectric Coatings Formed Using 𝑆𝑖𝑂2 , 𝑇𝑎2𝑂5 and 𝐴𝑙2𝑂3, Class. Quantum Grav. 23 (2006) 4953
  • G M. Harry, Material Downselect Rationale and Directions, LIGO Document G-G050088-00-R https://dcc.ligo.org/DocDB/0035/G050088/000/G050088-00.pdf
  • A.F. Brooks et al., Direct Measurement of Absorption-InducedWavefront Distortion in High Optical Power Systems, Appl. Opt. 48 (2009) 355
  • G.M. Harry et al., Titania-Doped Tantala/Silica Coatings for Gravitational-Wave Detection, Class. Quantum Grav. 24 (2007) 405
  • R. Flaminio et al., A Study of Coating Mechanical and Optical Losses in View of Reducing Mirror Thermal Noise in Gravitational Wave Detectors, Class Quantum Grav. 27 (2010) 084030
  • R.M. Netterfeld, M. Gross, Investigation of Ion-Beam-Sputtered Silica-Titania Mixtures for Use in Gravitational Wave Interferometer Optics, Proc. OSA-OIC-2007, paper ThD2
  • J. Franc et al., Mirror Thermal Noise in Laser Interferometer Gravitational Wave Detectors Operating at Room and Cryogenic Temperature, Einstein Telescope Note ET-021-09, arXiv:0912.0107
  • M. Granata et al., Optical and Mechanical Properties of Ion-Beam-Sputtered 𝑀𝑔𝐹2 Thin Films for Gravitational-Wave Interferometers, Phys. Rev. Appl. 17 (2022) 034058
  • M. Bischi et al., Characterization of Ion-Beam-Sputtered 𝐴𝑙𝐹3 Thin Films for Gravitational-Wave Interferometers, Phys. Rev. Applied 18 (2022) 054074
  • G. Favaro et al., Measurement and Simulation of Mechanical and Optical Properties of Sputtered Amorphous 𝑆𝑖𝐶 Coatings, Phys. Rev. Appl. 18 (2022) 044030
  • M. Segreti et al., Mechanical and Optical Characterization of Sputtered Amorphous GaN Thin Film for High-Reflectvity and Low-Loss Coatings, GWADW 2023 (poster) , https://agenda.infn.it/event/32907/contributions/200157/attachments/106040/149266/Poster_versione6-2.pdf
  • K. Craig et al., Mirror Coating Solution for the Cryogenic Einstein Telescope, Phys. Rev. Lett. 122 (2019) 231102 1
  • M. Fazio et al., Growth and Characterization of 𝑆𝑐2𝑂3 Doped 𝑇𝑎2𝑂5 Thin Films, Appl. Opt. 5 (2020) A106
  • A. Amato et al., Optical and Mechanical Properties of Ion-Beam-Sputtered 𝑁𝑏2𝑂5 and 𝑇𝑖𝑂2 − 𝑁𝑏2𝑂5 Thin Films for Gravitational-Wave Interferometers and an Improved Measurement of Coating Thermal Noise in Advanced LIGO, Phys. Rev. D. 103 (2021) 072001
  • M. Abernathy et al., Exploration of Co-sputtered 𝑇𝑎2𝑂5−𝑍𝑟𝑂2 Thin Films for Gravitational Wave Detectors, Class. Quantum Grav. 38 (2021) 195021
  • E. Lalande et al., Zirconia-Titania-Doped Tantala Optical Coatings for Low Mechanical Loss Bragg Mirrors, J. Vac. Sci. Technol. A. 39 (2021) 1
  • M. Granata et al., Progress in the Measurement and Reduction of Thermal Noise in Optical Coatings for Gravitational-Wave Detectors , Appl. Opt. 59 (2020) A229
  • M. Fazio et al., Comprehensive Study of Amorphous Metal Oxide and 𝑇𝑎2𝑂5-based Mixed Oxide Coatings for Gravitational-Wave Detectors, Phys. Rev. D 105 (2022) 102008,
  • G. Vajente et al., Low Mechanical Loss TiO2:GeO2 Coatings for Reduced Thermal Noise in Gravitational Wave Interferometers, Phys. Rev. Lett. 127 (2021) 071101
  • S. Khadka et al.,Cryogenic Mechanical Loss of Amorphous Germania and Titania-Doped Germania Thin Films, Class. Quantum Grav. 40 (2023) 205002
  • A. Davenport, Investigation of 𝑇𝑖𝑂2 : 𝐺𝑒𝑂2 for High Reflector Stacks, LIGO document G2302140, https://dcc.ligo.org/LIGO-G2302140
  • E. Lalande et al, 𝐴𝑟 Transport and Blister Growth Kinetics in Titania-doped Germania-based Optical Coatings, LIGO Document P2300328, https://dcc.ligo.org/LIGO-P2300328
  • G.I. McGhee et al., Titania Mixed with Silica: A Low Thermal-Noise Coating Material for Gravitational-Wave Detectors, Phys. Rev. Lett. 131 (2023) 171401
  • I.M. Pinto et al., nm-Layered Amorphous Glassy Oxide Composites for 3rd Generation Interferometric Gravitational Wave Detectors, LIGO Document-G1401358 (2014), https://dcc.ligo.org/DocDB/0116/G1401358/001/G1401358.pdf
  • H.-W. Pan et al., Thickness-Dependent Crystallization on Thermal Anneal for Titania/Silica nm-Layer Composites Deposited by Ion-Beam Sputter Method, Opt. Express 22 (2014) 29847
  • P. Amico et al., Investigation on Mechanical Losses in 𝑇𝑖𝑂2/𝑆𝑖𝑂2 Dielectric Coatings, J. Phys. Conf. Ser. 32 (2006) 413
  • L.-C. Kuo et al., Low Cryogenic Mechanical Loss Composite Silica Thin Film for Low Thermal Noise Dielectric Mirror Coatings, Optics Lett. 44 (2019) 247
  • L.-C. Kuo et al., Annealing Effect on the Nano-meter Scale Titania/Silica Multi-layers for Mirror Coatings of the Laser Interferometer Gravitational Waves Detector, Proc. of the 2019 PhotonIcs & Electromagnetics Research Symposium (PIERS), p. 2347
  • I. Pinto, Which Nanolayers are Worth a Try„ LIGO Document G2000413 (2020) https://dcc.ligo.org/LIGO-G2000413
  • I. Pinto, Nanolayered Silica/Alumina Composites, LIGO Document G2001499 (2020) https://dcc.ligo.org/LIGO-G2001499
  • B. Larsen et al., Crystallization in Zirconia Film Nano-Layered with Silica, Nanomaterials 11 (2021) 344
  • Le Yang et al., Structural Evolution that Affects the Room-Temperature Internal Friction of Binary Oxide Nanolaminates: Implications for Ultrastable Optical Cavities, ACS Appl. Nano Mater. 3 (2020) 12308
  • M. Steinecke et al., Quantizing Nanolaminates as Versatile Materials for Optical Interference Coatings, Appl. Optics 59 (2020) A236
  • D.E. Aspnes, Local Field Effects and Effectve-Medium Theory: a Microscopic Perspective, Am. J. Phys. 50 (1981) 704
  • O. Stenzel et al., Mixed Oxide Coatings for Optics, Appl. Opt. 50 (2011) C69
  • S. Barta, Effective Young’s Modulus and Poisson’s Ratio for the Particulate Composite, J. Appl. Phys. 75 (1994) 3258
  • M. Principe et al., Material Loss Angles from Direct Measurements of Broadband Thermal Noise, Phys. Rev. D. 91 (2015) 022005
  • K.S. Gilroy, W.A. Phillips, An Asymmetric Double-Well Potential Model for Structural Relaxation Processes in Amorphous Materials, Phil. Mag. B. 43 (1981) 735
  • A. Amato et al., Observation of a Correlation Between Internal Friction and Urbach Energy in Amorphous Oxides Thin Films, Sci. Rep. 10 (2020) 1670
  • R. Bassiri et al., Correlations Between the Mechanical Loss and Atomic Structure of Amorphous 𝑇𝑖𝑂2-doped 𝑇𝑎2𝑂5 Coatings, Acta Mater. 61 (2013) 1070
  • J.P. Trinastic et al., Molecular Dynamics Modeling of Mechanical Loss in Amorphous Tantala and Titania-Doped Tantala, Phys. Rev. B. 93 (2016) 014105
  • T. Damart, D. Rodney, Atomistic Study of Two-level Systems in Amorphous Silica, Phys. Rev. B. 97 (2018) 014201
  • K. Prasai et al., Annealing-Induced Changes in the Atomic Structure of Amorphous Silica, Germania, and Tantala Using Accelerated Molecular Dynamic, Phys. Stat. Sol. B. 258 (2021) 2000519
  • J. Jiang et al., Amorphous Zirconia-doped Tantala Modeling and Simulations using Explicit Multi- Element Spectral Neighbor Analysis Machine Learning Potentials (EME-SNAP), Phys. Rev. Mater. 7 (2023) 045602
  • M. Kim et al., Atomic Structure Characterization of Titania-doped Germania, LIGO Document G2301799, https://dcc.ligo.org/LIGO-G2301799
  • M. Turowski, et al., Practice-Oriented Optical Thin Film Growth Simulation via Multiple Scale Approach, Thin Solid Films 592 (2015) 240
  • F.V. Grigoriev, V.B. Sulimov, A.V.Tikhonravov, Application of a Large-Scale molecular dynamics approach to modelling the Deposition of 𝑇𝑖𝑂2 Thin Films, Computat. Mater. Sci. 188 (2021) 110202
  • F.V. Grigoriev, V.B. Sulimov,Atomistic Simulation of Physical Vapor Deposition of Optical Thin Films, Nanomaterials, 13 (2023) 1717
  • A. Alexandrovski et al., Photothermal Common-Path Interferometry (PCI): New Developments, SPIE Proceedings 7193 (2009) 71930D
  • K.V. Vlasova et al., High-sensitive Absorption Measurement in Transparent Isotropic Dielectrics with Time-resolved Photothermal Common-Path Interferometry, Appl. Opt., 57 (2018) 6318
  • J.R. Smith et al., Apparatus to Measure Optical Scatter of Coatings Versus Annealing Temperature, Proc. OSA-OIC 2019, FA.2
  • G.H. Ogin et al., Measuring the Thermo-Optic Response of Dielectric Stack Mirrors, Proc. OSA-OIC 2016, MB.7
  • E.M. Gretarsson, A.M. Gretarsson, Three Methods for Characterizing Thermo-Optic Noise in Optical Cavities, Phys. Rev. D. 98 (2018) 122004
  • E. Cesarini et al., A ‘Gentle’ Nodal Suspension for Measurements of the Acoustic Attenuation in Materials, Rev. Sci. Instrum. 80 (2009) 053904
  • G. Vajente et al., Method for the Experimental Measurement of Bulk and Shear Loss Angles in Amorphous Thin Films, Phys. Rev. D. 101 (2020) 042004
  • K. Numata et al., Wide-Band Direct Measurement of Thermal Fluctuations in an Interferometer, Phys. Rev. Lett. 91 (2003) 260602
  • E.D. Black et al., Direct Observation of Broadband Coating Thermal Noise in a Suspended Interferometer, Phys. Lett. A. 328 (2004) 1
  • T. Chalermsongsak et al., Broadband Measurement of Coating Thermal Noise in Rigid Fabry–Perot Cavities, Metrologia 52 (2015) 17
  • S. Gras, M. Evans, Direct Measurement of Coating Thermal Noise in Optical Resonators, Phys. Rev. D 98 (2018) 122001
  • R. Pedurand, Instrumentation for Thermal Noise Spectroscopy, PhD Thesis (2019), Univ. Lyon (FR), 2019, https://theses.hal.science/tel-02612035
  • G.D. Cole et al., Tenfold Reduction of Brownian Noise in High-Reflectivity Optical Coatings, Nature Photonics 7 (2013) 644
  • A.C. Lin et al., Epitaxial Growth of GaP/AlGaP Mirrors on Si for Low Thermal Noise Optical Coatings, Opt. Mater. Express 8 (2015) 1890
  • A.V. Cumming et al., Measurement of the Mechanical Loss of Prototype GaP/AlGaP Crystalline Coatings for Future Gravitational Wave Detectors, Class. Quantum Grav. 32 (2015) 035002
  • P.G. Murray et al., Cryogenic Mechanical Loss of a Single-Crystalline GaP Coating Layer for Precision Measurement Applications, Phys. Rev. D. 95 (2017) 042004
  • G.D. Cole et al., High-Performance Near- and Mid-Infrared Crystalline Coatings, Optica 3 (2016) 647
  • G.D. Cole et al., Substrate-Transferred GaAs/AlGaAs Crystalline Coatings for Gravitational-Wave Detectors, Appl. Phys. Lett. 122 (2023) 110502
  • M.L. Gorodetsky, Thermal Noises and Noise Compensation in High-Reflection Multilayer Coating, Phys. Lett. A. 372 (2008) 6813
  • M. Evans et al., Thermo-Optic Noise in Coated Mirrors for High-Precision optical Measurements, Phys. Rev. D. 78 (2008) 102003
  • T. Chalermsongsak et al., Coherent Cancellation of Photothermal Noise in 𝐺𝑎𝐴𝑠/𝐴𝑙0.92𝐺𝑎0.08𝐴𝑠 Bragg Mirrors, Metrologia 53 2016 860
  • S. Kryhin, E.D. Hall, V. Sudhir, Thermorefringent Noise in Crystalline Optical Materials, Phys. Rev. D. 107 (2023) 022001
  • J. Yu et al., Excess Noise and Photoinduced Effects in Highly Reflective Crystalline Mirror Coatings, Phys. Rev. X. 13 (2023) 041002
  • H.-W. Pan et al., Silicon Nitride Films Fabricated by a Plasma-Enhanced Chemical Vapor Deposition Method for Coatings of the Laser Interferometer Gravitational Wave Detector, Phys. Rev. D. 87 (2018) 022004
  • D.-S. Tsai et al., Amorphous Silicon Nitride Deposited by an 𝑁𝐻3-free Plasma Enhanced Chemical Vapor Deposition Method for the Coatings of the Next Generation Laser Interferometer Gravitational Waves Detector, Class. Quantum Grav. 39 (2022) 15LT01
  • G.S. Wallace et al., Non-stoichiometric Silicon Nitride for Future Gravitational Wave Detectors, LIGO Document P-2300539 (2023), https://dcc.ligo.org/LIGO-P2300359
  • P. G. Murray et al., Ion-beam Sputtered Amorphous Silicon Films for Cryogenic Precision Measurement Systems, Phys. Rev. D 92 (2015) 062001
  • J. Steinlechner et al., Optical Absorption of Ion-Beam Sputtered Amorphous Silicon Coatings, Phys. Rev. D 93 (2016) 062005
  • J. Steinlechner et al., Silicon-Based Optical Mirror Coatings for Ultrahigh Precision Metrology and Sensing, Phys. Rev. Lett. 120 (2018) 3602
  • R. Birney et al., Amorphous Silicon with Extremely Low Absorption: Beating Thermal Noise in Gravitational Astronomy, Phys. Rev. Lett. 121 (2018) 191101
  • L. Terkowsky et al., Influence of Deposition Parameters on the Optical Absorption of Amorphous Silicon Thin Films, Phys. Rev. Res. 2 (2020) 033308
  • M. Molina-Ruiz, Hydrogen-Induced Ultralow Optical Absorption and Mechanical Loss in Amorphous Silicon for Gravitational-Wave Detectors, Phys. Rev. Lett. 131 (2023) 256902
  • M. Kinley-Hanlon et al., Update on Nanolayer 𝑎𝑆𝑖/𝑆𝑖𝑂2 Coatings and Ion Implantation (SIMOX) Layers for Mechanical Loss,LIGO Document G2300684 (2023) https://dcc.ligo.org/LIGO-G2300684
  • A. V. Vinogradov and Ya. B. Zel’dovich, X-ray and Far UV Multilayer Mirrors: Principles and Possibilities, Appl. Opt., 16 (1977) pp. 89-93
  • J.I. Larruquert, Reflectance Enhancement in the Extreme Ultraviolet and Soft X Rays by Means of Multilayers with More than Two Materials, J. Opt. Soc. Am. 19 (2002) pp. 391-397
  • J.I. Larruquert. Inreflectance: a New Function for the Optimization of Multilayers with Absorbing Materials, J. Opt. Soc. Am. A22 (2005) 1607.
  • J.I. Larruquert et al., Constructing Multilayers with Absorbing Materials, Chinese Opt. Lett. 8 (2010) 159
  • J. Agresti et al., Optimized Multilayer Dielectric Mirror Coatings for Gravitational Wave Interferometers, Proc. of SPIE, 6286 (2006) 628608,
  • A.E. Villar et al., Measurement of Thermal Noise in Multilayer Coatings with Optimized Layer Thickness, Phys. Rev. D 81 (2010) 122001
  • L.Pinard et al., Mirrors Used in the LIGO Interferometers for First Detection of Gravitational Waves, Appl. Optics 56 (2017) C11
  • D.V. Martynov et al., Sensitivity of the Advanced LIGO Detectors at the Beginning of Gravitational Wave Astronomy, Phys. Rev. D. 93 (2016) 112004,
  • N.M. Kondratiev, A.G. Gurkovsky, M.L. Gorodetsky, Thermal Noise and Coating Optimization in Multilayer Dielectric Mirrors, Phys. Rev. D. 84 (2011), 022001
  • V. Pierro et al., On the Performance Limits of Coatings for Gravitational Wave Detectors Made of Alternating Layers of Two Materials, Optical Mater. 96 (2019) 109269
  • J. Steinlechner et al., Thermal Noise Reduction and Absorption Optimization via Multimaterial Coatings, Phys. Rev. D 91 (2015) 042001
  • W. Yam, S. Gras, M. Evans, Multimaterial Coatings with Reduced Thermal Noise, Phys. Rev. D 91 (2015) 042002
  • J. Steinlechner, I.W. Martin, High Index Top Layer for Multimaterial Coatings, Phys. Rev. D. 93 (2016) 102001
  • S. Tait et al., ’Demonstration of the Multimaterial Coating Concept to Reduce Thermal Noise in Gravitational-Wave Detectors, Phys. Rev. Lett. 125 (2020) 011102
  • V. Pierro et al., Ternary Quarter Wavelength Coatings for Gravitational Wave Detector Mirrors: Design Optimization via Exhaustive Search, Phys. Rev. Res. 3 (2021) 023172
  • M. Granata et al., Present Results and Future Perspectives of SiNx-based Multi-Material Mirror Coatings, LIGO Document G2300642 https://dcc.ligo.org/LIGO-G2300642
  • C.A. Coello-Coello et al., Evolutionary Multiobjective Optimization: Open Research Areas and Some Challenges Lying Ahead , Complex & Intelligent Sys. 6 (2020) 221
  • C. Blum, A. Roli, Metaheuristics in Combinatorial Optimization: Overview and Conceptual Comparison, ACM Comput. Surv. 35 (2003) 268
  • A. Konak, D.W. Coit, A.E. Smith, Multi-Objective Optimization Using Genetic Algorithms: A Tutorial, J. RESS 91 (2006) 992
  • M. Dorigo et al., Ant Colony Optimization: Artificial Ants as a Computational Intelligence Technique, IEEE Computat. Intell. Mag., 1 (2006) 28
  • D. Hadka , P.M. Reed , BORG: An Auto-Adaptive Many-Objective Evolutionary Computing Framework, Evolutionary Computation 21 (2013) 231
  • http://borgmoea.org/
  • I.M. Pinto et al., Optimized Ternary Coatings : Options and Performance, LIGO Document G2201509 https://dcc.ligo.org/LIGO-G2201509
  • R. Schnabel et al., Building Blocks for Future Detectors: Silicon Test Masses and 1550 nm Laser Light, J. Phys. Conf. Ser. 228 (1010) 012029.
  • R.X. Adikhari et al.,A Cryogenic Silicon Interferometer for Gravitational-wave Detection, Class. Quantum Grav. 37 (2020) 165003
  • P.R. Saulson, Fundamentals of Interferometric Gravitational Wave Detectors, World Scientific, Singapore, 2017, ISBN 978-9813143074
  • Yu. Levin, Internal Thermal Noise in the LIGO Test Masses: a Direct Approach, Phys. Rev D. 57 (1998) 659
  • M.L. Gorodetsky, Thermal Noises and Noise Compensation in High-Reflection Multilayer Coating, Phys. Lett. A. 372 (2008) 6813
  • V.B. Braginsky, M.L. Gorodetsky, S.P. Vyatchanin, Compendium of Thermal Noises in Optical Mirrors, Ch. 3 in Optical Coatings and Thermal Noise in Precision Measurements, G. Harry et al. (Eds.), Cambridge Univ. Press, Cambridge (UK), 2012, ISBN 978-1-107-00338-5.
  • G.M. Harry et al., Optical Coatings for Gravitational Wave Detection, Proc. SPIE 5527 (2004) 33
  • A.G. Gurkovsky and S.P. Vyatchanin, The Thermal Noise in Multilayer Coatings, Phys. Lett. A. 374 (2010) 3267
  • M. Fejer, Effective Medium Description of Multilayer Coatings , LIGO Document T-T2100186, https://dcc.ligo.org/LIGO-T2100186
  • K. Somiya, K. Yamamoto, Coating thermal Noise of a Finite-Size Cylindrical Mirror, Phys. Rev. D. 79 (2009) 102004
  • T. Hong et al., Brownian Thermal Noise in Multilayer Coated Mirrors, Phys. Rev. D. 87 (2013) 082001
  • V. Pierro et al., Perspectives on Beam-Shaping Optimization for Thermal-Noise Reduction in Advanced Gravitational-Wave Interferometric Detectors: Bounds, Profiles, and Critical Parameters, Phys. Rev. D. 76 (2007) 122003
  • https://cosmicexplorer.org/
  • https://apps.et-gw.eu/tds/?call_file=ET-0028A-20_EinsteinTelescopeScienceCaseDe.pdf
  • I.W. Martin et al., Low Temperature Mechanical Dissipation of an Ion-Beam Sputtered Silica Film, Class. Quantum Grav. 31 (2014) 035019
  • I.W. Martin et al., Comparison of the Temperature Dependence of the Mechanical Dissipation in Thin Films of 𝑇𝑎2𝑂5 and 𝑇𝑎2𝑂5 doped with 𝑇𝑖𝑂2, Class. Quantum Grav. 26 (2009) 155012
  • M. Granata et al., Cryogenic Measurements of Mechanical Loss of High-Reflectivity Coating and Estimation of Thermal Noise, Optics Lett. 38 (2013) 5268
  • E. Hirose et al., Mechanical Loss of a Multilayer Tantala/Silica Coating on a Sapphire Disk at Cryogenic Temperatures: Toward the KAGRA GravitationalWave Detector, Phys. Rev. D. 90 (2014) 102004
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