Applied Physics B

, 124:140 | Cite as

Simulation of force-insensitive optical cavities in cubic spacers

  • Eugen Wiens
  • Stephan SchillerEmail author


We analyze the properties of optical cavities contained in spacers with approximate octahedral symmetry and made of different materials, following the design of Webster and Gill (Opt Lett 36:3572, 2011). We show that, for isotropic materials with Young’s modulus less than 200 GPa, the Poisson’s ratio \(\nu\) must lie in a “magic” range \(0.13<\nu <0.23\) to null the influence of the forces supporting the spacer. This restriction can be overcome with the use of anisotropic materials such as silicon. A detailed study aiming at identification of all suitable crystal orientations of silicon with respect to the resonator body is performed, and the relation to the Poisson’s ratio and the Young’s modulus along these orientations is discussed. We also perform an analysis of the sensitivity of the cavity performance to errors in spacer manufacturing. We find that the orientation of the [110] or [100] crystallographic directions oriented along one of the three optical axes of the resonator provides low sensitivities to imprecise manufacturing and interesting options for fundamental physics experiments.



We thank T. Legero (PTB) for providing us with the design of the biconical Si resonator allowing us to test our simulations, A. Nevsky for stimulating discussions, and D. Sutyrin for his help with the simulations. This work was performed in the framework of project SCHI 431/21-1 of the Deutsche Forschungsgemeinschaft.


  1. 1.
    N. Huntemann, C. Sanner, B. Lipphardt, C. Tamm, E. Peik, Phys. Rev. Lett. 116, 063001 (2016)ADSCrossRefGoogle Scholar
  2. 2.
    A.D. Ludlow, M.M. Boyd, J. Ye, E. Peik, P.O. Schmidt, Rev. Mod. Phys. 87, 637 (2015)ADSCrossRefGoogle Scholar
  3. 3.
    T. Nicholson, S. Campbell, R. Hutson, G. Marti, B. Bloom, R. McNally, W. Zhang, M. Barrett, M. Safronova, W. Strouse, G.F. Tew, J. Ye, Nat. Commun. 6, 6896 (2015)ADSCrossRefGoogle Scholar
  4. 4.
    P. Antonini, M. Okhapkin, E. Göklü, S. Schiller, Phys. Rev. A 71, 050101(R) (2005)ADSCrossRefGoogle Scholar
  5. 5.
    C. Eisele, A.Y. Nevsky, S. Schiller, Phys. Rev. Lett. 103, 090401 (2009)ADSCrossRefGoogle Scholar
  6. 6.
    E. Wiens, A.Y. Nevsky, S. Schiller, Phys. Rev. Lett. 117, 271102 (2016)CrossRefGoogle Scholar
  7. 7.
    S. Webster, P. Gill, Opt. Lett. 36, 3572 (2011)ADSCrossRefGoogle Scholar
  8. 8.
    K. Numata, A. Kemery, J. Camp, Phys. Rev. Lett. 93, 250602 (2004)ADSCrossRefGoogle Scholar
  9. 9.
    M. Notcutt, L.S. Ma, A.D. Ludlow, S.M. Foreman, J. Ye, J.L. Hall, Phys. Rev. A 73, 031804 (2006)ADSCrossRefGoogle Scholar
  10. 10.
    J. Davila-Rodriguez, F.N. Baynes, A.D. Ludlow, T.M. Fortier, H. Leopardi, S.A. Diddams, F. Quinlan, Opt. Lett. 42, 1277 (2017)ADSCrossRefGoogle Scholar
  11. 11.
    S. Seel, R. Storz, G. Ruoso, J. Mlynek, S. Schiller, Phys. Rev. Lett. 78, 4741 (1997)ADSCrossRefGoogle Scholar
  12. 12.
    D.G. Matei, T. Legero, S. Häfner, C. Grebing, R. Weyrich, W. Zhang, L. Sonderhouse, J.M. Robinson, J. Ye, F. Riehle, U. Sterr, Phys. Rev. Lett. 118, 263202 (2017)ADSCrossRefGoogle Scholar
  13. 13.
    W. Zhang, J.M. Robinson, L. Sonderhouse, E. Oelker, C. Benko, J.L. Hall, T. Legero, D.G. Matei, F. Riehle, U. Sterr, J. Ye, Phys. Rev. Lett. 119, 243601 (2017)ADSCrossRefGoogle Scholar
  14. 14.
    E. Wiens, Q. Chen, I. Ernsting, H. Luckmann, A.Y. Nevsky, U. Rosowski, S. Schiller, Opt. Lett. 39, 3242 (2014)ADSCrossRefGoogle Scholar
  15. 15.
    E. Wiens, Q. Chen, I. Ernsting, H. Luckmann, A.Y. Nevsky, U. Rosowski, S. Schiller, Opt. Lett. 40, 68 (2015)ADSCrossRefGoogle Scholar
  16. 16.
    C. Hagemann, C. Grebing, C. Lisdat, S. Falke, T. Legero, U. Sterr, F. Riehle, M.J. Martin, J. Ye, Opt. Lett. 39, 5102 (2014)ADSCrossRefGoogle Scholar
  17. 17.
    P.R. Cromwell, Polyhedra (Cambridge University Press, Cambridge, 2008)zbMATHGoogle Scholar
  18. 18.
    Product sheet from Rohm and Haas Co. Accessed 12 June 2018
  19. 19.
    Product sheet from Corning, Inc. Accessed 12 June 2018
  20. 20.
    N118C Product sheet from Krosaki Harima. Accessed 12 June 2018
  21. 21.
    Product sheet from SCHOTT North America, Inc. Accessed 12 June 2018
  22. 22.
    M. Bass, Handbook of Optics, 2nd edn. (McGraw-Hill, New York, 1995)Google Scholar
  23. 23.
    J.F. Nye, Physical Properties of Crystals: Their Representation by Tensors and Matrices (Clarendon Press, Oxford, 1964)zbMATHGoogle Scholar
  24. 24.
    J.J. Wortman, R.A. Evans, J. Appl. Phys. 36, 153 (1965)ADSCrossRefGoogle Scholar
  25. 25.
    M.A. Hopcroft, W.D. Nix, T.W. Kenny, J. Microelectromech. Syst. 19, 229 (2010)CrossRefGoogle Scholar
  26. 26.
    L. Zhang, R. Barrett, P. Cloetens, C. Detlefs, M. Sanchez del Rio, J. Synchrotron Radiat. 21, 507 (2014)CrossRefGoogle Scholar
  27. 27.
    R.H. Battin, An introduction to the mathematics and methods of astrodynamics, rev. AIAA Education Series (American Institute of Aeronautics and Astronautics Inc, Reston, 1999)zbMATHGoogle Scholar
  28. 28.
    B. Parker, G. Marra, L.A.M. Johnson, H.S. Margolis, S.A. Webster, L. Wright, S.N. Lea, P. Gill, P. Bayvel, Appl. Opt. 53, 8157 (2014)ADSCrossRefGoogle Scholar
  29. 29.
    J. Millo, C. Lacroute, A. Didier, E. Rubiola, Y. Kersal, J. Paris, in Proc. of the 2014 European Frequency and Time Forum, pp. 531–534 (IEEE, 2014).
  30. 30.
    T. Kessler, C. Hagemann, C. Grebing, T. Legero, U. Sterr, F. Riehle, M.J. Martin, L. Chen, J. Ye, Nat. Photon. 6, 687 (2012)ADSCrossRefGoogle Scholar
  31. 31.
    C.J. Glassbrenner, G.A. Slack, Phys. Rev. 134, A1058 (1964)ADSCrossRefGoogle Scholar
  32. 32.
    K.G. Lyon, G.L. Salinger, C.A. Swenson, G.K. White, J. Appl. Phys. 48, 865 (1977)ADSCrossRefGoogle Scholar
  33. 33.
    J.P. Richard, J.J. Hamilton, Rev. Sci. Instrum. 62, 2375 (1991)ADSCrossRefGoogle Scholar
  34. 34.
    W.P. Mason, Physical Acoustics and the Properties of Solids (Van Nostrand, Princeton, 1958)Google Scholar
  35. 35.
    D.G. Matei, T. Legero, C. Grebing, S. Häfner, C. Lisdat, R. Weyrich, W. Zhang, L. Sonderhouse, J.M. Robinson, F. Riehle, J. Phys. Conf. Ser. 723, 012031 (2016)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institut für ExperimentalphysikHeinrich-Heine-Universität DüsseldorfDüsseldorfGermany

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