Technology for the next gravitational wave detectors

  • Valery P. Mitrofanov
  • Shiuh ChaoEmail author
  • Huang-Wei Pan
  • Ling-Chi Kuo
  • Garrett Cole
  • Jerome Degallaix
  • Benno Willke
Invited Review
Part of the following topical collections:
  1. Special Topic: the Next Detectors for Gravitational Wave Astronomy


This paper reviews some of the key enabling technologies for advanced and future laser interferometer gravitational wave detectors, which must combine test masses with the lowest possible optical and acoustic losses, with high stability lasers and various techniques for suppressing noise. Sect. 1 of this paper presents a review of the acoustic properties of test masses. Sect. 2 reviews the technology of the amorphous dielectric coatings which are currently universally used for the mirrors in advanced laser interferometers, but for which lower acoustic loss would be very advantageous. In sect. 3 a new generation of crystalline optical coatings that offer a substantial reduction in thermal noise is reviewed. The optical properties of test masses are reviewed in sect. 4, with special focus on the properties of silicon, an important candidate material for future detectors. Sect. 5 of this paper presents the very low noise, high stability laser technology that underpins all advanced and next generation laser interferometers.


gravitational waves advanced techniques thermal noise coating laser 


  1. 1.
    Nawrodt R, Rowan S, Hough J, et al. Challenges in thermal noise for 3rd generation of gravitational wave detectors. Gen Relativ Gravit, 2011, 43: 593–622ADSzbMATHCrossRefGoogle Scholar
  2. 2.
    Cagnoli G, Hough J, DeBra D, et al. Damping dilution factor for a pendulum in an interferometric gravitational waves detector. Phys Lett A, 2000, 272: 39–45ADSCrossRefGoogle Scholar
  3. 3.
    Corbitt T, Wipf C, Bodiya T, et al. Optical dilution and feedback cooling of a gram-scale oscillator to 6.9 mK. Phys Rev Lett, 2007, 99: 160801ADSCrossRefGoogle Scholar
  4. 4.
    Braginsky V B, Mitrofanov V P, Panov V I. Systems with Small Dissipation. Chicago: Chicago University Press, 1985Google Scholar
  5. 5.
    Zener C M. Elasticity and Anelasticity of Metals. Chicago: Chicago University Press, 1948Google Scholar
  6. 6.
    Lifshitz R, Roukes M L. Thermoelastic damping in micro- and nanomechanical systems. Phys Rev B, 2000, 61: 5600–5609ADSCrossRefGoogle Scholar
  7. 7.
    Li P, Fang Y, Hu R. Thermoelastic damping in rectangular and circular microplate resonators. J Sound Vib, 2012, 331: 721–733ADSCrossRefGoogle Scholar
  8. 8.
    Dmitriev A V, Gritsenko D S, Mitrofanov V P. Non-axisymmetric flexural vibrations of free-edge circular silicon wafers. Phys Lett A, 2014, 378: 673–676ADSCrossRefGoogle Scholar
  9. 9.
    Braginsky V B, Gorodetsky M L, Vyatchanin S P. Thermodynamical fluctuations and photo-thermal shot noise in gravitational wave antennae. Phys Lett A, 1999, 264: 1–10ADSCrossRefGoogle Scholar
  10. 10.
    Nowick A S, Berry B S. Anelastic Relaxation in Crystalline Solids. New York: Academic Press, 1972Google Scholar
  11. 11.
    Kunal K, Aluru N R. Akhiezer damping in nanostructures. Phys Rev B, 2011, 84: 245450ADSCrossRefGoogle Scholar
  12. 12.
    Lindenfeld Z, Lifshitz R. Damping of mechanical vibrations by free electrons in metallic nanoresonators. Phys Rev B, 2013, 87: 085448ADSCrossRefGoogle Scholar
  13. 13.
    Haucke H, Liu X, Vignola J F, et al. Effects of annealing and temperature on acoustic dissipation in a micromechanical silicon oscillator. Appl Phys Lett, 2005, 86: 181903ADSCrossRefGoogle Scholar
  14. 14.
    Blom F R, Bouwstra S, Elwenspoek M, et al. Dependence of the quality factor of micromachined silicon beam resonators on pressure and geometry. J Vac Sci Technol B, 1992, 10: 19–26Google Scholar
  15. 15.
    Bao M, Yang H. Squeeze film air damping in MEMS. Sens Actuators A, 2007, 136: 3–27CrossRefGoogle Scholar
  16. 16.
    Frangia A, Cremonesia M, Jaakkolab A, et al. Analysis of anchor and interface losses in piezoelectric MEMS resonators. Sens Actuators A, 2013, 190: 127–135CrossRefGoogle Scholar
  17. 17.
    Schnabel R, Britzger M, Brueckner F, et al. Building blocks for future detectors: Silicon test masses and 1550 nm laser light. J Phys-Conf Ser, 2010, 228: 012029ADSCrossRefGoogle Scholar
  18. 18.
    Lunin B S. Physical and Chemical Bases for the Development of Hemispherical Resonators for Solid-State Giroscopes. Moscow: Moscow Aviation Institute, 2005Google Scholar
  19. 19.
    Penn S D, Ageev A, Busby D, et al. Frequency and surface dependence of the mechanical loss in fused silica. Phys Lett A, 2006, 352: 3–6ADSCrossRefGoogle Scholar
  20. 20.
    Heptonstall A, Barton M A, Bell A, et al. Invited Article: CO2 laser production of fused silica fibers for use in interferometric gravitational wave detector mirror suspensions. Rev Sci Instrum, 2011, 82(1): 011301ADSCrossRefGoogle Scholar
  21. 21.
    Braginsky V B, Mitrofanov V P, Tokmakov K V. Energy dissipation in the test mass suspension of a gravitational wave antenna. Phys Lett A, 1996, 218: 164–166ADSCrossRefGoogle Scholar
  22. 22.
    Hirose E, Bajuk D, Billingsley G, et al. Sapphire mirror for the KAGRA gravitational wave detector. Phys Rev D, 2014, 89: 062003ADSCrossRefGoogle Scholar
  23. 23.
    McGuigan D F, Lam C C, Gram R Q, et al. Measurements of the mechanical Q of single-crystal silicon at low temperatures. J Low Temp Phys, 1978, 30: 621–629Google Scholar
  24. 24.
    Mitrofanov V P. Temperature dependent dissipation in silicon mechanical resonators. Document LIGO-T1200178-v3, 2012, Scholar
  25. 25.
    Reid S, Cagnoli G, Crooks D R M, et al. Mechanical dissipation in silicon flexures. Phys Lett A, 2006, 351: 205–211ADSCrossRefGoogle Scholar
  26. 26.
    Nawrodt R, Schwarz C, Kroker S, et al. Investigation of mechanical losses of thin silicon flexures at low temperatures. Class Quantum Grav, 2013, 30: 115008ADSCrossRefGoogle Scholar
  27. 27.
    Prokhorov L G, Mitrofanov V P. Mechanical losses of oscillators fabricated in silicon wafers. Class Quantum Grav, 2015, 32: 195002ADSCrossRefGoogle Scholar
  28. 28.
    Macleod H A. Thin-Film Optical Filters. Boca Raton, FL: CRC Press, 2010. 165Google Scholar
  29. 29.
    LIGO Scientific Collaboration. Instrument science white paper. 2015, LIGO-T1400316-v4Google Scholar
  30. 30.
    Callen H B, Welton T A. Irreversibility and generalized noise. Phys Rev, 1951, 83: 34–40ADSMathSciNetzbMATHCrossRefGoogle Scholar
  31. 31.
    Harry G M, Gretarsson A M, Saulson P R, et al. Thermal noise in interferometric gravitational wave detectors due to dielectric optical coatings. Class Quantum Grav, 2002, 19: 897–917ADSzbMATHCrossRefGoogle Scholar
  32. 32.
    Harry G, Bodiya T P, DeSalvo R. Optical Coatings and Thermal Noise in Precision Measurement. Cambridge, New York: Cambridge University Press, 2012. chap 3: 24–35ADSGoogle Scholar
  33. 33.
    Gorodetsky M L. Thermal noises and noise compensation in highreflection multilayer coating. Phys Lett A, 2008, 372: 6813–6822ADSCrossRefGoogle Scholar
  34. 34.
    Harry G, Bodiya T P, DeSalvo R. Optical Coatings and Thermal Noise in Precision Measurement. Cambridge, New York: Cambridge University Press, 2012. chap 9: 154–171ADSGoogle Scholar
  35. 35.
    Aso Y, Michimura Y, Somiya K, et al. Interferometer design of the KAGRA gravitational wave detector. Phys Rev D, 2013, 88: 043007ADSCrossRefGoogle Scholar
  36. 36.
    Abernathy M, Acernese F, Ajith P, et al. Einstein gravitational wave telescope conceptual design study. European Commission FP7, Grant Agreement 211743, ET-0106C-10Google Scholar
  37. 37.
    Stolz C J, Taylor J R. Damage threshold study of ion beam sputtered coatings for a visible high-repetition laser at LLNL. SPIE 1848 Laser- Induced Damage in Optical Materials, 1992. 182–191Google Scholar
  38. 38.
    Harry G, Bodiya T P, DeSalvo R. Optical Coatings and Thermal Noise in Precision Measurement. Cambridge, New York: Cambridge University Press, 2012Google Scholar
  39. 39.
    Gibson U J. Ion-beam processing of optical thin films. Phys Thin Films, 1987, 13: 109–150MathSciNetCrossRefGoogle Scholar
  40. 40.
    Martin I W, Bassiri R, Nawrodt R, et al. Effect of heat treatment on mechanical dissipation in Ta2O5 coatings. Class Quantum Grav, 2010, 27: 225020ADSCrossRefGoogle Scholar
  41. 41.
    Penn S, Podkaminer J, Luongo C, et al. Exploring coating thermal noise via loss in fused silica coatings. LIGO-G0900600Google Scholar
  42. 42.
    Abernathy M R, Reid S, Chalkley E, et al. Cryogenic mechanical loss measurements of heat-treated hafnium dioxide. Class Quantum Grav, 2011, 28: 195017ADSCrossRefGoogle Scholar
  43. 43.
    Martin N, Rousselot C, Rondot D, et al. Microstructure modification of amorphous titanium oxide thin films during annealing treatment. Thin Solid Films, 1997, 300: 113–121ADSCrossRefGoogle Scholar
  44. 44.
    Chao S, Lin Y F, Lin J F, et al. Scattering loss of an optimum pair high reflectance dielectric mirror. Appl Opt, 1990, 29: 1960–1963ADSCrossRefGoogle Scholar
  45. 45.
    Khalili F Y. Reducing the mirrors coating noise in laser gravitationalwave antennae by means of double mirrors. Phys Lett A, 2005, 334: 67–72ADSCrossRefGoogle Scholar
  46. 46.
    Steinlechner J, Martin I W, Hough J, et al. Thermal noise reduction and absorption optimization via multimaterial coatings. Phys Rev D, 2015, 91: 042001ADSCrossRefGoogle Scholar
  47. 47.
    Harry G, Bodiya T P, DeSalvo R. Optical Coatings and Thermal Noise in Precision Measurement. Cambridge, New York: Cambridge University Press, 2012. Chapter 12: 207–233ADSGoogle Scholar
  48. 48.
    Pinto I M, Principe M, DeSalvo R. Review of optimized coatings and plans for nanometer layer sandwich coatings. Workshop on Coating Modeling, Caltech, March, 2010, LIGO-G1000380Google Scholar
  49. 49.
    Pan H W, Wang S J, Kuo L C, et al. Thickness-dependent crystallization on thermal anneal for titania/silica nm-layer composites deposited by ion beam sputter method. Opt Express, 2014, 22: 29847–29854ADSCrossRefGoogle Scholar
  50. 50.
    Chao S, Kuo L C, Pan H W. Mechanical loss reduction for nmlayered SiO2/TiO2 composites by thermal annealing. LVC meeting, Budapest Hungary, Sep. 2015, LIGO-G1501024Google Scholar
  51. 51.
    Harry G, Bodiya T P, DeSalvo R. Optical Coatings and Thermal Noise in Precision Measurement. Cambridge, New York: Cambridge University Press, 2012. Chapter 2: 7–23ADSGoogle Scholar
  52. 52.
    Wei D T, Louderback AW.Method for fabricating multi-layer optical films. United States Patent, US4142958 A, 1979-03-06Google Scholar
  53. 53.
    Wei D T. Ion beam interference coating for ultralow optical loss. Appl Opt, 1989, 28: 2813–2816ADSCrossRefGoogle Scholar
  54. 54.
    Maissel L I, Glang R. Handbook of Thin Film Technology. New York: McGraw-Hill Book Company, 1970. 31–338Google Scholar
  55. 55.
    Wehner G K, Rosenberg D. Angular distribution of sputtered material. J Appl Phys, 1960, 31: 177Google Scholar
  56. 56.
    Pinard L. advanced LIGO test masses coatings a LIGO and CHALLENGING story final results. LVC meeting, Pasadena, CA, USA, March 2015, LIGO-G1500296-v2Google Scholar
  57. 57.
    Pinard L. The VIRGO large mirrors: A challenge for low loss coatings—Amaldi presentation, Lyon, France, 2003, LIGOG030490- x0Google Scholar
  58. 58.
    Beauville F, Buskulic D, Flaminio R, et al. Low loss coatings for the VIRGO large mirrors. Proc SPIE, 2004, 483–492, in2p3- 00024327Google Scholar
  59. 59.
    Netterfield R P, Gross M, Baynes F N, et al. Low mechanical loss coatings for LIGO optics: Progress report. Proc SPIE, 2005, 5870: 58700HGoogle Scholar
  60. 60.
    Stoffel A, Kovacs A, Kronast W, et al. LPCVD against PECVD for micromechanical applications, J Micromech Microeng, 1996, 6(1): 1–13Google Scholar
  61. 61.
    Nguyen S V, Fridmann S. Plasma deposition and characterization of thin silicon-rich silicon nitride films. J Electrochem Soc, 1987, 134: 2324–2329CrossRefGoogle Scholar
  62. 62.
    Kalb A, Mildebrath M, Sanders V. Neutral ion beam deposition of high reflectance coatings for use in ring laser gyroscopes. J Vac Sci Technol A, 1986 4: 436–437ADSCrossRefGoogle Scholar
  63. 63.
    Franc J, Morgado N, Flaminio R, et al. Mirror thermal noise in laser interferometer gravitational wave detectors operating at room and cryogenic temperature. arXiv:0912.0107vlGoogle Scholar
  64. 64.
    Martin I. Studies of Materials for Use in Future Interferometric Gravitational Wave Detectors. Dissertation for the Doctoral Degree. Glasgow: The university of Glasgow, 2009Google Scholar
  65. 65.
    Penn S, Podkaminer J, Luo J, et al. Recent measurements of mechanical loss for aLIGO coating research. LSC meeting, Embassy Suites, March 2010, LIGO-G1000356Google Scholar
  66. 66.
    Penn S, Sneddon P H, Armandula H, et al. Mechanical loss in tantala/ silica dielectric mirror coatings. Class Quantum Grav, 2003, 20: 2917–2928ADSzbMATHCrossRefGoogle Scholar
  67. 67.
    Martin I W, Nawrodt R, Craig K, et al. Low temperature mechanical dissipation of an ion-beam sputtered silica film. Class Quantum Grav, 2014, 31: 035019ADSCrossRefGoogle Scholar
  68. 68.
    Gilroy K S, Phillips W A. An asymmetric double-well potential model for structural relaxation processes in amorphous materials. Philos Mag B, 1981, 43: 735–746ADSCrossRefGoogle Scholar
  69. 69.
    Topp K A, Cahill D G. Elastic properties of several amorphous solids and disordered crystals below 100 K. Z Phys B, 1996, 101: 235–245ADSCrossRefGoogle Scholar
  70. 70.
    Martin I, Armandula H, Comtet C, et al. Measurements of a lowtemperature mechanical dissipation peak in a single layer of Ta2O5 doped with TiO2. Class Quantum Grav, 2008, 25: 055005ADSCrossRefGoogle Scholar
  71. 71.
    Murray P G, Martin I W, Abernathy M R, et al. Ion-beam sputtered amorphous silicon films for cryogenic precision measurement systems. 2015, LIGO-P1500080Google Scholar
  72. 72.
    Phillips W A. Amorphous Solids Low Temperature Properties. Berlin: Springer, 1981CrossRefGoogle Scholar
  73. 73.
    Anderson P W, Halperin B I, Varma C M. Anomalous lowtemperature thermal properties of glasses and spin glasses. Philos Mag, 1972, 25: 1–9ADSzbMATHCrossRefGoogle Scholar
  74. 74.
    Liu X, White J B E, Pohl R O. Amorphous solid without low energy excitations. Phys Rev Lett, 1997, 78: 4418–4421ADSCrossRefGoogle Scholar
  75. 75.
    Liu X, Queen D R, Metcalf T H, et al. Hydrogen-free amorphous silicon with no tunneling states. Phys Rev Lett, 2014, 113: 025503ADSCrossRefGoogle Scholar
  76. 76.
    Liu X, Queen D R, Metcalf T H, et al. Amorphous dielectric thin films with extremely low mechanical loss. Arch Metall Mater, 2015, 60: 359–363Google Scholar
  77. 77.
    Pinto I M, Principe M, DeSalvo R, et al. Nm-layered amorphous glassy oxide composites for 3rd generation interferometric gravitational wave detectors. 6th ET symposium, Lyon France, Nov. 2014, LIGO-G1401358Google Scholar
  78. 78.
    Harry GM, Abernathy MR, Becerra-Toledo A E, et al. Titania-doped tantala/silica coatings for gravitational-wave detection. Class Quantum Grav, 2007, 24: 405–415ADSCrossRefGoogle Scholar
  79. 79.
    Martin I W, Chalkley E, Nawrodt R, et al. Comparison of the temperature dependence of the mechanical dissipation in thin films of Ta2O5 and Ta2O5 doped with TiO2. Class Quantum Grav, 2009, 26: 155012ADSCrossRefGoogle Scholar
  80. 80.
    Martin I, Craig K, Murray P, et al. Mechanical loss of crystalline and amorphous coatings. GWADW, Takayama, May 2014, http:// Martin.pdfGoogle Scholar
  81. 81.
    Chao S, Wang W H, Lee C C. Low-loss dielectric mirror with ionbeam- sputtered TiO2SiO2 mixed films. Appl Opt, 2001, 40: 2177–2182ADSCrossRefGoogle Scholar
  82. 82.
    Murray P, Bassiri R, Bell A, et al. Coating mechanical loss investigations. LSC meeting, Nice, France, March 2014, LIGO-G1400275Google Scholar
  83. 83.
    Penn S. Mechanical loss in annealed amorphous and AlGaAs coatings. LVC meeting, Nice, France, March 2014, LIGO-G1400257Google Scholar
  84. 84.
    Flaminio R, Michel C, Morgado N, et al. A study of coating mechanical and optical losses in view of reducing mirror thermal noise in gravitational wave detectors. Class Quantum Grav, 2010, 27: 084030ADSMathSciNetCrossRefGoogle Scholar
  85. 85.
    DeSalvo R. Status of nano-layered coating developments. LVC meeting, Pasadena, CA, USA, March 2015, LIGO-G1500330Google Scholar
  86. 86.
    Netterfield R P, Gross M, Investigation of ion beam sputtered silica titania mixtures for use in GW interferometer optics. Optical Interference Coatings (OIC) Conference, Tucson AZ, USA, 2007, paper Thd2Google Scholar
  87. 87.
    Martin I, Steinlechner J, Murray P, et al. Asi coatings optical absorption and mechanical loss. LVC meeting, Pasadena, CA, USA, March 2015, LIGO-G1500385Google Scholar
  88. 88.
    Philipp H R. Optical properties of silicon nitride. J Electrochem Soc, 1973, 120: 295–300CrossRefGoogle Scholar
  89. 89.
    Poenar D P, Wolffenbuttel R F. Optical properties of thin-film silicon compatible materials. Appl Opt, 1997, 36: 5122–5128ADSCrossRefGoogle Scholar
  90. 90.
    Chao S, Pan H W, Juang Y H, et al. Mechanical loss of silicon cantilever coated with a high-stress SiNx film. LVC meeting, Stanford, CA, USA, 2014, LIGO-G1400851Google Scholar
  91. 91.
    Zwickl B M, Shanks W E, Jayich A M, et al. High quality mechanical and optical properties of commercial silicon nitride membrances. Appl Phys Lett, 2008, 92: 103125ADSCrossRefGoogle Scholar
  92. 92.
    Southworth D R, Barton R A, Verbridge S S, et al. Stress and silicon nitride: A crack in the universal dissipation of glasses. Phys Rev Lett, 2009, 102: 225503ADSCrossRefGoogle Scholar
  93. 93.
    Wu J, Yu C C. How stress can reduce dissipation in glasses. Phys Rev B, 2011, 84: 174109ADSCrossRefGoogle Scholar
  94. 94.
    Chao S, Pan H W, Huang S Y, et al. Room temperature mechanical loss of high stress silicon nitride film measured by cantilever ringdown method on double-side coated cantilever. LVC meeting, Budapest, Hungary, 2015, LIGO-G1501068Google Scholar
  95. 95.
    Juang Y H. Stress Effect on Mechanical Loss of the SiNx Film Deposited with PECVD Method on Silicon Cantilever and Setup for the LossMeasurement Improvement. Dissertation for theMaster Degree. Hsinchu: Tsing Hua University, 2014Google Scholar
  96. 96.
    Bassiri R, Evans, Borisenko K B, et al. Correlations between the mechanical loss and atomic structure of amorphous TiO2-doped Ta2O5 coatings. Acta Mater, 2013, 61: 1070–1077CrossRefGoogle Scholar
  97. 97.
    Bassiri R, Abernathy M R, Byer R L, et al. Atomic structure investigations of heat-treated and doped tantala coatings. LVC meeting, Nice, France, March 2014, LIGO-G1400271Google Scholar
  98. 98.
    Bassiri R, Liou F, Abernathy M R, et al. Order within disorder: The atomic structure of ion-beam sputtered amorphous tantala (a-Ta2O5). APL Mater, 2015, 3: 036103ADSCrossRefGoogle Scholar
  99. 99.
    Bassiri R, Borisenko K B, Cockayne D J, et al. Probing the atomic structure of amorphous Ta2O5 coatings. Appl Phys Lett, 2011, 98: 031904ADSCrossRefGoogle Scholar
  100. 100.
    Wu Y N, Li L, Cheng H P. A first-principle study of Ta2O5. 2011, LIGO-G1100362Google Scholar
  101. 101.
    Nawrodt R, Zimmer A, Nietzsche S, et al. A new apparatus for mechanical Q-factor measurements between 5 and 300 K. Cryogenics, 2006, 46: 718–723ADSCrossRefGoogle Scholar
  102. 102.
    Cesarini E, Lorenzini M, Cagnoli G, et al. A gentle nodal suspension for measurements of the acoustic attenuation in materials. Rev Sci Instrum, 2009, 80: 053904ADSCrossRefGoogle Scholar
  103. 103.
    Nicolas D S. A technique for continuous measurement of the quality factor of mechanical oscillators. Rev Sci Instrum, 2015, 86: 053907CrossRefGoogle Scholar
  104. 104.
    Vander-Hyde D, Amra C, Lequime M, et al. Optical scatter of quantum noise filter cavity optics. Class Quantum Grav, 2015, 32: 135019ADSCrossRefGoogle Scholar
  105. 105.
    Alexandrovski A, Fejer M, Markosyan A, et al. Photothermal common path interferometry: New development. Proc SPIE, 7193: 71930D-1Google Scholar
  106. 106.
    Schiller S, Lammerzahl C, Muller H, et al. Experimental limits for low-frequency space-time fluctuations from ultrastable optical resonators. Phys Rev D, 2004, 69(2): 027504ADSCrossRefGoogle Scholar
  107. 107.
    Ludlow A D, Boyd M M, Ye J, et al. Optical atomic clocks. Rev Mod Phys, 2015, 87(2): 637–701ADSCrossRefGoogle Scholar
  108. 108.
    Abbott B P, Abbott R, Adhikari R, et al. LIGO: The laser interferometer gravitational-wave observatory. Rep Prog Phys, 2009, 72(7): 076901ADSCrossRefGoogle Scholar
  109. 109.
    Saulson P R. Thermal noise in mechanical experiments. Phys Rev D, 1990, 42(8): 2437–2445ADSCrossRefGoogle Scholar
  110. 110.
    Young B C, Cruz F C, Itano W M, et al. Visible lasers with subhertz linewidths. Phys Rev Lett, 1999, 82(19): 3799–3802ADSCrossRefGoogle Scholar
  111. 111.
    Ludlow A D, Huang X, Notcutt M, et al. Compact, thermal-noiselimited optical cavity for diode laser stabilization at 1 × 10(-15). Opt Lett, 2007, 32(6): 641–643ADSCrossRefGoogle Scholar
  112. 112.
    Millo J, Magalhaes D V, Mandache C, et al. Ultrastable lasers based on vibration insensitive cavities. Phys Rev A, 2009, 79(5): 053829ADSCrossRefGoogle Scholar
  113. 113.
    Jiang Y Y, Ludlow A D, Lemke N D, et al. Making optical atomic clocks more stable with 10–16-level laser stabilization. Nat Photonics, 2011, 5(3): 158–161ADSCrossRefGoogle Scholar
  114. 114.
    Kessler T, Hagemann C, Grebing C, et al. A sub-40-mHz-linewidth laser based on a silicon single-crystal optical cavity. Nat Photonics, 2012, 6(10): 687–692Google Scholar
  115. 115.
    Nicholson T L, Martin M J, Williams J R, et al. Comparison of two independent Sr optical clocks with 1 × 10-17 stability at 103 s. Phys Rev Lett, 2012, 109(23): 230801ADSCrossRefGoogle Scholar
  116. 116.
    Martin M J, Bishof M, Swallows M D, et al. A quantum many-body spin system in an optical lattice clock. Science, 2013, 341(6146): 632–636Google Scholar
  117. 117.
    Aasi J, Abbott B P, Abbott R, et al. (LIGO Scientific Collaboration). Advanced LIGO. Class Quantum Grav, 2015, 32(7): 074001ADSCrossRefGoogle Scholar
  118. 118.
    Numata K, Kemery A, Camp J. Thermal-noise limit in the frequency stabilization of lasers with rigid cavities. Phys Rev Lett, 2004, 93(25): 250602ADSCrossRefGoogle Scholar
  119. 119.
    Bishof M, Zhang X, Martin MJ, et al. Optical spectrum analyzer with quantum-limited noise floor. Phys Rev Lett, 2013, 111(9): 093604ADSCrossRefGoogle Scholar
  120. 120.
    Landau L D, Lifshitz E M. Statistical Physics. New York: Elsevier, 1996Google Scholar
  121. 121.
    Aspelmeyer M, Kippenberg T J, Marquardt F. Cavity optomechanics. Rev Mod Phys, 2014, 86(4): 1391–1452ADSCrossRefGoogle Scholar
  122. 122.
    Iga K. Surface-emitting laser-its birth and generation of new optoelectronics field. IEEE J Sel Top Quantum Electron, 2000, 6(6): 1201–1215CrossRefGoogle Scholar
  123. 123.
    Madsen M, Takei K, Kapadia R, et al. Nanoscale semiconductor “X” on substrate “Y” processes, devices, and applications. Adv Mater, 2011, 23(28): 3115–3127CrossRefGoogle Scholar
  124. 124.
    Cole G D, ZhangW, Martin MJ, et al. Tenfold reduction of Brownian noise in high-reflectivity optical coatings. Nat Photonics, 2013, 7(8): 644–650ADSCrossRefGoogle Scholar
  125. 125.
    Cole G D. Cavity optomechanics with low-noise crystalline mirrors. Proc SPIE 8458, Optics & Photonics, Optical Trapping and Optical Micromanipulation IX. San Diego: Proceedings of SPIE, 2012. 845807CrossRefGoogle Scholar
  126. 126.
    Cole G D, Follman D, Heu P, et al. Crystalline coatings with optical losses below 5 ppm. 8th Symposium on Frequency Standards and Metrology, Potsdam, Germany, 2015Google Scholar
  127. 127.
    Rempe G, Thompson R J, Kimble H J, et al. Measurement of ultralow losses in an optical interferometer. Opt Lett, 1992, 17(5): 363–365ADSCrossRefGoogle Scholar
  128. 128.
    Crooks D R M, Sneddon P, Cagnoli G, et al. Excess mechanical loss associated with dielectric mirror coatingson test masses in interferometric gravitational wave detectors. Class Quantum Grav, 2002, 19(5): 883–896ADSzbMATHCrossRefGoogle Scholar
  129. 129.
    Amairi S, Legero T, Kessler T, et al. Reducing the effect of thermal noise in optical cavities. Appl Phys B, 2013, 113(2): 233–242ADSCrossRefGoogle Scholar
  130. 130.
    Bondarescu M, Kogan O, Chen Y, et al. Optimal light beams and mirror shapes for future LIGO interferometers. Phys Rev D, 2008, 78(8): 082002ADSCrossRefGoogle Scholar
  131. 131.
    Kimble H J, Lev B L, Ye J, et al. Optical interferometers with reduced sensitivity to thermal noise. Phys Rev Lett, 2008, 101(26): 260602ADSCrossRefGoogle Scholar
  132. 132.
    Friedrich D, Barr B W, Brueckner F, et al. Waveguide grating mirror in a fully suspended 10 meter Fabry-Perot cavity. Opt Express, 2011, 19(16): 14955–14963Google Scholar
  133. 133.
    Kemiktarak U, Metcalfe M, Durand M, et al. Mechanically compliant grating reflectors for optomechanics. Appl Phys Lett, 2012, 100(6): 061124ADSCrossRefGoogle Scholar
  134. 134.
    Alnis J, Schliesser A, Wang C Y, et al. Thermal-noise-limited crystalline whispering-gallery-mode resonator for laser stabilization. Phys Rev A, 2011, 84(1): 011804ADSCrossRefGoogle Scholar
  135. 135.
    Cole G D, Groeblacher S, Gugler K, et al. Monocrystalline AlxGa1-xAs heterostructures for high-reflectivity high-Q micromechanical resonators in the megahertz regime. Appl Phys Lett, 2008, 92(26): 261108ADSCrossRefGoogle Scholar
  136. 136.
    Cole G D, Wilson-Rae I, Vanner M R, et al. Megahertz monocrystalline optomechanical resonators with minimal dissipation. In: 23rd IEEE International Conference onMicro ElectroMechanical Systems (MEMS). Hong Kong: Proceedings: IEEE Micro electro mechanical systems, 2010. 847–850Google Scholar
  137. 137.
    Vanderziel J P, Ilegems M. Multilayer GaAs-Al0.3Ga0.7As dielectric quarter wave stacks grown by molecular beam epitaxy. Appl Opt, 1975, 14(11): 2627–2630ADSCrossRefGoogle Scholar
  138. 138.
    Brodoceanu D, Cole G D, Kiesel N, et al. Femtosecond laser fabrication of high reflectivity micromirrors. Appl Phys Lett, 2010, 97(4): 041104ADSCrossRefGoogle Scholar
  139. 139.
    Cole G D, Bai Y, Aspelmeyer M, et al. Free-standing AlxGa1-xAs heterostructures by gas-phase etching of germanium. Appl Phys Lett, 2010, 96(26): 261102ADSCrossRefGoogle Scholar
  140. 140.
    Cole G D, Wilson-Rae I, Werbach K, et al. Phonon-tunnelling dissipation in mechanical resonators. Nat Commun, 2011, 2: 231ADSCrossRefGoogle Scholar
  141. 141.
    Black A, Hawkins A R, Margalit N M. Wafer fusion: Materials issues and device results. IEEE J Sel Top Quantum Electron, 1997, 3(3): 943–951CrossRefGoogle Scholar
  142. 142.
    Konagai M, Sugimoto M, Takahashi K, et al. High efficiency GaAs thin film solar cells by peeled film technology. J Crystal Growth, 1978, 45(1): 277–280Google Scholar
  143. 143.
    Yablonovitch E, Hwang D M, Gmitter T J, et al. Vanderwaals bonding of GaAs epitaxial liftoff films onto arbitrary substrates. Appl Phys Lett, 1990, 56(24): 2419–2421ADSCrossRefGoogle Scholar
  144. 144.
    Evans M, Ballmer S, Fejer M, et al. Thermo-optic noise in coated mirrors for high-precision optical measurements. Phys Rev D, 2008, 78(10): 102003ADSCrossRefGoogle Scholar
  145. 145.
    Chalermsongsak T, Hall E D, Cole G D. Coherent cancellation of photothermal noise in GaAs/Al0.92Ga0.08As bragg mirrors. arXiv:1506.07088Google Scholar
  146. 146.
    Steinlechner J, Martin I W, Bell A, et al. Mapping the optical absorption of a substrate-transferred crystalline AlGaAs coating at 1.5 mu m. Class Quantum Grav, 2015, 32(10): 105008ADSCrossRefGoogle Scholar
  147. 147.
    Schreiber K U, Thirkettle R J, Hurst R B, et al. Sensing earth’s rotation with a helium-neon ring laser operating at 1.15 mu m. Opt Lett, 2015, 40(8): 1705–1708ADSCrossRefGoogle Scholar
  148. 148.
    Yamamoto K, Miyoki S, Uchiyama T, et al. Measurement of the mechanical loss of a cooled reflective coating for gravitational wave detection. Phys Rev D, 2006, 74(2): 022002ADSCrossRefGoogle Scholar
  149. 149.
    Ting S M, Fitzgerald E A. Metal-organic chemical vapor deposition of single domain GaAs on Ge/GexSi1-x/Si and Ge substrates. J Appl Phys, 2000, 87(5): 2618–2628ADSCrossRefGoogle Scholar
  150. 150.
    Aasi J, Abbott B P, Abbott, R, et al. Advanced LIGO. Class Quantum Grav, 2015, 32(7): 074001ADSCrossRefGoogle Scholar
  151. 151.
    Acernese F, Agathos M, Agatsuma K, et al. Advanced Virgo: A second-generation interferometric gravitational wave detector. Class Quantum Grav, 2015, 32(2): 024001ADSCrossRefGoogle Scholar
  152. 152.
    Somiya K. Detector configuration of KAGRA—The Japanese cryogenic gravitational-wave detector. Class Quantum Grav, 2012, 29(12): 124007ADSCrossRefGoogle Scholar
  153. 153.
    Degallaix J, Zhao C, Ju L, et al. Simulation of bulk-absorption thermal lensing in transmissive optics of gravitational waves detectors. Appl Phys B, 2003, 77(4): 409–414ADSCrossRefGoogle Scholar
  154. 154.
    Lawrence R, Ottaway D, Zucker M, et al. Active correction of thermal lensing through external radiative thermal actuation. Opt lett, 2004, 29(22): 2635–2637ADSCrossRefGoogle Scholar
  155. 155.
    Tomaru T, Suzuki T, Miyoki S, et al. Thermal lensing in cryogenic sapphire substrates. Class Quantum Grav, 2002, 19(7): 2045ADSCrossRefGoogle Scholar
  156. 156.
    Komma J, Schwarz C, Hofmann G, et al. Thermo-optic coefficient of silicon at 1550 nm and cryogenic temperatures. Appl Phys Lett, 2012, 101(4): 041905ADSCrossRefGoogle Scholar
  157. 157.
    Tomaru T, Suzuki T, Uchiyama T, et al. Maximum heat transfer along a sapphire suspension fiber for a cryogenic interferometric gravitational wave detector. Phys Lett A, 2002, 301(3): 215–219ADSCrossRefGoogle Scholar
  158. 158.
    Barriga P, Bhawal B, Ju L, et al. Numerical calculations of diffraction losses in advanced interferometric gravitational wave detectors. J Opt Soc Am A, 2007, 24(6): 1731–1741Google Scholar
  159. 159.
    Buonanno A, Chen Y. Quantum noise in second generation, signalrecycled laser interferometric gravitational-wave detectors. Phys Rev D, 2001, 64(4): 042006ADSCrossRefGoogle Scholar
  160. 160.
    Lorenzini M. (Virgo Collaboration). The monolithic suspension for the virgo interferometer. Class Quantum Grav, 2010, 27(8): 084021CrossRefGoogle Scholar
  161. 161.
    Fritschel P. Second generation instruments for the laser interferometer gravitational wave observatory (LIGO). In: Astronomical Telescopes and Instrumentation, International Society for Optics and Photonics, 2003. 282–291Google Scholar
  162. 162.
    Benabid F, Notcutt M, Loriette, V, et al. X-ray induced absorption of high-purity sapphire and investigation of the origin of the residual absorption at 1064 nm. J Phys D-Appl Phys, 2000, 33(6): 589ADSCrossRefGoogle Scholar
  163. 163.
    Tomaru T, Uchiyama T, Tatsumi D, et al. Cryogenic measurement of the optical absorption coefficient in sapphire crystals at 1.064 mu m for the large-scale cryogenic gravitational wave telescope. Phys Lett A, 2001, 283(1): 80–84ADSCrossRefGoogle Scholar
  164. 164.
    Hirose E, Sekiguchi T, Kumar R, et al. Update on the development of cryogenic sapphire mirrors and their seismic attenuation system for KAGRA. Class Quantum Grav, 2014, 31(22): 224004–224018ADSCrossRefGoogle Scholar
  165. 165.
    Punturo M, Abernathy M, Acernese F, et al. The Einstein Telescope: A third-generation gravitational wave observatory. Class Quantum Grav, 2010, 27(19): 194002ADSCrossRefGoogle Scholar
  166. 166.
    Degallaix J, Flaminio R, Forest D, et al. Bulk optical absorption of high resistivity silicon at 1550 nm. Opt Lett, 2013, 38(12): 2047–2049ADSCrossRefGoogle Scholar
  167. 167.
    ET Science Team. Einstein telescope design study, 2009, http://www. Scholar
  168. 168.
    Smith N, Brooks A, Barsotti L, et al. A cryogenic silicon LIGO upgrade (LIGO-T1400226-v5), 2014, Scholar
  169. 169.
    Freise A, Hild S, Somiya K, et al. Optical detector topology for thirdgeneration gravitational wave observatories. Gen Relat Grav, 2011, 43(2): 537–567ADSCrossRefGoogle Scholar
  170. 170.
    Kwee P, Bogan C, Danzmann K, et al. Stabilized high-power laser system for the gravitational wave detector advanced LIGO. Opt Express, 2012, 20(10): 10617–10634ADSCrossRefGoogle Scholar
  171. 171.
    Meier T, Willke B, Danzmann K. Continuous-wave single-frequency 532 nm laser source emitting 130 W into the fundamental transversal mode. Opt Lett, 2010, 35(22): 3742–3744ADSCrossRefGoogle Scholar
  172. 172.
    Carbone L, Bogan C, Fulda P, et al. Generation of high-purity higherorder Laguerre-Gauss beams at high laser power. Phys Rev Lett, 2013, 110(25): 251101ADSCrossRefGoogle Scholar
  173. 173.
    Theeg T, Sayinc H, Neumann J, et al. All-fiber counter-propagation pumped single frequency amplifier stage with 300-W output power. IEEE Photonics Technol Lett, 2012, 24(20): 1864–1867ADSCrossRefGoogle Scholar
  174. 174.
    Kane T J, Byer R L. Monolithic, unidirectional single-mode Nd:YAG ring laser. Opt Lett, 1985, 10(2): 65–67ADSCrossRefGoogle Scholar
  175. 175.
    Theeg T, Sayinc H, Neumann J, et al. Pump and signal combiner for bi-directional pumping of all-fiber lasers and amplifiers. Opt Express, 2012, 20(27): 28125–28141ADSCrossRefGoogle Scholar
  176. 176.
    Steinke M, Croteau A, Zheng H, et al. Co-seeded Er3+:Yb3+ single frequency fiber amplifier with 60 W output power and over 90% TEM00 content. Opt Express, 2014, 22(14): 16722–16730ADSCrossRefGoogle Scholar
  177. 177.
    Kuhn V, Kracht D, Neumann J, et al. 67 W of output power from an Yb-free Er-doped fiber amplifier cladding pumped at 976 nm. IEEE Photonics Technol Lett, 2011, 23(7): 432–434Google Scholar
  178. 178.
    Kuhn V, Unger S, Jetschke S, et al. Experimental comparison of fundamental mode content in Er:Yb-codoped LMA fibers with multifilament-and pedestal-design cores. J Lightwave Technol, 2010, 28(22): 3212–3219Google Scholar
  179. 179.
    Kuhn V, Kracht D, Neumann J, et al. Er-doped photonic crystal fiber amplifier with 70 W of output power. Opt Lett, 2011, 36(16): 3030–3032ADSCrossRefGoogle Scholar
  180. 180.
    Tunnermann H, Pold J H, Neumann J, et al. Beam quality and noise properties of coherently combined ytterbium doped single frequency fiber amplifiers. Opt Express, 2011, 19(20): 19600–19606ADSCrossRefGoogle Scholar
  181. 181.
    Innolight. Mephisto Product Line, (now Coherent, http://www., 2009Google Scholar
  182. 182.
    Frede M, Schulz B, Wilhelm R, et al. Fundamental mode, singlefrequency laser amplifier for gravitational wave detectors. Opt Express, 2007, 15(2): 459–465ADSCrossRefGoogle Scholar
  183. 183.
    Winkelmann L, Puncken O, Kluzik R, et al. Injection-locked singlefrequency laser with an output power of 220 W. Appl Phys B-Lasers Opt, 2011, 102(3): 529–538ADSCrossRefGoogle Scholar
  184. 184.
    Drever R W P, Hall J L, Kowalski F V, et al. Laser phase and frequency stabilization using an optical resonator. Appl Phys B-Lasers Opt, 1983, 31(2): 97–105ADSCrossRefGoogle Scholar
  185. 185.
    Black E D. An introduction to Pound-Drever-Hall laser frequency stabilization. Am J Phys, 2001, 69: 79–87ADSCrossRefGoogle Scholar
  186. 186.
    Kwee P, Willke B, Danzmann K. Shot-noise-limited laser power stabilization with a high-power photodiode array. Opt Lett, 2009, 34(19): 2912–2914ADSCrossRefGoogle Scholar
  187. 187.
    Kwee P, Willke B, Danzmann K. Optical ac coupling to overcome limitations in the detection of optical power fluctuations. Opt Lett, 2008, 33(13): 1509–1511ADSCrossRefGoogle Scholar
  188. 188.
    Kwee P, Willke B, Danzmann K. Laser power stabilization using optical ac coupling and its quantum and technical limits. Appl Opt, 2009, 48(28): 5423–5431ADSCrossRefGoogle Scholar
  189. 189.
    Kwee P, Willke B, Danzmann K. Laser power noise detection at the quantum-noise limit of 32 A photocurrent. Opt Lett, 2011, 36(18): 3563–3565ADSCrossRefGoogle Scholar

Copyright information

© Science China Press and Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Valery P. Mitrofanov
    • 1
  • Shiuh Chao
    • 2
    Email author
  • Huang-Wei Pan
    • 2
  • Ling-Chi Kuo
    • 2
  • Garrett Cole
    • 3
    • 4
    • 5
  • Jerome Degallaix
    • 6
  • Benno Willke
    • 7
  1. 1.Faculty of PhysicsMoscow State UniversityMoscowRussia
  2. 2.Institute of Photonics TechnologiesNational Tsing Hua UniversityBeijingChina
  3. 3.Crystalline Mirror Solutions LLCSanta BarbaraUSA
  4. 4.Crystalline Mirror Solutions GmbHViennaAustria
  5. 5.Vienna Center for Quantum Science and Technology (VCQ), Faculty of PhysicsUniversity of ViennaViennaAustria
  6. 6.Laboratoire des Matériaux AvancésVilleurbanneFrance
  7. 7.Max Planck Institute for Gravitational PhysicsAlbert Einstein Institute and Leibniz Universität HannoverBerlinGermany

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