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Journal of the Optical Society of America B

Journal of the Optical Society of America B

| OPTICAL PHYSICS

  • Editor: Henry van Driel
  • Vol. 29, Iss. 1 — Jan. 1, 2012
  • pp: 178–184

Thermal noise in optical cavities revisited

Thomas Kessler, Thomas Legero, and Uwe Sterr  »View Author Affiliations


JOSA B, Vol. 29, Issue 1, pp. 178-184 (2012)
http://dx.doi.org/10.1364/JOSAB.29.000178


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Abstract

Thermal noise of optical reference cavities sets a fundamental limit to the frequency instability of ultrastable lasers. Using Levin’s formulation of the fluctuation-dissipation theorem, we correct the analytical estimate for the spacer contribution given by Numata et al. [ Phys. Rev. Lett. 93, 250602 (2004)]. For detailed analysis, finite- element calculations of the thermal noise focusing on the spacer geometry, support structure, and the usage of different materials have been carried out. We find that the increased dissipation close to the contact area between spacer and mirrors can contribute significantly to the thermal noise. From an estimate of the support structure contribution, we give guidelines for a low-noise mounting of the cavity. For mixed-material cavities, we show that the thermal expansion can be compensated without deteriorating the thermal noise.

© 2011 Optical Society of America

OCIS Codes
(120.2230) Instrumentation, measurement, and metrology : Fabry-Perot
(120.3940) Instrumentation, measurement, and metrology : Metrology
(160.2750) Materials : Glass and other amorphous materials
(230.5750) Optical devices : Resonators
(140.3425) Lasers and laser optics : Laser stabilization

ToC Category:
Instrumentation, Measurement, and Metrology

History
Original Manuscript: June 29, 2011
Manuscript Accepted: October 18, 2011
Published: December 16, 2011

Citation
Thomas Kessler, Thomas Legero, and Uwe Sterr, "Thermal noise in optical cavities revisited," J. Opt. Soc. Am. B 29, 178-184 (2012)
http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-29-1-178


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References

  1. T. Rosenband, D. B. Hume, P. O. Schmidt, C. W. Chou, A. Brusch, L. Lorini, W. H. Oskay, R. E. Drullinger, T. M. Fortier, J. E. Stalnaker, S. A. Diddams, W. C. Swann, N. R. Newbury, W. M. Itano, D. J. Wineland, and J. C. Bergquist, “Frequency ratio of Al+ and Hg+ single-ion optical clocks; metrology at the 17th decimal place,” Science 319, 1808–1812 (2008). [CrossRef] [PubMed]
  2. A. D. Ludlow, T. Zelevinsky, G. K. Campbell, S. Blatt, M. M. Boyd, M. H. G. de Miranda, M. J. Martin, J. W. Thomsen, S. M. Foreman, J. Ye, T. M. Fortier, J. E. Stalnaker, S. A. Diddams, Y. Le Coq, Z. W. Barber, N. Poli, N. D. Lemke, K. M. Beck, and C. W. Oates, “Sr lattice clock at 1×10−16 fractional uncertainty by remote optical evaluation with a Ca clock,” Science 319, 1805–1808 (2008). [CrossRef] [PubMed]
  3. A. Bartels, S. A. Diddams, C. W. Oates, G. Wilpers, J. C. Bergquist, W. H. Oskay, and L. Hollberg, “Femtosecond-laser-based synthesis of ultrastable microwave signals from optical frequency references,” Opt. Lett. 30, 667–669 (2005). [CrossRef] [PubMed]
  4. J. Millo, M. Abgrall, M. Lours, E. English, H. Jiang, J. Guéna, A. Clairon, S. Bize, Y. L. Coq, G. Santarelli, and M. Tobar, “Ultra-low noise microwave generation with fiber-based optical frequency comb and application to atomic fountain clock,” Opt. Lett. 34, 3707–3709 (2009). [CrossRef] [PubMed]
  5. B. Lipphardt, G. Grosche, U. Sterr, C. Tamm, S. Weyers, and H. Schnatz, “The stability of an optical clock laser transferred to the interrogation oscillator for a Cs fountain,” IEEE Trans. Instrum. Meas. 58, 1258–1262 (2009). [CrossRef]
  6. P. A. Williams, W. C. Swann, and N. R. Newbury, “High-stability transfer of an optical frequency over long fiber-optic links,” J. Opt. Soc. Am. B 25, 1284–1293 (2008). [CrossRef]
  7. H. Jiang, F. Kéfélian, S. Crane, O. Lopez, M. Lours, J. Millo, D. Holleville, P. Lemonde, C. Chardonnet, A. Amy-Klein, and G. Santarelli, “Transfer of an optical frequency over an urban fiber link,” J. Opt. Soc. Am. B 25, 2029–2035 (2008). [CrossRef]
  8. O. Terra, G. Grosche, K. Predehl, R. Holzwarth, T. Legero, U. Sterr, B. Lipphardt, and H. Schnatz, “Phase-coherent comparison of two optical frequency standards over 146 km using a telecommunication fiber link,” Appl. Phys. B 97, 541–551 (2009). [CrossRef]
  9. B. C. Young, F. C. Cruz, W. M. Itano, and J. C. Bergquist, “Visible lasers with subhertz linewidths,” Phys. Rev. Lett. 82, 3799–3802(1999). [CrossRef]
  10. H. Stoehr, F. Mensing, J. Helmcke, and U. Sterr, “Diode laser with 1 Hz linewidth,” Opt. Lett. 31, 736–738 (2006). [CrossRef] [PubMed]
  11. M. Notcutt, L.-S. Ma, A. D. Ludlow, S. M. Foreman, J. Ye, and J. L. Hall, “Contribution of thermal noise to frequency stability of rigid optical cavity via Hertz-linewidth lasers,” Phys. Rev. A 73, 031804 (2006). [CrossRef]
  12. A. D. Ludlow, X. Huang, M. Notcutt, T. Zanon-Willette, S. M. Foreman, M. M. Boyd, S. Blatt, and J. Ye, “Compact, thermal-noise-limited optical cavity for diode laser stabilization at 1×10−15,” Opt. Lett. 32, 641–643 (2007). [CrossRef] [PubMed]
  13. S. A. Webster, M. Oxborrow, S. Pugla, J. Millo, and P. Gill, “Thermal-noise-limited optical cavity,” Phys. Rev. A 77, 033847(2008). [CrossRef]
  14. P. Dubé, A. Madej, J. Bernard, L. Marmet, and A. Shiner, “A narrow linewidth and frequency-stable probe laser source for the Sr+88 single ion optical frequency standard,” Appl. Phys. B 95, 43–54 (2009). [CrossRef]
  15. J. Lodewyck, P. G. Westergaard, A. Lecallier, L. Lorini, and P. Lemonde, “Frequency stability of optical lattice clocks,” New J. Phys. 12, 065026 (2010). [CrossRef]
  16. J. Millo, D. V. Magalhães, C. Mandache, Y. Le Coq, E. M. L. English, P. G. Westergaard, J. Lodewyck, S. Bize, P. Lemonde, and G. Santarelli, “Ultrastable lasers based on vibration insensitive cavities,” Phys. Rev. A 79, 053829 (2009). [CrossRef]
  17. Y. Levin, “Internal thermal noise in the LIGO test masses: a direct approach,” Phys. Rev. D 57, 659–663 (1998). [CrossRef]
  18. K. Numata, A. Kemery, and J. Camp, “Thermal-noise limit in the frequency stabilization of lasers with rigid cavities,” Phys. Rev. Lett. 93, 250602 (2004). [CrossRef]
  19. T. Legero, T. Kessler, and U. Sterr, “Tuning the thermal expansion properties of optical reference cavities with fused silica mirrors,” J. Opt. Soc. Am. B 27, 914–919 (2010). [CrossRef]
  20. T. Kessler, “Development of an ultrastable monocrystalline silicon resonator for optical clocks,” presented at the European Frequency and Time Forum 2010, Noordwijk, The Netherlands, 13–16 April 2010.
  21. M. Notcutt, C. T. Taylor, A. G. Mann, and D. G. Blair, “Temperature compensation for cryogenic cavity stabilized lasers,” J. Phys. D 28, 1807–1810 (1995). [CrossRef]
  22. F. Bondu, P. Hello, and J.-Y. Vinet, “Thermal noise in mirrors of interferometric gravitational wave antennas,” Phys. Lett. A 246, 227–236 (1998). [CrossRef]
  23. V. B. Braginsky, M. L. Gorodetsky, and S. P. Vyatchanin, “Thermodynamical fluctuations and photo-thermal shot noise in gravitational wave antennae,” Phys. Lett. A 264, 1–10(1999). [CrossRef]
  24. Y. T. Liu and K. S. Thorne, “Thermoelastic noise and homogeneous thermal noise in finite sized gravitational-wave test masses,” Phys. Rev. D 62, 122002 (2000). [CrossRef]
  25. V. B. Braginsky and S. P. Vyatchanin, “Thermodynamical fluctuations in optical mirror coatings,” Phys. Lett. A 312, 244–255 (2003). [CrossRef]
  26. M. M. Fejer, S. Rowan, G. Cagnoli, D. R. M. Crooks, A. Gretarsson, G. M. Harry, J. Hough, S. D. Penn, P. H. Sneddon, and S. P. Vyatchanin, “Thermoelastic dissipation in inhomogeneous media: loss measurements and displacement noise in coated test masses for interferometric gravitational wave detectors,” Phys. Rev. D 70, 082003 (2004). [CrossRef]
  27. M. Evans, S. Ballmer, M. Fejer, P. Fritschel, G. Harry, and G. Ogin, “Thermo-optic noise in coated mirrors for high-precision optical measurements,” Phys. Rev. D 78, 102003(2008). [CrossRef]
  28. Y. Levin, “Fluctuation-dissipation theorem for thermo-refractive noise,” Phys. Lett. A 372, 1941–1944 (2008). [CrossRef]
  29. M. L. Gorodetsky, “Thermal noises and noise compensation in high-reflection multilayer coating,” Phys. Lett. A 372, 6813–6822 (2008). [CrossRef]
  30. H. B. Callen and T. A. Welton, “Irreversibility and generalized noise,” Phys. Rev. 83, 34–40 (1951). [CrossRef]
  31. D. W. Allan, “Statistics of atomic frequency standards,” Proc. IEEE 54, 221–230 (1966). [CrossRef]
  32. G. M. Harry, A. M. Gretarsson, P. R. Saulson, S. E. Kittelberger, S. D. Penn, W. J. Startin, S. Rowan, M. M. Fejer, D. R. M. Crooks, G. Cagnoli, J. Hough, and N. Nakagawa, “Thermal noise in interferometric gravitational wave detectors due to dielectric optical coatings,” Class. Quantum Grav. 19, 897–917 (2002). [CrossRef]
  33. K. Yamamoto, “Study of the thermal noise caused by inhomogeneously distributed loss,” Ph.D. dissertation (University of Tokyo, 2000).
  34. COMSOL AB, “COMSOL Multiphysics Version 4.1” (2010).
  35. S. A. Webster and P. Gill, “Low-thermal-noise optical cavity,” in Proceedings of the 2010 IEEE International Frequency Control Symposium (2010), pp. 470–473. [CrossRef]
  36. T. Nazarova, F. Riehle, and U. Sterr, “Vibration-insensitive reference cavity for an ultra-narrow-linewidth laser,” Appl. Phys. B 83, 531–536 (2006). [CrossRef]
  37. S. A. Webster, M. Oxborrow, and P. Gill, “Vibration insensitive optical cavity,” Phys. Rev. A 75, 011801(R) (2007). [CrossRef]
  38. F. Phelps, “Airy points of a meter bar,” Am. J. Phys. 34, 419–422(1966). [CrossRef]
  39. J. J. Wortman and R. A. Evans, “Young’s modulus, shear modulus, and Poisson’s ratio in silicon and germanium,” J. Appl. Phys. 36, 153–156 (1965). [CrossRef]
  40. D. F. McGuigan, C. C. Lam, R. Q. Gram, A. W. Hoffman, D. H. Douglass, and H. W. Gutche, “Measurements of the mechanical Q of single-crystal silicon at low temperatures,” J. Low Temp. Phys. 30, 621–629 (1978). [CrossRef]
  41. F. Brückner, D. Friedrich, T. Clausnitzer, M. Britzger, O. Burmeister, K. Danzmann, E.-B. Kley, A. Tünnermann, and R. Schnabel, “Realization of a monolithic high-reflectivity cavity mirror from a single silicon crystal,” Phys. Rev. Lett. 104, 163903 (2010). [CrossRef] [PubMed]
  42. G. D. Cole, S. Gröblacher, K. Gugler, S. Gigan, and M. Aspelmeyer, “Monocrystalline AlxGa1−xAs heterostructures for high-reflectivity high-Q micromechanical resonators in the megahertz regime,” Appl. Phys. Lett. 92, 261108 (2008). [CrossRef]
  43. B. Mours, E. Tournefier, and J.-Y. Vinet, “Thermal noise reduction in interferometric gravitational wave antennas: using high order TEM modes,” Class. Quantum Grav. 23, 5777–5784 (2006). [CrossRef]
  44. D. Hoffman, “Dynamic mechanical signatures of Viton A and plastic bonded explosives based on this polymer,” Polym. Eng. Sci. 43, 139–156 (2003). [CrossRef]
  45. J. Giaime, P. Saha, D. Shoemaker, and L. Sievers, “A passive vibration isolation stack for LIGO: design, modeling, and testing,” Rev. Sci. Instrum. 67, 208–214 (1996). [CrossRef]

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