Abstract

We investigate the thermal expansion of low thermal noise Fabry–Pérot cavities made of low thermal expansion (LTE) glass spacers and fused silica (FS) mirrors. The different thermal expansion of mirror and spacer deforms the mirror. This deformation strongly contributes to the cavity’s effective coefficient of thermal expansion (CTE), decreasing the zero crossing temperature by about 20K compared to an all-LTE glass cavity. Finite element simulations and CTE measurements show that LTE rings optically contacted to the back surface of the FS mirrors allow to tune the zero crossing temperature over a range of 30K.

© 2010 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef]

2009 (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]

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]

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: Photophys. Laser Chem. 95, 43–54 (2009).
[CrossRef]

J. Millo, D. V. Magalhães, C. Mandache, Y. L. 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]

2008 (6)

S. A. Webster, M. Oxborrow, S. Pugla, J. Millo, and P. Gill, “Thermal-noise-limited optical cavity,” Phys. Rev. A 77, 033847 (2008).
[CrossRef]

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]

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]

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]

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. L. 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]

R. W. Fox, “Fabry-Perot temperature dependence and surface-mounted optical cavities,” Proc. SPIE 7099, 70991R, (2008).
[CrossRef]

2007 (2)

2006 (3)

T. Nazarova, F. Riehle, and U. Sterr, “Vibration-insensitive reference cavity for an ultra-narrow-linewidth laser,” Appl. Phys. B: Photophys. Laser Chem. 83, 531–536 (2006).
[CrossRef]

H. Stoehr, F. Mensing, J. Helmcke, and U. Sterr, “Diode laser with 1 Hz linewidth,” Opt. Lett. 31, 736–738 (2006).
[CrossRef] [PubMed]

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]

2005 (2)

2004 (1)

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]

1999 (1)

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]

1998 (2)

F. Riehle, “Use of optical frequency standards for measurements of dimensional stability,” Meas. Sci. Technol. 9, 1042–1048 (1998).
[CrossRef]

Y. Levin, “Internal thermal noise in the LIGO test masses: A direct approach,” Phys. Rev. D 57, 659–663 (1998).
[CrossRef]

1997 (1)

1995 (1)

M. Notcutt, C. T. Taylor, A. G. Mann, and D. G. Blair, “Temperature compensation for cryogenic cavity stabilized lasers,” J. Phys. D: Appl. Phys. 28, 1807–1810 (1995).
[CrossRef]

1977 (1)

J. W. Berthold III, S. F. Jacobs, and M. A. Norton, “Dimensional stability of fused silica, invar, and several ultra-low thermal expansion material,” Metrologia 13, 9–16 (1977).
[CrossRef]

1976 (1)

Abgrall, M.

Amy-Klein, A.

Barber, Z. W.

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. L. 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]

Bartels, A.

Beck, K. M.

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. L. 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]

Bergquist, J. C.

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]

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]

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]

Bernard, J.

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: Photophys. Laser Chem. 95, 43–54 (2009).
[CrossRef]

Berthold, J. W.

J. W. Berthold III, S. F. Jacobs, and M. A. Norton, “Dimensional stability of fused silica, invar, and several ultra-low thermal expansion material,” Metrologia 13, 9–16 (1977).
[CrossRef]

J. W. Berthold III and S. F. Jacobs, “Ultraprecise thermal expansion measurements of seven low expansion materials,” Appl. Opt. 15, 2344–2347 (1976).
[CrossRef]

Bize, S.

J. Millo, D. V. Magalhães, C. Mandache, Y. L. 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]

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]

Blair, D. G.

E. K. Wong, M. Notcutt, C. T. Taylor, A. G. Mann, and D. G. Blair, “Temperature-compensated cryogenic Fabry–Perot cavity,” Appl. Opt. 36, 8563–8566 (1997).
[CrossRef]

M. Notcutt, C. T. Taylor, A. G. Mann, and D. G. Blair, “Temperature compensation for cryogenic cavity stabilized lasers,” J. Phys. D: Appl. Phys. 28, 1807–1810 (1995).
[CrossRef]

Blatt, S.

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. L. 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]

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]

Boyd, M. M.

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. L. 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]

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]

Brusch, A.

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]

Camp, J.

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]

Campbell, G. K.

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. L. 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]

Chardonnet, C.

Chou, C. W.

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]

Clairon, A.

Coq, Y. L.

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]

J. Millo, D. V. Magalhães, C. Mandache, Y. L. 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]

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. L. 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]

Crane, S.

Cruz, F. C.

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]

de Miranda, M. H. G.

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. L. 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]

Diddams, S. A.

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. L. 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]

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]

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]

Drullinger, R. E.

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]

Dubé, P.

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: Photophys. Laser Chem. 95, 43–54 (2009).
[CrossRef]

English, E.

English, E. M. L.

J. Millo, D. V. Magalhães, C. Mandache, Y. L. 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]

Foreman, S. M.

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. L. 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]

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]

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]

Fortier, T. M.

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. L. 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]

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]

Fox, R. W.

R. W. Fox, “Fabry-Perot temperature dependence and surface-mounted optical cavities,” Proc. SPIE 7099, 70991R, (2008).
[CrossRef]

Gill, P.

S. A. Webster, M. Oxborrow, S. Pugla, J. Millo, and P. Gill, “Thermal-noise-limited optical cavity,” Phys. Rev. A 77, 033847 (2008).
[CrossRef]

S. A. Webster, M. Oxborrow, and P. Gill, “Vibration insensitive optical cavity,” Phys. Rev. A 75, 011801(R) (2007).
[CrossRef]

Grosche, G.

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]

Guéna, J.

Hall, J. L.

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]

M. Notcutt, L.-S. Ma, J. Ye, and J. L. Hall, “Simple and compact 1-Hz laser system via an improved mounting configuration of a reference cavity,” Opt. Lett. 30, 1815–1817 (2005).
[CrossRef] [PubMed]

Helmcke, J.

Hollberg, L.

Holleville, D.

Huang, X.

Hume, D. B.

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]

Itano, W. M.

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]

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]

Jacobs, S. F.

J. W. Berthold III, S. F. Jacobs, and M. A. Norton, “Dimensional stability of fused silica, invar, and several ultra-low thermal expansion material,” Metrologia 13, 9–16 (1977).
[CrossRef]

J. W. Berthold III and S. F. Jacobs, “Ultraprecise thermal expansion measurements of seven low expansion materials,” Appl. Opt. 15, 2344–2347 (1976).
[CrossRef]

Jiang, H.

Kéfélian, F.

Kemery, A.

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]

Legero, T.

T. Legero and U. Sterr, “Spiegelbauteil für einen optischen Resonator,” German patent DE 10 2008 049 367 B3 (2008).

Lemke, N. D.

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. L. 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]

Lemonde, P.

J. Millo, D. V. Magalhães, C. Mandache, Y. L. 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]

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]

Levin, Y.

Y. Levin, “Internal thermal noise in the LIGO test masses: A direct approach,” Phys. Rev. D 57, 659–663 (1998).
[CrossRef]

Lipphardt, B.

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]

Lodewyck, J.

J. Millo, D. V. Magalhães, C. Mandache, Y. L. 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]

Lopez, O.

Lorini, L.

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]

Lours, M.

Ludlow, A. D.

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. L. 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]

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]

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]

Ma, L.-S.

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]

M. Notcutt, L.-S. Ma, J. Ye, and J. L. Hall, “Simple and compact 1-Hz laser system via an improved mounting configuration of a reference cavity,” Opt. Lett. 30, 1815–1817 (2005).
[CrossRef] [PubMed]

Madej, A.

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: Photophys. Laser Chem. 95, 43–54 (2009).
[CrossRef]

Magalhães, D. V.

J. Millo, D. V. Magalhães, C. Mandache, Y. L. 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]

Mandache, C.

J. Millo, D. V. Magalhães, C. Mandache, Y. L. 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]

Mann, A. G.

E. K. Wong, M. Notcutt, C. T. Taylor, A. G. Mann, and D. G. Blair, “Temperature-compensated cryogenic Fabry–Perot cavity,” Appl. Opt. 36, 8563–8566 (1997).
[CrossRef]

M. Notcutt, C. T. Taylor, A. G. Mann, and D. G. Blair, “Temperature compensation for cryogenic cavity stabilized lasers,” J. Phys. D: Appl. Phys. 28, 1807–1810 (1995).
[CrossRef]

Marmet, L.

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: Photophys. Laser Chem. 95, 43–54 (2009).
[CrossRef]

Martin, M. J.

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. L. 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]

Mensing, F.

Millo, J.

Nazarova, T.

T. Nazarova, F. Riehle, and U. Sterr, “Vibration-insensitive reference cavity for an ultra-narrow-linewidth laser,” Appl. Phys. B: Photophys. Laser Chem. 83, 531–536 (2006).
[CrossRef]

Newbury, N. R.

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]

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]

Norton, M. A.

J. W. Berthold III, S. F. Jacobs, and M. A. Norton, “Dimensional stability of fused silica, invar, and several ultra-low thermal expansion material,” Metrologia 13, 9–16 (1977).
[CrossRef]

Notcutt, M.

Numata, K.

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]

Oates, C. W.

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. L. 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]

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]

Oskay, W. H.

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]

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]

Oxborrow, M.

S. A. Webster, M. Oxborrow, S. Pugla, J. Millo, and P. Gill, “Thermal-noise-limited optical cavity,” Phys. Rev. A 77, 033847 (2008).
[CrossRef]

S. A. Webster, M. Oxborrow, and P. Gill, “Vibration insensitive optical cavity,” Phys. Rev. A 75, 011801(R) (2007).
[CrossRef]

Poli, N.

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. L. 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]

Pugla, S.

S. A. Webster, M. Oxborrow, S. Pugla, J. Millo, and P. Gill, “Thermal-noise-limited optical cavity,” Phys. Rev. A 77, 033847 (2008).
[CrossRef]

Riehle, F.

T. Nazarova, F. Riehle, and U. Sterr, “Vibration-insensitive reference cavity for an ultra-narrow-linewidth laser,” Appl. Phys. B: Photophys. Laser Chem. 83, 531–536 (2006).
[CrossRef]

F. Riehle, “Use of optical frequency standards for measurements of dimensional stability,” Meas. Sci. Technol. 9, 1042–1048 (1998).
[CrossRef]

Rosenband, T.

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]

Santarelli, G.

Schmidt, P. O.

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]

Schnatz, H.

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]

Shiner, A.

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: Photophys. Laser Chem. 95, 43–54 (2009).
[CrossRef]

Stalnaker, J. E.

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]

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. L. 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]

Sterr, U.

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]

T. Nazarova, F. Riehle, and U. Sterr, “Vibration-insensitive reference cavity for an ultra-narrow-linewidth laser,” Appl. Phys. B: Photophys. Laser Chem. 83, 531–536 (2006).
[CrossRef]

H. Stoehr, F. Mensing, J. Helmcke, and U. Sterr, “Diode laser with 1 Hz linewidth,” Opt. Lett. 31, 736–738 (2006).
[CrossRef] [PubMed]

T. Legero and U. Sterr, “Spiegelbauteil für einen optischen Resonator,” German patent DE 10 2008 049 367 B3 (2008).

Stoehr, H.

Swann, W. C.

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]

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]

Tamm, C.

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]

Taylor, C. T.

E. K. Wong, M. Notcutt, C. T. Taylor, A. G. Mann, and D. G. Blair, “Temperature-compensated cryogenic Fabry–Perot cavity,” Appl. Opt. 36, 8563–8566 (1997).
[CrossRef]

M. Notcutt, C. T. Taylor, A. G. Mann, and D. G. Blair, “Temperature compensation for cryogenic cavity stabilized lasers,” J. Phys. D: Appl. Phys. 28, 1807–1810 (1995).
[CrossRef]

Thomsen, J. W.

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. L. 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]

Tobar, M.

Webster, S. A.

S. A. Webster, M. Oxborrow, S. Pugla, J. Millo, and P. Gill, “Thermal-noise-limited optical cavity,” Phys. Rev. A 77, 033847 (2008).
[CrossRef]

S. A. Webster, M. Oxborrow, and P. Gill, “Vibration insensitive optical cavity,” Phys. Rev. A 75, 011801(R) (2007).
[CrossRef]

Westergaard, P. G.

J. Millo, D. V. Magalhães, C. Mandache, Y. L. 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]

Weyers, S.

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]

Williams, P. A.

Wilpers, G.

Wineland, D. J.

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]

Wong, E. K.

Ye, J.

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. L. 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]

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]

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]

M. Notcutt, L.-S. Ma, J. Ye, and J. L. Hall, “Simple and compact 1-Hz laser system via an improved mounting configuration of a reference cavity,” Opt. Lett. 30, 1815–1817 (2005).
[CrossRef] [PubMed]

Young, B. C.

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]

Zanon-Willette, T.

Zelevinsky, T.

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. L. 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]

Appl. Opt. (2)

Appl. Phys. B: Photophys. Laser Chem. (2)

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: Photophys. Laser Chem. 95, 43–54 (2009).
[CrossRef]

T. Nazarova, F. Riehle, and U. Sterr, “Vibration-insensitive reference cavity for an ultra-narrow-linewidth laser,” Appl. Phys. B: Photophys. Laser Chem. 83, 531–536 (2006).
[CrossRef]

IEEE Trans. Instrum. Meas. (1)

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]

J. Opt. Soc. Am. B (2)

J. Phys. D: Appl. Phys. (1)

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Phys. Rev. A (4)

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Other (2)

Use of tradenames is for informational purpose only.

T. Legero and U. Sterr, “Spiegelbauteil für einen optischen Resonator,” German patent DE 10 2008 049 367 B3 (2008).

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Figures (6)

Fig. 1
Fig. 1

FEM simulations of the elastic cavity deformation after a 1 K temperature step: (a) FS mirror optically contacted to an ULE spacer. (b) Additional ULE ring on the back side of the FS mirror to suppress its axial bending. Due to cylindrical symmetry only a quarter of the cavity is simulated. Color scale shows the axial displacement.

Fig. 2
Fig. 2

Coupling coefficient δ versus spacer diameter for a spacer length of 105.5 mm . The mirrors have a diameter of 25.4 mm and a thickness of 6.3 mm .

Fig. 3
Fig. 3

FEM simulation of the axial mirror displacement along a radial line on the mirror surface for a 1 K temperature step starting at T 0 of the spacer. An additional ULE ring (thickness 6 mm , inner diameter 9 mm ) effectively reduces the mirror displacement around its center (dotted curve).

Fig. 4
Fig. 4

FEM results of the coupling coefficient δ for an ULE cavity with FS mirrors and additional ULE rings. The coupling coefficient is shown for three different spacer diameters D ( 25.4 mm , 32 mm , and 104 mm ). The results at zero ring thickness and inner ring diameter of 25.4 mm , respectively, correspond to no ring at all (circled points). The corresponding zero crossing temperature applies to the cavity mentioned in the text.

Fig. 5
Fig. 5

Beat frequency and temperature for the CTE measurement of cavity configuration A over a period of 30  days . The triangles indicate the data used for further analysis.

Fig. 6
Fig. 6

Thermal relative length change of the four cavity configurations. Shown are the measured values (filled squares) with their fit curves (solid curves) as well as theory curves calculated from the according coupling coefficients δ (dashed curve).

Tables (2)

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Table 1 Young’s Modulus E and Poisson Ratio σ of LTE Glasses and Glass-Ceramics Taken from the Manufacturer Data Sheets

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Table 2 CTE Parameters of the Four Cavity Configurations with the Results and Error Bars of a Least Square Fit of Eq. (3) to the Thermal Expansion Curves

Equations (3)

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α eff ( T ) = α s ( T ) + 2 δ R L [ α m ( T ) α s ( T ) ] .
α ULE ( T ) = a ( T T 0 ) + b ( T T 0 ) 2 .
Δ L L = a 2 ( T T 0 ) 2 + b 3 ( T T 0 ) 3 + γ ( t t 0 ) + C 0 .

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