Abstract

Modern experiments aiming at tests of fundamental physics, like measuring gravitational waves or testing Lorentz Invariance with unprecedented accuracy, require thermal environments that are highly stable over long times. To achieve such a stability, the experiment including typically an optical resonator is nested in a thermal enclosure, which passively attenuates external temperature fluctuations to acceptable levels. These thermal shields are usually designed using tedious numerical simulations or with simple analytical models. In this paper, we propose an accurate analytical method to estimate the performance of passive thermal shields in the frequency domain, which allows for fast evaluation and optimization. The model analysis has also unveiled interesting properties of the shields, such as dips in the transfer function for some frequencies under certain combinations of materials and geometries. We validate the results by comparing them to numerical simulations performed with commercial software based on finite element methods.

© 2015 Optical Society of America

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References

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2014 (1)

J. D. Tasson, “What do we know about Lorentz invariance,” Reports on Progress in Physics 77(6), 062001 (2014).
[Crossref]

2013 (2)

S. Amairi, T. Legero, T. Kessler, U. Sterr, J. Wbbena, O. Mandel, and P. Schmidt, “Reducing the effect of thermal noise in optical cavities,” Appl. Phys. B 113(2), 233–242 (2013).
[Crossref]

M. Nofrarias, F. Gibert, N. Karnesis, A. F. García, M. Hewitson, G. Heinzel, and K. Danzmann, “Subtraction of temperature induced phase noise in the LISA frequency band,” Phys. Rev. D 87(10), 102003 (2013).

2012 (3)

P. Amaro-Seoane, S. Aoudia, S. Babak, P. Binétruy, E. Berti, A. Bohé, C. Caprini, M. Colpi, N. J. Cornish, K. Danzmann, J.-F. Dufaux, J. Gair, O. Jennrich, P. Jetzer, A. Klein, R. N. Lang, A. Lobo, T. Littenberg, S. T. McWilliams, G. Nelemans, A. Petiteau, E. K. Porter, B. F. Schutz, A. Sesana, R. Stebbins, T. Sumner, M. Vallisneri, S. Vitale, M. Volonteri, and H. Ward, “Low-frequency gravitational-wave science with eLISA/NGO,” Class. Quantum Grav. 29(12), 124016 (2012).
[Crossref]

B. S. Sheard, G. Heinzel, K. Danzmann, D. A. Shaddock, W. M. Klipstein, and W. M Folkner, “Intersatellite laser ranging instrument for the GRACE follow-on mission,” J. Geodesy 86(12), 1083–1095 (2012).
[Crossref]

B. Argence, E. Prevost, T. Lévèque, R. Le Goff, S. Bize, P. Lemonde, and G. Santarelli, “Prototype of an ultra-stable optical cavity for space applications,” Opt. Express 20(23), 25409–25420 (2012).
[Crossref] [PubMed]

2011 (1)

A. Alan Kostelecký and N. Russell, “Data tables for Lorentz and CPT violation,” Rev. Mod. Phys. 83, 11–31 (2011).
[Crossref]

2010 (2)

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(5), 914–919 (2010).
[Crossref]

M. E. Tobar, P. Wolf, S. Bize, G. Santarelli, and V. Flambaum, “Testing local Lorentz and position invariance and variation of fundamental constants by searching the derivative of the comparison frequency between a cryogenic sapphire oscillator and hydrogen maser,” Phys. Rev. D 81, 022003 (2010).
[Crossref]

2009 (2)

S. Herrmann, A. Senger, K. Möhle, M. Nagel, E. V. Kovalchuk, and A. Peters, “Rotating optical cavity experiment testing Lorentz invariance at the 10−17 level,” Phys. Rev. D 80, 105011 (2009).
[Crossref]

O. Jennrich, “LISA technology and instrumentation,” Class. Quantum Grav. 26(15), 153001 (2009).
[Crossref]

2008 (2)

J. Alnis, A. Matveev, N. Kolachevsky, T. Udem, and T. W. Hänsch, “Subhertz linewidth diode lasers by stabilization to vibrationally and thermally compensated ultralow-expansion glass Fabry-Pérot cavities,” Phys. Rev. A 77(5), 053809 (2008).
[Crossref]

S. A. Webster, M. Oxborrow, S. Pugla, J. Millo, and P. Gill, “Thermal-noise-limited optical cavity,” Phys. Rev. A 77(3), 033847 (2008).
[Crossref]

2006 (1)

A. Lobo, M. Nofrarias, J. Ramos-Castro, and J. Sanjuan, “On-ground tests of the LISA PathFinder thermal diagnostics system,” Class. Quantum Grav. 23(17), 5177 (2006).
[Crossref]

2003 (1)

H. Müller, S. Herrmann, C. Braxmaier, S. Schiller, and A. Peters, “Modern Michelson-Morley experiment using cryogenic optical resonators,” Phys. Rev. Lett. 91, 020401 (2003).
[Crossref] [PubMed]

2001 (2)

C. Lämmerzahl, H. Dittus, A. Peters, and S. Schiller, “OPTIS: a satellite-based test of special and general relativity,” Class. Quantum Grav. 18(13), 2499 (2001).
[Crossref]

C. Braxmaier, H. Müller, O. Pradl, J. Mlynek, A. Peters, and S. Schiller, “Tests of relativity using a cryogenic optical resonator,” Phys. Rev. Lett. 88, 010401 (2001).
[Crossref]

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(9), 1807 (1995).
[Crossref]

1988 (1)

Aguilera, D. N

A. Milke, D. N Aguilera, N. Gürlebeck, T. Schuldt, S. Herrmann, K. Doringshoff, R. Spannagel, C. Lammerzahl, A. Peters, B. Biering, H. Dittus, and C. Braxmaier, “A space-based optical Kennedy-Thorndike experiment testing special relativity,” European Frequency and Time Forum International Frequency Control Symposium (EFTF/IFC), 912–914 (2013).

Alan Kostelecký, A.

A. Alan Kostelecký and N. Russell, “Data tables for Lorentz and CPT violation,” Rev. Mod. Phys. 83, 11–31 (2011).
[Crossref]

Alfauwaz, A.

J. A. Lipa, S. Buchman, S. Saraf, J. Zhou, A. Alfauwaz, J. Conklin, G. D. Cutler, and R. L. Byer, “Prospects for an advanced Kennedy-Thorndike experiment in low Earth orbit,” ArXiv e-prints 1203.3914 gr-qc (2012).

Alnis, J.

J. Alnis, A. Matveev, N. Kolachevsky, T. Udem, and T. W. Hänsch, “Subhertz linewidth diode lasers by stabilization to vibrationally and thermally compensated ultralow-expansion glass Fabry-Pérot cavities,” Phys. Rev. A 77(5), 053809 (2008).
[Crossref]

Amairi, S.

S. Amairi, T. Legero, T. Kessler, U. Sterr, J. Wbbena, O. Mandel, and P. Schmidt, “Reducing the effect of thermal noise in optical cavities,” Appl. Phys. B 113(2), 233–242 (2013).
[Crossref]

Amaro-Seoane, P.

P. Amaro-Seoane, S. Aoudia, S. Babak, P. Binétruy, E. Berti, A. Bohé, C. Caprini, M. Colpi, N. J. Cornish, K. Danzmann, J.-F. Dufaux, J. Gair, O. Jennrich, P. Jetzer, A. Klein, R. N. Lang, A. Lobo, T. Littenberg, S. T. McWilliams, G. Nelemans, A. Petiteau, E. K. Porter, B. F. Schutz, A. Sesana, R. Stebbins, T. Sumner, M. Vallisneri, S. Vitale, M. Volonteri, and H. Ward, “Low-frequency gravitational-wave science with eLISA/NGO,” Class. Quantum Grav. 29(12), 124016 (2012).
[Crossref]

Aoudia, S.

P. Amaro-Seoane, S. Aoudia, S. Babak, P. Binétruy, E. Berti, A. Bohé, C. Caprini, M. Colpi, N. J. Cornish, K. Danzmann, J.-F. Dufaux, J. Gair, O. Jennrich, P. Jetzer, A. Klein, R. N. Lang, A. Lobo, T. Littenberg, S. T. McWilliams, G. Nelemans, A. Petiteau, E. K. Porter, B. F. Schutz, A. Sesana, R. Stebbins, T. Sumner, M. Vallisneri, S. Vitale, M. Volonteri, and H. Ward, “Low-frequency gravitational-wave science with eLISA/NGO,” Class. Quantum Grav. 29(12), 124016 (2012).
[Crossref]

Argence, B.

Babak, S.

P. Amaro-Seoane, S. Aoudia, S. Babak, P. Binétruy, E. Berti, A. Bohé, C. Caprini, M. Colpi, N. J. Cornish, K. Danzmann, J.-F. Dufaux, J. Gair, O. Jennrich, P. Jetzer, A. Klein, R. N. Lang, A. Lobo, T. Littenberg, S. T. McWilliams, G. Nelemans, A. Petiteau, E. K. Porter, B. F. Schutz, A. Sesana, R. Stebbins, T. Sumner, M. Vallisneri, S. Vitale, M. Volonteri, and H. Ward, “Low-frequency gravitational-wave science with eLISA/NGO,” Class. Quantum Grav. 29(12), 124016 (2012).
[Crossref]

Bergman, T. L.

T. L. Bergman, A. S. Lavine, F. P. Incropera, and D. P. DeWitt, Fundamentals of Heat and Mass Transfer (Wiley, 2011).

Berti, E.

P. Amaro-Seoane, S. Aoudia, S. Babak, P. Binétruy, E. Berti, A. Bohé, C. Caprini, M. Colpi, N. J. Cornish, K. Danzmann, J.-F. Dufaux, J. Gair, O. Jennrich, P. Jetzer, A. Klein, R. N. Lang, A. Lobo, T. Littenberg, S. T. McWilliams, G. Nelemans, A. Petiteau, E. K. Porter, B. F. Schutz, A. Sesana, R. Stebbins, T. Sumner, M. Vallisneri, S. Vitale, M. Volonteri, and H. Ward, “Low-frequency gravitational-wave science with eLISA/NGO,” Class. Quantum Grav. 29(12), 124016 (2012).
[Crossref]

Biering, B.

A. Milke, D. N Aguilera, N. Gürlebeck, T. Schuldt, S. Herrmann, K. Doringshoff, R. Spannagel, C. Lammerzahl, A. Peters, B. Biering, H. Dittus, and C. Braxmaier, “A space-based optical Kennedy-Thorndike experiment testing special relativity,” European Frequency and Time Forum International Frequency Control Symposium (EFTF/IFC), 912–914 (2013).

Binétruy, P.

P. Amaro-Seoane, S. Aoudia, S. Babak, P. Binétruy, E. Berti, A. Bohé, C. Caprini, M. Colpi, N. J. Cornish, K. Danzmann, J.-F. Dufaux, J. Gair, O. Jennrich, P. Jetzer, A. Klein, R. N. Lang, A. Lobo, T. Littenberg, S. T. McWilliams, G. Nelemans, A. Petiteau, E. K. Porter, B. F. Schutz, A. Sesana, R. Stebbins, T. Sumner, M. Vallisneri, S. Vitale, M. Volonteri, and H. Ward, “Low-frequency gravitational-wave science with eLISA/NGO,” Class. Quantum Grav. 29(12), 124016 (2012).
[Crossref]

Birch, K. P.

Bize, S.

B. Argence, E. Prevost, T. Lévèque, R. Le Goff, S. Bize, P. Lemonde, and G. Santarelli, “Prototype of an ultra-stable optical cavity for space applications,” Opt. Express 20(23), 25409–25420 (2012).
[Crossref] [PubMed]

M. E. Tobar, P. Wolf, S. Bize, G. Santarelli, and V. Flambaum, “Testing local Lorentz and position invariance and variation of fundamental constants by searching the derivative of the comparison frequency between a cryogenic sapphire oscillator and hydrogen maser,” Phys. Rev. D 81, 022003 (2010).
[Crossref]

Blair, D. G.

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(9), 1807 (1995).
[Crossref]

Bohé, A.

P. Amaro-Seoane, S. Aoudia, S. Babak, P. Binétruy, E. Berti, A. Bohé, C. Caprini, M. Colpi, N. J. Cornish, K. Danzmann, J.-F. Dufaux, J. Gair, O. Jennrich, P. Jetzer, A. Klein, R. N. Lang, A. Lobo, T. Littenberg, S. T. McWilliams, G. Nelemans, A. Petiteau, E. K. Porter, B. F. Schutz, A. Sesana, R. Stebbins, T. Sumner, M. Vallisneri, S. Vitale, M. Volonteri, and H. Ward, “Low-frequency gravitational-wave science with eLISA/NGO,” Class. Quantum Grav. 29(12), 124016 (2012).
[Crossref]

Braxmaier, C.

H. Müller, S. Herrmann, C. Braxmaier, S. Schiller, and A. Peters, “Modern Michelson-Morley experiment using cryogenic optical resonators,” Phys. Rev. Lett. 91, 020401 (2003).
[Crossref] [PubMed]

C. Braxmaier, H. Müller, O. Pradl, J. Mlynek, A. Peters, and S. Schiller, “Tests of relativity using a cryogenic optical resonator,” Phys. Rev. Lett. 88, 010401 (2001).
[Crossref]

A. Milke, D. N Aguilera, N. Gürlebeck, T. Schuldt, S. Herrmann, K. Doringshoff, R. Spannagel, C. Lammerzahl, A. Peters, B. Biering, H. Dittus, and C. Braxmaier, “A space-based optical Kennedy-Thorndike experiment testing special relativity,” European Frequency and Time Forum International Frequency Control Symposium (EFTF/IFC), 912–914 (2013).

Buchman, S.

J. A. Lipa, S. Buchman, S. Saraf, J. Zhou, A. Alfauwaz, J. Conklin, G. D. Cutler, and R. L. Byer, “Prospects for an advanced Kennedy-Thorndike experiment in low Earth orbit,” ArXiv e-prints 1203.3914 gr-qc (2012).

Bullock, E. H.

M. J. Edwards, E. H. Bullock, and D. E. Morton, “Improved precision of absolute thermal-expansion measurements for ULE glass,” Advanced Materials for Optical and Precision Structures, Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series2857, 58–63 (1996).

Byer, R. L.

J. A. Lipa, S. Buchman, S. Saraf, J. Zhou, A. Alfauwaz, J. Conklin, G. D. Cutler, and R. L. Byer, “Prospects for an advanced Kennedy-Thorndike experiment in low Earth orbit,” ArXiv e-prints 1203.3914 gr-qc (2012).

Camp, J.

G. Mueller, P. McNamara, I. Thorpe, and J. Camp, “Laser frequency stabilization for LISA,” NASA GSFC Tech. Report 20060012084 (2005).

Caprini, C.

P. Amaro-Seoane, S. Aoudia, S. Babak, P. Binétruy, E. Berti, A. Bohé, C. Caprini, M. Colpi, N. J. Cornish, K. Danzmann, J.-F. Dufaux, J. Gair, O. Jennrich, P. Jetzer, A. Klein, R. N. Lang, A. Lobo, T. Littenberg, S. T. McWilliams, G. Nelemans, A. Petiteau, E. K. Porter, B. F. Schutz, A. Sesana, R. Stebbins, T. Sumner, M. Vallisneri, S. Vitale, M. Volonteri, and H. Ward, “Low-frequency gravitational-wave science with eLISA/NGO,” Class. Quantum Grav. 29(12), 124016 (2012).
[Crossref]

Cardace, M.

Q-F. Chen, A. Nevsky, M. Cardace, S. Schiller, T. Legero, S. Häfner, A. Uhde, and U. Sterr, “A compact, robust, and transportable ultra-stable laser with a fractional frequency instability of 1×1015,” Rev. Sci. Instrum.85(11) (2014).
[Crossref]

Carslaw, H. S.

H. S. Carslaw and J. C. Jaeger, Heat Conduction in Solids (Oxford Science Publications, 1986).

Chen, Q-F.

Q-F. Chen, A. Nevsky, M. Cardace, S. Schiller, T. Legero, S. Häfner, A. Uhde, and U. Sterr, “A compact, robust, and transportable ultra-stable laser with a fractional frequency instability of 1×1015,” Rev. Sci. Instrum.85(11) (2014).
[Crossref]

Colpi, M.

P. Amaro-Seoane, S. Aoudia, S. Babak, P. Binétruy, E. Berti, A. Bohé, C. Caprini, M. Colpi, N. J. Cornish, K. Danzmann, J.-F. Dufaux, J. Gair, O. Jennrich, P. Jetzer, A. Klein, R. N. Lang, A. Lobo, T. Littenberg, S. T. McWilliams, G. Nelemans, A. Petiteau, E. K. Porter, B. F. Schutz, A. Sesana, R. Stebbins, T. Sumner, M. Vallisneri, S. Vitale, M. Volonteri, and H. Ward, “Low-frequency gravitational-wave science with eLISA/NGO,” Class. Quantum Grav. 29(12), 124016 (2012).
[Crossref]

Conklin, J.

J. A. Lipa, S. Buchman, S. Saraf, J. Zhou, A. Alfauwaz, J. Conklin, G. D. Cutler, and R. L. Byer, “Prospects for an advanced Kennedy-Thorndike experiment in low Earth orbit,” ArXiv e-prints 1203.3914 gr-qc (2012).

Cornish, N. J.

P. Amaro-Seoane, S. Aoudia, S. Babak, P. Binétruy, E. Berti, A. Bohé, C. Caprini, M. Colpi, N. J. Cornish, K. Danzmann, J.-F. Dufaux, J. Gair, O. Jennrich, P. Jetzer, A. Klein, R. N. Lang, A. Lobo, T. Littenberg, S. T. McWilliams, G. Nelemans, A. Petiteau, E. K. Porter, B. F. Schutz, A. Sesana, R. Stebbins, T. Sumner, M. Vallisneri, S. Vitale, M. Volonteri, and H. Ward, “Low-frequency gravitational-wave science with eLISA/NGO,” Class. Quantum Grav. 29(12), 124016 (2012).
[Crossref]

Cutler, G. D.

J. A. Lipa, S. Buchman, S. Saraf, J. Zhou, A. Alfauwaz, J. Conklin, G. D. Cutler, and R. L. Byer, “Prospects for an advanced Kennedy-Thorndike experiment in low Earth orbit,” ArXiv e-prints 1203.3914 gr-qc (2012).

Danzmann, K.

M. Nofrarias, F. Gibert, N. Karnesis, A. F. García, M. Hewitson, G. Heinzel, and K. Danzmann, “Subtraction of temperature induced phase noise in the LISA frequency band,” Phys. Rev. D 87(10), 102003 (2013).

P. Amaro-Seoane, S. Aoudia, S. Babak, P. Binétruy, E. Berti, A. Bohé, C. Caprini, M. Colpi, N. J. Cornish, K. Danzmann, J.-F. Dufaux, J. Gair, O. Jennrich, P. Jetzer, A. Klein, R. N. Lang, A. Lobo, T. Littenberg, S. T. McWilliams, G. Nelemans, A. Petiteau, E. K. Porter, B. F. Schutz, A. Sesana, R. Stebbins, T. Sumner, M. Vallisneri, S. Vitale, M. Volonteri, and H. Ward, “Low-frequency gravitational-wave science with eLISA/NGO,” Class. Quantum Grav. 29(12), 124016 (2012).
[Crossref]

B. S. Sheard, G. Heinzel, K. Danzmann, D. A. Shaddock, W. M. Klipstein, and W. M Folkner, “Intersatellite laser ranging instrument for the GRACE follow-on mission,” J. Geodesy 86(12), 1083–1095 (2012).
[Crossref]

Davis, M.

W. Folkner, G. de Vine, W. Klipstein, K. McKenzie, D. Shaddock, R. Spero, R. Thompson, D. Wuchenich, N. Yu, M. Stephens, J. Leitch, M. Davis, J. de Cino, C. Pace, and R. Pierce, “Laser frequency stabilization for GRACE-II,” Jet Propulsion Laboratory, California Institute of Technology Tech. Report (2010).

de Cino, J.

W. Folkner, G. de Vine, W. Klipstein, K. McKenzie, D. Shaddock, R. Spero, R. Thompson, D. Wuchenich, N. Yu, M. Stephens, J. Leitch, M. Davis, J. de Cino, C. Pace, and R. Pierce, “Laser frequency stabilization for GRACE-II,” Jet Propulsion Laboratory, California Institute of Technology Tech. Report (2010).

de Vine, G.

W. Folkner, G. de Vine, W. Klipstein, K. McKenzie, D. Shaddock, R. Spero, R. Thompson, D. Wuchenich, N. Yu, M. Stephens, J. Leitch, M. Davis, J. de Cino, C. Pace, and R. Pierce, “Laser frequency stabilization for GRACE-II,” Jet Propulsion Laboratory, California Institute of Technology Tech. Report (2010).

DeWitt, D. P.

T. L. Bergman, A. S. Lavine, F. P. Incropera, and D. P. DeWitt, Fundamentals of Heat and Mass Transfer (Wiley, 2011).

Dittus, H.

C. Lämmerzahl, H. Dittus, A. Peters, and S. Schiller, “OPTIS: a satellite-based test of special and general relativity,” Class. Quantum Grav. 18(13), 2499 (2001).
[Crossref]

A. Milke, D. N Aguilera, N. Gürlebeck, T. Schuldt, S. Herrmann, K. Doringshoff, R. Spannagel, C. Lammerzahl, A. Peters, B. Biering, H. Dittus, and C. Braxmaier, “A space-based optical Kennedy-Thorndike experiment testing special relativity,” European Frequency and Time Forum International Frequency Control Symposium (EFTF/IFC), 912–914 (2013).

Doringshoff, K.

A. Milke, D. N Aguilera, N. Gürlebeck, T. Schuldt, S. Herrmann, K. Doringshoff, R. Spannagel, C. Lammerzahl, A. Peters, B. Biering, H. Dittus, and C. Braxmaier, “A space-based optical Kennedy-Thorndike experiment testing special relativity,” European Frequency and Time Forum International Frequency Control Symposium (EFTF/IFC), 912–914 (2013).

Dufaux, J.-F.

P. Amaro-Seoane, S. Aoudia, S. Babak, P. Binétruy, E. Berti, A. Bohé, C. Caprini, M. Colpi, N. J. Cornish, K. Danzmann, J.-F. Dufaux, J. Gair, O. Jennrich, P. Jetzer, A. Klein, R. N. Lang, A. Lobo, T. Littenberg, S. T. McWilliams, G. Nelemans, A. Petiteau, E. K. Porter, B. F. Schutz, A. Sesana, R. Stebbins, T. Sumner, M. Vallisneri, S. Vitale, M. Volonteri, and H. Ward, “Low-frequency gravitational-wave science with eLISA/NGO,” Class. Quantum Grav. 29(12), 124016 (2012).
[Crossref]

Edwards, M. J.

M. J. Edwards, E. H. Bullock, and D. E. Morton, “Improved precision of absolute thermal-expansion measurements for ULE glass,” Advanced Materials for Optical and Precision Structures, Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series2857, 58–63 (1996).

Flambaum, V.

M. E. Tobar, P. Wolf, S. Bize, G. Santarelli, and V. Flambaum, “Testing local Lorentz and position invariance and variation of fundamental constants by searching the derivative of the comparison frequency between a cryogenic sapphire oscillator and hydrogen maser,” Phys. Rev. D 81, 022003 (2010).
[Crossref]

Folkner, W.

W. Folkner, G. de Vine, W. Klipstein, K. McKenzie, D. Shaddock, R. Spero, R. Thompson, D. Wuchenich, N. Yu, M. Stephens, J. Leitch, M. Davis, J. de Cino, C. Pace, and R. Pierce, “Laser frequency stabilization for GRACE-II,” Jet Propulsion Laboratory, California Institute of Technology Tech. Report (2010).

Folkner, W. M

B. S. Sheard, G. Heinzel, K. Danzmann, D. A. Shaddock, W. M. Klipstein, and W. M Folkner, “Intersatellite laser ranging instrument for the GRACE follow-on mission,” J. Geodesy 86(12), 1083–1095 (2012).
[Crossref]

Gair, J.

P. Amaro-Seoane, S. Aoudia, S. Babak, P. Binétruy, E. Berti, A. Bohé, C. Caprini, M. Colpi, N. J. Cornish, K. Danzmann, J.-F. Dufaux, J. Gair, O. Jennrich, P. Jetzer, A. Klein, R. N. Lang, A. Lobo, T. Littenberg, S. T. McWilliams, G. Nelemans, A. Petiteau, E. K. Porter, B. F. Schutz, A. Sesana, R. Stebbins, T. Sumner, M. Vallisneri, S. Vitale, M. Volonteri, and H. Ward, “Low-frequency gravitational-wave science with eLISA/NGO,” Class. Quantum Grav. 29(12), 124016 (2012).
[Crossref]

García, A. F.

M. Nofrarias, F. Gibert, N. Karnesis, A. F. García, M. Hewitson, G. Heinzel, and K. Danzmann, “Subtraction of temperature induced phase noise in the LISA frequency band,” Phys. Rev. D 87(10), 102003 (2013).

Gibert, F.

M. Nofrarias, F. Gibert, N. Karnesis, A. F. García, M. Hewitson, G. Heinzel, and K. Danzmann, “Subtraction of temperature induced phase noise in the LISA frequency band,” Phys. Rev. D 87(10), 102003 (2013).

Gill, P.

S. A. Webster, M. Oxborrow, S. Pugla, J. Millo, and P. Gill, “Thermal-noise-limited optical cavity,” Phys. Rev. A 77(3), 033847 (2008).
[Crossref]

Gürlebeck, N.

A. Milke, D. N Aguilera, N. Gürlebeck, T. Schuldt, S. Herrmann, K. Doringshoff, R. Spannagel, C. Lammerzahl, A. Peters, B. Biering, H. Dittus, and C. Braxmaier, “A space-based optical Kennedy-Thorndike experiment testing special relativity,” European Frequency and Time Forum International Frequency Control Symposium (EFTF/IFC), 912–914 (2013).

Häfner, S.

Q-F. Chen, A. Nevsky, M. Cardace, S. Schiller, T. Legero, S. Häfner, A. Uhde, and U. Sterr, “A compact, robust, and transportable ultra-stable laser with a fractional frequency instability of 1×1015,” Rev. Sci. Instrum.85(11) (2014).
[Crossref]

Hänsch, T. W.

J. Alnis, A. Matveev, N. Kolachevsky, T. Udem, and T. W. Hänsch, “Subhertz linewidth diode lasers by stabilization to vibrationally and thermally compensated ultralow-expansion glass Fabry-Pérot cavities,” Phys. Rev. A 77(5), 053809 (2008).
[Crossref]

Heinzel, G.

M. Nofrarias, F. Gibert, N. Karnesis, A. F. García, M. Hewitson, G. Heinzel, and K. Danzmann, “Subtraction of temperature induced phase noise in the LISA frequency band,” Phys. Rev. D 87(10), 102003 (2013).

B. S. Sheard, G. Heinzel, K. Danzmann, D. A. Shaddock, W. M. Klipstein, and W. M Folkner, “Intersatellite laser ranging instrument for the GRACE follow-on mission,” J. Geodesy 86(12), 1083–1095 (2012).
[Crossref]

Herrmann, S.

S. Herrmann, A. Senger, K. Möhle, M. Nagel, E. V. Kovalchuk, and A. Peters, “Rotating optical cavity experiment testing Lorentz invariance at the 10−17 level,” Phys. Rev. D 80, 105011 (2009).
[Crossref]

H. Müller, S. Herrmann, C. Braxmaier, S. Schiller, and A. Peters, “Modern Michelson-Morley experiment using cryogenic optical resonators,” Phys. Rev. Lett. 91, 020401 (2003).
[Crossref] [PubMed]

A. Milke, D. N Aguilera, N. Gürlebeck, T. Schuldt, S. Herrmann, K. Doringshoff, R. Spannagel, C. Lammerzahl, A. Peters, B. Biering, H. Dittus, and C. Braxmaier, “A space-based optical Kennedy-Thorndike experiment testing special relativity,” European Frequency and Time Forum International Frequency Control Symposium (EFTF/IFC), 912–914 (2013).

Hewitson, M.

M. Nofrarias, F. Gibert, N. Karnesis, A. F. García, M. Hewitson, G. Heinzel, and K. Danzmann, “Subtraction of temperature induced phase noise in the LISA frequency band,” Phys. Rev. D 87(10), 102003 (2013).

Incropera, F. P.

T. L. Bergman, A. S. Lavine, F. P. Incropera, and D. P. DeWitt, Fundamentals of Heat and Mass Transfer (Wiley, 2011).

Jaeger, J. C.

H. S. Carslaw and J. C. Jaeger, Heat Conduction in Solids (Oxford Science Publications, 1986).

Jennrich, O.

P. Amaro-Seoane, S. Aoudia, S. Babak, P. Binétruy, E. Berti, A. Bohé, C. Caprini, M. Colpi, N. J. Cornish, K. Danzmann, J.-F. Dufaux, J. Gair, O. Jennrich, P. Jetzer, A. Klein, R. N. Lang, A. Lobo, T. Littenberg, S. T. McWilliams, G. Nelemans, A. Petiteau, E. K. Porter, B. F. Schutz, A. Sesana, R. Stebbins, T. Sumner, M. Vallisneri, S. Vitale, M. Volonteri, and H. Ward, “Low-frequency gravitational-wave science with eLISA/NGO,” Class. Quantum Grav. 29(12), 124016 (2012).
[Crossref]

O. Jennrich, “LISA technology and instrumentation,” Class. Quantum Grav. 26(15), 153001 (2009).
[Crossref]

Jetzer, P.

P. Amaro-Seoane, S. Aoudia, S. Babak, P. Binétruy, E. Berti, A. Bohé, C. Caprini, M. Colpi, N. J. Cornish, K. Danzmann, J.-F. Dufaux, J. Gair, O. Jennrich, P. Jetzer, A. Klein, R. N. Lang, A. Lobo, T. Littenberg, S. T. McWilliams, G. Nelemans, A. Petiteau, E. K. Porter, B. F. Schutz, A. Sesana, R. Stebbins, T. Sumner, M. Vallisneri, S. Vitale, M. Volonteri, and H. Ward, “Low-frequency gravitational-wave science with eLISA/NGO,” Class. Quantum Grav. 29(12), 124016 (2012).
[Crossref]

Karnesis, N.

M. Nofrarias, F. Gibert, N. Karnesis, A. F. García, M. Hewitson, G. Heinzel, and K. Danzmann, “Subtraction of temperature induced phase noise in the LISA frequency band,” Phys. Rev. D 87(10), 102003 (2013).

Kessler, T.

S. Amairi, T. Legero, T. Kessler, U. Sterr, J. Wbbena, O. Mandel, and P. Schmidt, “Reducing the effect of thermal noise in optical cavities,” Appl. Phys. B 113(2), 233–242 (2013).
[Crossref]

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(5), 914–919 (2010).
[Crossref]

Klein, A.

P. Amaro-Seoane, S. Aoudia, S. Babak, P. Binétruy, E. Berti, A. Bohé, C. Caprini, M. Colpi, N. J. Cornish, K. Danzmann, J.-F. Dufaux, J. Gair, O. Jennrich, P. Jetzer, A. Klein, R. N. Lang, A. Lobo, T. Littenberg, S. T. McWilliams, G. Nelemans, A. Petiteau, E. K. Porter, B. F. Schutz, A. Sesana, R. Stebbins, T. Sumner, M. Vallisneri, S. Vitale, M. Volonteri, and H. Ward, “Low-frequency gravitational-wave science with eLISA/NGO,” Class. Quantum Grav. 29(12), 124016 (2012).
[Crossref]

Klipstein, W.

W. Folkner, G. de Vine, W. Klipstein, K. McKenzie, D. Shaddock, R. Spero, R. Thompson, D. Wuchenich, N. Yu, M. Stephens, J. Leitch, M. Davis, J. de Cino, C. Pace, and R. Pierce, “Laser frequency stabilization for GRACE-II,” Jet Propulsion Laboratory, California Institute of Technology Tech. Report (2010).

Klipstein, W. M.

B. S. Sheard, G. Heinzel, K. Danzmann, D. A. Shaddock, W. M. Klipstein, and W. M Folkner, “Intersatellite laser ranging instrument for the GRACE follow-on mission,” J. Geodesy 86(12), 1083–1095 (2012).
[Crossref]

Kolachevsky, N.

J. Alnis, A. Matveev, N. Kolachevsky, T. Udem, and T. W. Hänsch, “Subhertz linewidth diode lasers by stabilization to vibrationally and thermally compensated ultralow-expansion glass Fabry-Pérot cavities,” Phys. Rev. A 77(5), 053809 (2008).
[Crossref]

Kovalchuk, E. V.

S. Herrmann, A. Senger, K. Möhle, M. Nagel, E. V. Kovalchuk, and A. Peters, “Rotating optical cavity experiment testing Lorentz invariance at the 10−17 level,” Phys. Rev. D 80, 105011 (2009).
[Crossref]

Lammerzahl, C.

A. Milke, D. N Aguilera, N. Gürlebeck, T. Schuldt, S. Herrmann, K. Doringshoff, R. Spannagel, C. Lammerzahl, A. Peters, B. Biering, H. Dittus, and C. Braxmaier, “A space-based optical Kennedy-Thorndike experiment testing special relativity,” European Frequency and Time Forum International Frequency Control Symposium (EFTF/IFC), 912–914 (2013).

Lämmerzahl, C.

C. Lämmerzahl, H. Dittus, A. Peters, and S. Schiller, “OPTIS: a satellite-based test of special and general relativity,” Class. Quantum Grav. 18(13), 2499 (2001).
[Crossref]

Lang, R. N.

P. Amaro-Seoane, S. Aoudia, S. Babak, P. Binétruy, E. Berti, A. Bohé, C. Caprini, M. Colpi, N. J. Cornish, K. Danzmann, J.-F. Dufaux, J. Gair, O. Jennrich, P. Jetzer, A. Klein, R. N. Lang, A. Lobo, T. Littenberg, S. T. McWilliams, G. Nelemans, A. Petiteau, E. K. Porter, B. F. Schutz, A. Sesana, R. Stebbins, T. Sumner, M. Vallisneri, S. Vitale, M. Volonteri, and H. Ward, “Low-frequency gravitational-wave science with eLISA/NGO,” Class. Quantum Grav. 29(12), 124016 (2012).
[Crossref]

Lavine, A. S.

T. L. Bergman, A. S. Lavine, F. P. Incropera, and D. P. DeWitt, Fundamentals of Heat and Mass Transfer (Wiley, 2011).

Le Goff, R.

Legero, T.

S. Amairi, T. Legero, T. Kessler, U. Sterr, J. Wbbena, O. Mandel, and P. Schmidt, “Reducing the effect of thermal noise in optical cavities,” Appl. Phys. B 113(2), 233–242 (2013).
[Crossref]

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(5), 914–919 (2010).
[Crossref]

Q-F. Chen, A. Nevsky, M. Cardace, S. Schiller, T. Legero, S. Häfner, A. Uhde, and U. Sterr, “A compact, robust, and transportable ultra-stable laser with a fractional frequency instability of 1×1015,” Rev. Sci. Instrum.85(11) (2014).
[Crossref]

Leitch, J.

W. Folkner, G. de Vine, W. Klipstein, K. McKenzie, D. Shaddock, R. Spero, R. Thompson, D. Wuchenich, N. Yu, M. Stephens, J. Leitch, M. Davis, J. de Cino, C. Pace, and R. Pierce, “Laser frequency stabilization for GRACE-II,” Jet Propulsion Laboratory, California Institute of Technology Tech. Report (2010).

Lemonde, P.

Lévèque, T.

Lipa, J. A.

J. A. Lipa, S. Buchman, S. Saraf, J. Zhou, A. Alfauwaz, J. Conklin, G. D. Cutler, and R. L. Byer, “Prospects for an advanced Kennedy-Thorndike experiment in low Earth orbit,” ArXiv e-prints 1203.3914 gr-qc (2012).

Littenberg, T.

P. Amaro-Seoane, S. Aoudia, S. Babak, P. Binétruy, E. Berti, A. Bohé, C. Caprini, M. Colpi, N. J. Cornish, K. Danzmann, J.-F. Dufaux, J. Gair, O. Jennrich, P. Jetzer, A. Klein, R. N. Lang, A. Lobo, T. Littenberg, S. T. McWilliams, G. Nelemans, A. Petiteau, E. K. Porter, B. F. Schutz, A. Sesana, R. Stebbins, T. Sumner, M. Vallisneri, S. Vitale, M. Volonteri, and H. Ward, “Low-frequency gravitational-wave science with eLISA/NGO,” Class. Quantum Grav. 29(12), 124016 (2012).
[Crossref]

Lobo, A.

P. Amaro-Seoane, S. Aoudia, S. Babak, P. Binétruy, E. Berti, A. Bohé, C. Caprini, M. Colpi, N. J. Cornish, K. Danzmann, J.-F. Dufaux, J. Gair, O. Jennrich, P. Jetzer, A. Klein, R. N. Lang, A. Lobo, T. Littenberg, S. T. McWilliams, G. Nelemans, A. Petiteau, E. K. Porter, B. F. Schutz, A. Sesana, R. Stebbins, T. Sumner, M. Vallisneri, S. Vitale, M. Volonteri, and H. Ward, “Low-frequency gravitational-wave science with eLISA/NGO,” Class. Quantum Grav. 29(12), 124016 (2012).
[Crossref]

A. Lobo, M. Nofrarias, J. Ramos-Castro, and J. Sanjuan, “On-ground tests of the LISA PathFinder thermal diagnostics system,” Class. Quantum Grav. 23(17), 5177 (2006).
[Crossref]

Mandel, O.

S. Amairi, T. Legero, T. Kessler, U. Sterr, J. Wbbena, O. Mandel, and P. Schmidt, “Reducing the effect of thermal noise in optical cavities,” Appl. Phys. B 113(2), 233–242 (2013).
[Crossref]

Mann, A. G.

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(9), 1807 (1995).
[Crossref]

Matveev, A.

J. Alnis, A. Matveev, N. Kolachevsky, T. Udem, and T. W. Hänsch, “Subhertz linewidth diode lasers by stabilization to vibrationally and thermally compensated ultralow-expansion glass Fabry-Pérot cavities,” Phys. Rev. A 77(5), 053809 (2008).
[Crossref]

McKenzie, K.

W. Folkner, G. de Vine, W. Klipstein, K. McKenzie, D. Shaddock, R. Spero, R. Thompson, D. Wuchenich, N. Yu, M. Stephens, J. Leitch, M. Davis, J. de Cino, C. Pace, and R. Pierce, “Laser frequency stabilization for GRACE-II,” Jet Propulsion Laboratory, California Institute of Technology Tech. Report (2010).

McNamara, P.

G. Mueller, P. McNamara, I. Thorpe, and J. Camp, “Laser frequency stabilization for LISA,” NASA GSFC Tech. Report 20060012084 (2005).

McWilliams, S. T.

P. Amaro-Seoane, S. Aoudia, S. Babak, P. Binétruy, E. Berti, A. Bohé, C. Caprini, M. Colpi, N. J. Cornish, K. Danzmann, J.-F. Dufaux, J. Gair, O. Jennrich, P. Jetzer, A. Klein, R. N. Lang, A. Lobo, T. Littenberg, S. T. McWilliams, G. Nelemans, A. Petiteau, E. K. Porter, B. F. Schutz, A. Sesana, R. Stebbins, T. Sumner, M. Vallisneri, S. Vitale, M. Volonteri, and H. Ward, “Low-frequency gravitational-wave science with eLISA/NGO,” Class. Quantum Grav. 29(12), 124016 (2012).
[Crossref]

Merkowitz, S. M.

H. Peabody and S. M. Merkowitz, “Low frequency thermal performance of the LISA sciencecraft,”

Milke, A.

A. Milke, D. N Aguilera, N. Gürlebeck, T. Schuldt, S. Herrmann, K. Doringshoff, R. Spannagel, C. Lammerzahl, A. Peters, B. Biering, H. Dittus, and C. Braxmaier, “A space-based optical Kennedy-Thorndike experiment testing special relativity,” European Frequency and Time Forum International Frequency Control Symposium (EFTF/IFC), 912–914 (2013).

Millo, J.

S. A. Webster, M. Oxborrow, S. Pugla, J. Millo, and P. Gill, “Thermal-noise-limited optical cavity,” Phys. Rev. A 77(3), 033847 (2008).
[Crossref]

Mlynek, J.

C. Braxmaier, H. Müller, O. Pradl, J. Mlynek, A. Peters, and S. Schiller, “Tests of relativity using a cryogenic optical resonator,” Phys. Rev. Lett. 88, 010401 (2001).
[Crossref]

Möhle, K.

S. Herrmann, A. Senger, K. Möhle, M. Nagel, E. V. Kovalchuk, and A. Peters, “Rotating optical cavity experiment testing Lorentz invariance at the 10−17 level,” Phys. Rev. D 80, 105011 (2009).
[Crossref]

Morton, D. E.

M. J. Edwards, E. H. Bullock, and D. E. Morton, “Improved precision of absolute thermal-expansion measurements for ULE glass,” Advanced Materials for Optical and Precision Structures, Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series2857, 58–63 (1996).

Mueller, G.

G. Mueller, P. McNamara, I. Thorpe, and J. Camp, “Laser frequency stabilization for LISA,” NASA GSFC Tech. Report 20060012084 (2005).

Müller, H.

H. Müller, S. Herrmann, C. Braxmaier, S. Schiller, and A. Peters, “Modern Michelson-Morley experiment using cryogenic optical resonators,” Phys. Rev. Lett. 91, 020401 (2003).
[Crossref] [PubMed]

C. Braxmaier, H. Müller, O. Pradl, J. Mlynek, A. Peters, and S. Schiller, “Tests of relativity using a cryogenic optical resonator,” Phys. Rev. Lett. 88, 010401 (2001).
[Crossref]

Nagel, M.

S. Herrmann, A. Senger, K. Möhle, M. Nagel, E. V. Kovalchuk, and A. Peters, “Rotating optical cavity experiment testing Lorentz invariance at the 10−17 level,” Phys. Rev. D 80, 105011 (2009).
[Crossref]

Nelemans, G.

P. Amaro-Seoane, S. Aoudia, S. Babak, P. Binétruy, E. Berti, A. Bohé, C. Caprini, M. Colpi, N. J. Cornish, K. Danzmann, J.-F. Dufaux, J. Gair, O. Jennrich, P. Jetzer, A. Klein, R. N. Lang, A. Lobo, T. Littenberg, S. T. McWilliams, G. Nelemans, A. Petiteau, E. K. Porter, B. F. Schutz, A. Sesana, R. Stebbins, T. Sumner, M. Vallisneri, S. Vitale, M. Volonteri, and H. Ward, “Low-frequency gravitational-wave science with eLISA/NGO,” Class. Quantum Grav. 29(12), 124016 (2012).
[Crossref]

Nevsky, A.

Q-F. Chen, A. Nevsky, M. Cardace, S. Schiller, T. Legero, S. Häfner, A. Uhde, and U. Sterr, “A compact, robust, and transportable ultra-stable laser with a fractional frequency instability of 1×1015,” Rev. Sci. Instrum.85(11) (2014).
[Crossref]

Nofrarias, M.

M. Nofrarias, F. Gibert, N. Karnesis, A. F. García, M. Hewitson, G. Heinzel, and K. Danzmann, “Subtraction of temperature induced phase noise in the LISA frequency band,” Phys. Rev. D 87(10), 102003 (2013).

A. Lobo, M. Nofrarias, J. Ramos-Castro, and J. Sanjuan, “On-ground tests of the LISA PathFinder thermal diagnostics system,” Class. Quantum Grav. 23(17), 5177 (2006).
[Crossref]

M. Nofrarias, “Thermal diagnostics in the LISA technology package,” Ph.D Thesis, Universitat de Barcelona (2007).

Notcutt, M.

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(9), 1807 (1995).
[Crossref]

Oxborrow, M.

S. A. Webster, M. Oxborrow, S. Pugla, J. Millo, and P. Gill, “Thermal-noise-limited optical cavity,” Phys. Rev. A 77(3), 033847 (2008).
[Crossref]

Pace, C.

W. Folkner, G. de Vine, W. Klipstein, K. McKenzie, D. Shaddock, R. Spero, R. Thompson, D. Wuchenich, N. Yu, M. Stephens, J. Leitch, M. Davis, J. de Cino, C. Pace, and R. Pierce, “Laser frequency stabilization for GRACE-II,” Jet Propulsion Laboratory, California Institute of Technology Tech. Report (2010).

Peabody, H.

H. Peabody and S. M. Merkowitz, “Low frequency thermal performance of the LISA sciencecraft,”

Peters, A.

S. Herrmann, A. Senger, K. Möhle, M. Nagel, E. V. Kovalchuk, and A. Peters, “Rotating optical cavity experiment testing Lorentz invariance at the 10−17 level,” Phys. Rev. D 80, 105011 (2009).
[Crossref]

H. Müller, S. Herrmann, C. Braxmaier, S. Schiller, and A. Peters, “Modern Michelson-Morley experiment using cryogenic optical resonators,” Phys. Rev. Lett. 91, 020401 (2003).
[Crossref] [PubMed]

C. Braxmaier, H. Müller, O. Pradl, J. Mlynek, A. Peters, and S. Schiller, “Tests of relativity using a cryogenic optical resonator,” Phys. Rev. Lett. 88, 010401 (2001).
[Crossref]

C. Lämmerzahl, H. Dittus, A. Peters, and S. Schiller, “OPTIS: a satellite-based test of special and general relativity,” Class. Quantum Grav. 18(13), 2499 (2001).
[Crossref]

A. Milke, D. N Aguilera, N. Gürlebeck, T. Schuldt, S. Herrmann, K. Doringshoff, R. Spannagel, C. Lammerzahl, A. Peters, B. Biering, H. Dittus, and C. Braxmaier, “A space-based optical Kennedy-Thorndike experiment testing special relativity,” European Frequency and Time Forum International Frequency Control Symposium (EFTF/IFC), 912–914 (2013).

Petiteau, A.

P. Amaro-Seoane, S. Aoudia, S. Babak, P. Binétruy, E. Berti, A. Bohé, C. Caprini, M. Colpi, N. J. Cornish, K. Danzmann, J.-F. Dufaux, J. Gair, O. Jennrich, P. Jetzer, A. Klein, R. N. Lang, A. Lobo, T. Littenberg, S. T. McWilliams, G. Nelemans, A. Petiteau, E. K. Porter, B. F. Schutz, A. Sesana, R. Stebbins, T. Sumner, M. Vallisneri, S. Vitale, M. Volonteri, and H. Ward, “Low-frequency gravitational-wave science with eLISA/NGO,” Class. Quantum Grav. 29(12), 124016 (2012).
[Crossref]

Pierce, R.

W. Folkner, G. de Vine, W. Klipstein, K. McKenzie, D. Shaddock, R. Spero, R. Thompson, D. Wuchenich, N. Yu, M. Stephens, J. Leitch, M. Davis, J. de Cino, C. Pace, and R. Pierce, “Laser frequency stabilization for GRACE-II,” Jet Propulsion Laboratory, California Institute of Technology Tech. Report (2010).

Porter, E. K.

P. Amaro-Seoane, S. Aoudia, S. Babak, P. Binétruy, E. Berti, A. Bohé, C. Caprini, M. Colpi, N. J. Cornish, K. Danzmann, J.-F. Dufaux, J. Gair, O. Jennrich, P. Jetzer, A. Klein, R. N. Lang, A. Lobo, T. Littenberg, S. T. McWilliams, G. Nelemans, A. Petiteau, E. K. Porter, B. F. Schutz, A. Sesana, R. Stebbins, T. Sumner, M. Vallisneri, S. Vitale, M. Volonteri, and H. Ward, “Low-frequency gravitational-wave science with eLISA/NGO,” Class. Quantum Grav. 29(12), 124016 (2012).
[Crossref]

Pradl, O.

C. Braxmaier, H. Müller, O. Pradl, J. Mlynek, A. Peters, and S. Schiller, “Tests of relativity using a cryogenic optical resonator,” Phys. Rev. Lett. 88, 010401 (2001).
[Crossref]

Prevost, E.

Pugla, S.

S. A. Webster, M. Oxborrow, S. Pugla, J. Millo, and P. Gill, “Thermal-noise-limited optical cavity,” Phys. Rev. A 77(3), 033847 (2008).
[Crossref]

Ramos-Castro, J.

A. Lobo, M. Nofrarias, J. Ramos-Castro, and J. Sanjuan, “On-ground tests of the LISA PathFinder thermal diagnostics system,” Class. Quantum Grav. 23(17), 5177 (2006).
[Crossref]

Russell, N.

A. Alan Kostelecký and N. Russell, “Data tables for Lorentz and CPT violation,” Rev. Mod. Phys. 83, 11–31 (2011).
[Crossref]

Sanjuan, J.

A. Lobo, M. Nofrarias, J. Ramos-Castro, and J. Sanjuan, “On-ground tests of the LISA PathFinder thermal diagnostics system,” Class. Quantum Grav. 23(17), 5177 (2006).
[Crossref]

Santarelli, G.

B. Argence, E. Prevost, T. Lévèque, R. Le Goff, S. Bize, P. Lemonde, and G. Santarelli, “Prototype of an ultra-stable optical cavity for space applications,” Opt. Express 20(23), 25409–25420 (2012).
[Crossref] [PubMed]

M. E. Tobar, P. Wolf, S. Bize, G. Santarelli, and V. Flambaum, “Testing local Lorentz and position invariance and variation of fundamental constants by searching the derivative of the comparison frequency between a cryogenic sapphire oscillator and hydrogen maser,” Phys. Rev. D 81, 022003 (2010).
[Crossref]

Saraf, S.

J. A. Lipa, S. Buchman, S. Saraf, J. Zhou, A. Alfauwaz, J. Conklin, G. D. Cutler, and R. L. Byer, “Prospects for an advanced Kennedy-Thorndike experiment in low Earth orbit,” ArXiv e-prints 1203.3914 gr-qc (2012).

Schiller, S.

H. Müller, S. Herrmann, C. Braxmaier, S. Schiller, and A. Peters, “Modern Michelson-Morley experiment using cryogenic optical resonators,” Phys. Rev. Lett. 91, 020401 (2003).
[Crossref] [PubMed]

C. Braxmaier, H. Müller, O. Pradl, J. Mlynek, A. Peters, and S. Schiller, “Tests of relativity using a cryogenic optical resonator,” Phys. Rev. Lett. 88, 010401 (2001).
[Crossref]

C. Lämmerzahl, H. Dittus, A. Peters, and S. Schiller, “OPTIS: a satellite-based test of special and general relativity,” Class. Quantum Grav. 18(13), 2499 (2001).
[Crossref]

Q-F. Chen, A. Nevsky, M. Cardace, S. Schiller, T. Legero, S. Häfner, A. Uhde, and U. Sterr, “A compact, robust, and transportable ultra-stable laser with a fractional frequency instability of 1×1015,” Rev. Sci. Instrum.85(11) (2014).
[Crossref]

Schmidt, P.

S. Amairi, T. Legero, T. Kessler, U. Sterr, J. Wbbena, O. Mandel, and P. Schmidt, “Reducing the effect of thermal noise in optical cavities,” Appl. Phys. B 113(2), 233–242 (2013).
[Crossref]

Schuldt, T.

A. Milke, D. N Aguilera, N. Gürlebeck, T. Schuldt, S. Herrmann, K. Doringshoff, R. Spannagel, C. Lammerzahl, A. Peters, B. Biering, H. Dittus, and C. Braxmaier, “A space-based optical Kennedy-Thorndike experiment testing special relativity,” European Frequency and Time Forum International Frequency Control Symposium (EFTF/IFC), 912–914 (2013).

Schutz, B. F.

P. Amaro-Seoane, S. Aoudia, S. Babak, P. Binétruy, E. Berti, A. Bohé, C. Caprini, M. Colpi, N. J. Cornish, K. Danzmann, J.-F. Dufaux, J. Gair, O. Jennrich, P. Jetzer, A. Klein, R. N. Lang, A. Lobo, T. Littenberg, S. T. McWilliams, G. Nelemans, A. Petiteau, E. K. Porter, B. F. Schutz, A. Sesana, R. Stebbins, T. Sumner, M. Vallisneri, S. Vitale, M. Volonteri, and H. Ward, “Low-frequency gravitational-wave science with eLISA/NGO,” Class. Quantum Grav. 29(12), 124016 (2012).
[Crossref]

Senger, A.

S. Herrmann, A. Senger, K. Möhle, M. Nagel, E. V. Kovalchuk, and A. Peters, “Rotating optical cavity experiment testing Lorentz invariance at the 10−17 level,” Phys. Rev. D 80, 105011 (2009).
[Crossref]

Sesana, A.

P. Amaro-Seoane, S. Aoudia, S. Babak, P. Binétruy, E. Berti, A. Bohé, C. Caprini, M. Colpi, N. J. Cornish, K. Danzmann, J.-F. Dufaux, J. Gair, O. Jennrich, P. Jetzer, A. Klein, R. N. Lang, A. Lobo, T. Littenberg, S. T. McWilliams, G. Nelemans, A. Petiteau, E. K. Porter, B. F. Schutz, A. Sesana, R. Stebbins, T. Sumner, M. Vallisneri, S. Vitale, M. Volonteri, and H. Ward, “Low-frequency gravitational-wave science with eLISA/NGO,” Class. Quantum Grav. 29(12), 124016 (2012).
[Crossref]

Shaddock, D.

W. Folkner, G. de Vine, W. Klipstein, K. McKenzie, D. Shaddock, R. Spero, R. Thompson, D. Wuchenich, N. Yu, M. Stephens, J. Leitch, M. Davis, J. de Cino, C. Pace, and R. Pierce, “Laser frequency stabilization for GRACE-II,” Jet Propulsion Laboratory, California Institute of Technology Tech. Report (2010).

Shaddock, D. A.

B. S. Sheard, G. Heinzel, K. Danzmann, D. A. Shaddock, W. M. Klipstein, and W. M Folkner, “Intersatellite laser ranging instrument for the GRACE follow-on mission,” J. Geodesy 86(12), 1083–1095 (2012).
[Crossref]

Sheard, B. S.

B. S. Sheard, G. Heinzel, K. Danzmann, D. A. Shaddock, W. M. Klipstein, and W. M Folkner, “Intersatellite laser ranging instrument for the GRACE follow-on mission,” J. Geodesy 86(12), 1083–1095 (2012).
[Crossref]

Spannagel, R.

A. Milke, D. N Aguilera, N. Gürlebeck, T. Schuldt, S. Herrmann, K. Doringshoff, R. Spannagel, C. Lammerzahl, A. Peters, B. Biering, H. Dittus, and C. Braxmaier, “A space-based optical Kennedy-Thorndike experiment testing special relativity,” European Frequency and Time Forum International Frequency Control Symposium (EFTF/IFC), 912–914 (2013).

Spero, R.

W. Folkner, G. de Vine, W. Klipstein, K. McKenzie, D. Shaddock, R. Spero, R. Thompson, D. Wuchenich, N. Yu, M. Stephens, J. Leitch, M. Davis, J. de Cino, C. Pace, and R. Pierce, “Laser frequency stabilization for GRACE-II,” Jet Propulsion Laboratory, California Institute of Technology Tech. Report (2010).

Stebbins, R.

P. Amaro-Seoane, S. Aoudia, S. Babak, P. Binétruy, E. Berti, A. Bohé, C. Caprini, M. Colpi, N. J. Cornish, K. Danzmann, J.-F. Dufaux, J. Gair, O. Jennrich, P. Jetzer, A. Klein, R. N. Lang, A. Lobo, T. Littenberg, S. T. McWilliams, G. Nelemans, A. Petiteau, E. K. Porter, B. F. Schutz, A. Sesana, R. Stebbins, T. Sumner, M. Vallisneri, S. Vitale, M. Volonteri, and H. Ward, “Low-frequency gravitational-wave science with eLISA/NGO,” Class. Quantum Grav. 29(12), 124016 (2012).
[Crossref]

Stephens, M.

W. Folkner, G. de Vine, W. Klipstein, K. McKenzie, D. Shaddock, R. Spero, R. Thompson, D. Wuchenich, N. Yu, M. Stephens, J. Leitch, M. Davis, J. de Cino, C. Pace, and R. Pierce, “Laser frequency stabilization for GRACE-II,” Jet Propulsion Laboratory, California Institute of Technology Tech. Report (2010).

Sterr, U.

S. Amairi, T. Legero, T. Kessler, U. Sterr, J. Wbbena, O. Mandel, and P. Schmidt, “Reducing the effect of thermal noise in optical cavities,” Appl. Phys. B 113(2), 233–242 (2013).
[Crossref]

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(5), 914–919 (2010).
[Crossref]

Q-F. Chen, A. Nevsky, M. Cardace, S. Schiller, T. Legero, S. Häfner, A. Uhde, and U. Sterr, “A compact, robust, and transportable ultra-stable laser with a fractional frequency instability of 1×1015,” Rev. Sci. Instrum.85(11) (2014).
[Crossref]

Sumner, T.

P. Amaro-Seoane, S. Aoudia, S. Babak, P. Binétruy, E. Berti, A. Bohé, C. Caprini, M. Colpi, N. J. Cornish, K. Danzmann, J.-F. Dufaux, J. Gair, O. Jennrich, P. Jetzer, A. Klein, R. N. Lang, A. Lobo, T. Littenberg, S. T. McWilliams, G. Nelemans, A. Petiteau, E. K. Porter, B. F. Schutz, A. Sesana, R. Stebbins, T. Sumner, M. Vallisneri, S. Vitale, M. Volonteri, and H. Ward, “Low-frequency gravitational-wave science with eLISA/NGO,” Class. Quantum Grav. 29(12), 124016 (2012).
[Crossref]

Tasson, J. D.

J. D. Tasson, “What do we know about Lorentz invariance,” Reports on Progress in Physics 77(6), 062001 (2014).
[Crossref]

Taylor, C. T.

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(9), 1807 (1995).
[Crossref]

Thompson, R.

W. Folkner, G. de Vine, W. Klipstein, K. McKenzie, D. Shaddock, R. Spero, R. Thompson, D. Wuchenich, N. Yu, M. Stephens, J. Leitch, M. Davis, J. de Cino, C. Pace, and R. Pierce, “Laser frequency stabilization for GRACE-II,” Jet Propulsion Laboratory, California Institute of Technology Tech. Report (2010).

Thorpe, I.

G. Mueller, P. McNamara, I. Thorpe, and J. Camp, “Laser frequency stabilization for LISA,” NASA GSFC Tech. Report 20060012084 (2005).

Tobar, M. E.

M. E. Tobar, P. Wolf, S. Bize, G. Santarelli, and V. Flambaum, “Testing local Lorentz and position invariance and variation of fundamental constants by searching the derivative of the comparison frequency between a cryogenic sapphire oscillator and hydrogen maser,” Phys. Rev. D 81, 022003 (2010).
[Crossref]

Udem, T.

J. Alnis, A. Matveev, N. Kolachevsky, T. Udem, and T. W. Hänsch, “Subhertz linewidth diode lasers by stabilization to vibrationally and thermally compensated ultralow-expansion glass Fabry-Pérot cavities,” Phys. Rev. A 77(5), 053809 (2008).
[Crossref]

Uhde, A.

Q-F. Chen, A. Nevsky, M. Cardace, S. Schiller, T. Legero, S. Häfner, A. Uhde, and U. Sterr, “A compact, robust, and transportable ultra-stable laser with a fractional frequency instability of 1×1015,” Rev. Sci. Instrum.85(11) (2014).
[Crossref]

Vallisneri, M.

P. Amaro-Seoane, S. Aoudia, S. Babak, P. Binétruy, E. Berti, A. Bohé, C. Caprini, M. Colpi, N. J. Cornish, K. Danzmann, J.-F. Dufaux, J. Gair, O. Jennrich, P. Jetzer, A. Klein, R. N. Lang, A. Lobo, T. Littenberg, S. T. McWilliams, G. Nelemans, A. Petiteau, E. K. Porter, B. F. Schutz, A. Sesana, R. Stebbins, T. Sumner, M. Vallisneri, S. Vitale, M. Volonteri, and H. Ward, “Low-frequency gravitational-wave science with eLISA/NGO,” Class. Quantum Grav. 29(12), 124016 (2012).
[Crossref]

Vitale, S.

P. Amaro-Seoane, S. Aoudia, S. Babak, P. Binétruy, E. Berti, A. Bohé, C. Caprini, M. Colpi, N. J. Cornish, K. Danzmann, J.-F. Dufaux, J. Gair, O. Jennrich, P. Jetzer, A. Klein, R. N. Lang, A. Lobo, T. Littenberg, S. T. McWilliams, G. Nelemans, A. Petiteau, E. K. Porter, B. F. Schutz, A. Sesana, R. Stebbins, T. Sumner, M. Vallisneri, S. Vitale, M. Volonteri, and H. Ward, “Low-frequency gravitational-wave science with eLISA/NGO,” Class. Quantum Grav. 29(12), 124016 (2012).
[Crossref]

Volonteri, M.

P. Amaro-Seoane, S. Aoudia, S. Babak, P. Binétruy, E. Berti, A. Bohé, C. Caprini, M. Colpi, N. J. Cornish, K. Danzmann, J.-F. Dufaux, J. Gair, O. Jennrich, P. Jetzer, A. Klein, R. N. Lang, A. Lobo, T. Littenberg, S. T. McWilliams, G. Nelemans, A. Petiteau, E. K. Porter, B. F. Schutz, A. Sesana, R. Stebbins, T. Sumner, M. Vallisneri, S. Vitale, M. Volonteri, and H. Ward, “Low-frequency gravitational-wave science with eLISA/NGO,” Class. Quantum Grav. 29(12), 124016 (2012).
[Crossref]

Ward, H.

P. Amaro-Seoane, S. Aoudia, S. Babak, P. Binétruy, E. Berti, A. Bohé, C. Caprini, M. Colpi, N. J. Cornish, K. Danzmann, J.-F. Dufaux, J. Gair, O. Jennrich, P. Jetzer, A. Klein, R. N. Lang, A. Lobo, T. Littenberg, S. T. McWilliams, G. Nelemans, A. Petiteau, E. K. Porter, B. F. Schutz, A. Sesana, R. Stebbins, T. Sumner, M. Vallisneri, S. Vitale, M. Volonteri, and H. Ward, “Low-frequency gravitational-wave science with eLISA/NGO,” Class. Quantum Grav. 29(12), 124016 (2012).
[Crossref]

Wbbena, J.

S. Amairi, T. Legero, T. Kessler, U. Sterr, J. Wbbena, O. Mandel, and P. Schmidt, “Reducing the effect of thermal noise in optical cavities,” Appl. Phys. B 113(2), 233–242 (2013).
[Crossref]

Webster, S. A.

S. A. Webster, M. Oxborrow, S. Pugla, J. Millo, and P. Gill, “Thermal-noise-limited optical cavity,” Phys. Rev. A 77(3), 033847 (2008).
[Crossref]

Wilton, P. T.

Wolf, P.

M. E. Tobar, P. Wolf, S. Bize, G. Santarelli, and V. Flambaum, “Testing local Lorentz and position invariance and variation of fundamental constants by searching the derivative of the comparison frequency between a cryogenic sapphire oscillator and hydrogen maser,” Phys. Rev. D 81, 022003 (2010).
[Crossref]

Wuchenich, D.

W. Folkner, G. de Vine, W. Klipstein, K. McKenzie, D. Shaddock, R. Spero, R. Thompson, D. Wuchenich, N. Yu, M. Stephens, J. Leitch, M. Davis, J. de Cino, C. Pace, and R. Pierce, “Laser frequency stabilization for GRACE-II,” Jet Propulsion Laboratory, California Institute of Technology Tech. Report (2010).

Yu, N.

W. Folkner, G. de Vine, W. Klipstein, K. McKenzie, D. Shaddock, R. Spero, R. Thompson, D. Wuchenich, N. Yu, M. Stephens, J. Leitch, M. Davis, J. de Cino, C. Pace, and R. Pierce, “Laser frequency stabilization for GRACE-II,” Jet Propulsion Laboratory, California Institute of Technology Tech. Report (2010).

Zhou, J.

J. A. Lipa, S. Buchman, S. Saraf, J. Zhou, A. Alfauwaz, J. Conklin, G. D. Cutler, and R. L. Byer, “Prospects for an advanced Kennedy-Thorndike experiment in low Earth orbit,” ArXiv e-prints 1203.3914 gr-qc (2012).

Appl. Opt. (1)

Appl. Phys. B (1)

S. Amairi, T. Legero, T. Kessler, U. Sterr, J. Wbbena, O. Mandel, and P. Schmidt, “Reducing the effect of thermal noise in optical cavities,” Appl. Phys. B 113(2), 233–242 (2013).
[Crossref]

Class. Quantum Grav. (4)

C. Lämmerzahl, H. Dittus, A. Peters, and S. Schiller, “OPTIS: a satellite-based test of special and general relativity,” Class. Quantum Grav. 18(13), 2499 (2001).
[Crossref]

P. Amaro-Seoane, S. Aoudia, S. Babak, P. Binétruy, E. Berti, A. Bohé, C. Caprini, M. Colpi, N. J. Cornish, K. Danzmann, J.-F. Dufaux, J. Gair, O. Jennrich, P. Jetzer, A. Klein, R. N. Lang, A. Lobo, T. Littenberg, S. T. McWilliams, G. Nelemans, A. Petiteau, E. K. Porter, B. F. Schutz, A. Sesana, R. Stebbins, T. Sumner, M. Vallisneri, S. Vitale, M. Volonteri, and H. Ward, “Low-frequency gravitational-wave science with eLISA/NGO,” Class. Quantum Grav. 29(12), 124016 (2012).
[Crossref]

O. Jennrich, “LISA technology and instrumentation,” Class. Quantum Grav. 26(15), 153001 (2009).
[Crossref]

A. Lobo, M. Nofrarias, J. Ramos-Castro, and J. Sanjuan, “On-ground tests of the LISA PathFinder thermal diagnostics system,” Class. Quantum Grav. 23(17), 5177 (2006).
[Crossref]

J. Geodesy (1)

B. S. Sheard, G. Heinzel, K. Danzmann, D. A. Shaddock, W. M. Klipstein, and W. M Folkner, “Intersatellite laser ranging instrument for the GRACE follow-on mission,” J. Geodesy 86(12), 1083–1095 (2012).
[Crossref]

J. Opt. Soc. Am. B (1)

J. Phys. D: Appl. Phys. (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(9), 1807 (1995).
[Crossref]

Opt. Express (1)

Phys. Rev. A (2)

S. A. Webster, M. Oxborrow, S. Pugla, J. Millo, and P. Gill, “Thermal-noise-limited optical cavity,” Phys. Rev. A 77(3), 033847 (2008).
[Crossref]

J. Alnis, A. Matveev, N. Kolachevsky, T. Udem, and T. W. Hänsch, “Subhertz linewidth diode lasers by stabilization to vibrationally and thermally compensated ultralow-expansion glass Fabry-Pérot cavities,” Phys. Rev. A 77(5), 053809 (2008).
[Crossref]

Phys. Rev. D (3)

M. Nofrarias, F. Gibert, N. Karnesis, A. F. García, M. Hewitson, G. Heinzel, and K. Danzmann, “Subtraction of temperature induced phase noise in the LISA frequency band,” Phys. Rev. D 87(10), 102003 (2013).

M. E. Tobar, P. Wolf, S. Bize, G. Santarelli, and V. Flambaum, “Testing local Lorentz and position invariance and variation of fundamental constants by searching the derivative of the comparison frequency between a cryogenic sapphire oscillator and hydrogen maser,” Phys. Rev. D 81, 022003 (2010).
[Crossref]

S. Herrmann, A. Senger, K. Möhle, M. Nagel, E. V. Kovalchuk, and A. Peters, “Rotating optical cavity experiment testing Lorentz invariance at the 10−17 level,” Phys. Rev. D 80, 105011 (2009).
[Crossref]

Phys. Rev. Lett. (2)

C. Braxmaier, H. Müller, O. Pradl, J. Mlynek, A. Peters, and S. Schiller, “Tests of relativity using a cryogenic optical resonator,” Phys. Rev. Lett. 88, 010401 (2001).
[Crossref]

H. Müller, S. Herrmann, C. Braxmaier, S. Schiller, and A. Peters, “Modern Michelson-Morley experiment using cryogenic optical resonators,” Phys. Rev. Lett. 91, 020401 (2003).
[Crossref] [PubMed]

Reports on Progress in Physics (1)

J. D. Tasson, “What do we know about Lorentz invariance,” Reports on Progress in Physics 77(6), 062001 (2014).
[Crossref]

Rev. Mod. Phys. (1)

A. Alan Kostelecký and N. Russell, “Data tables for Lorentz and CPT violation,” Rev. Mod. Phys. 83, 11–31 (2011).
[Crossref]

Other (10)

J. A. Lipa, S. Buchman, S. Saraf, J. Zhou, A. Alfauwaz, J. Conklin, G. D. Cutler, and R. L. Byer, “Prospects for an advanced Kennedy-Thorndike experiment in low Earth orbit,” ArXiv e-prints 1203.3914 gr-qc (2012).

A. Milke, D. N Aguilera, N. Gürlebeck, T. Schuldt, S. Herrmann, K. Doringshoff, R. Spannagel, C. Lammerzahl, A. Peters, B. Biering, H. Dittus, and C. Braxmaier, “A space-based optical Kennedy-Thorndike experiment testing special relativity,” European Frequency and Time Forum International Frequency Control Symposium (EFTF/IFC), 912–914 (2013).

Q-F. Chen, A. Nevsky, M. Cardace, S. Schiller, T. Legero, S. Häfner, A. Uhde, and U. Sterr, “A compact, robust, and transportable ultra-stable laser with a fractional frequency instability of 1×1015,” Rev. Sci. Instrum.85(11) (2014).
[Crossref]

M. J. Edwards, E. H. Bullock, and D. E. Morton, “Improved precision of absolute thermal-expansion measurements for ULE glass,” Advanced Materials for Optical and Precision Structures, Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series2857, 58–63 (1996).

W. Folkner, G. de Vine, W. Klipstein, K. McKenzie, D. Shaddock, R. Spero, R. Thompson, D. Wuchenich, N. Yu, M. Stephens, J. Leitch, M. Davis, J. de Cino, C. Pace, and R. Pierce, “Laser frequency stabilization for GRACE-II,” Jet Propulsion Laboratory, California Institute of Technology Tech. Report (2010).

G. Mueller, P. McNamara, I. Thorpe, and J. Camp, “Laser frequency stabilization for LISA,” NASA GSFC Tech. Report 20060012084 (2005).

T. L. Bergman, A. S. Lavine, F. P. Incropera, and D. P. DeWitt, Fundamentals of Heat and Mass Transfer (Wiley, 2011).

M. Nofrarias, “Thermal diagnostics in the LISA technology package,” Ph.D Thesis, Universitat de Barcelona (2007).

H. S. Carslaw and J. C. Jaeger, Heat Conduction in Solids (Oxford Science Publications, 1986).

H. Peabody and S. M. Merkowitz, “Low frequency thermal performance of the LISA sciencecraft,”

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Figures (11)

Fig. 1
Fig. 1

Left: transfer functions using the coupled case Eq. (9) (solid lines) and the uncoupled case Eq. (10) (dashed lines) for N = 3, 4 and 5. The cut-off angular frequency of each layer is ωc (cf. Eq. 6). Notice that some of the poles of the exact solution (cross marks) are at lower frequencies than ωc (C: coupled filters. U: uncoupled filters), which improves the damping for frequencies around ωc. For ω ≳ 10ωc the results are the same. The bottom plot shows the ratio between the coupled and uncoupled solutions. Right: | H ˜ ( ω ) | as a function of the frequency and the number of layers (in logarithmic scale).

Fig. 2
Fig. 2

Ratio between |H(ω, ωc)| and |H(ω, 0.9ωc)| as a function of N and angular frequency. The relative error of the cut-off angular frequency is −10%. The errors in the transfer function are tolerable even for large N if the relative error in ωc is kept smaller than −10%.

Fig. 3
Fig. 3

Top: relative error in ωc due to approximating the volume of a layer to 4πr2h (or 2πrhℓ for cylinders). Bottom: relative error in ωc due to the assumption that the distance between two consecutive layers is zero (ri = rj) when it is not.

Fig. 4
Fig. 4

Number of shields needed as a function of the required attenuation for 0.1 mHz and 1 mHz and different shield thickness, h.

Fig. 5
Fig. 5

Transfer function for different support lengths and cross-sections for two materials and h=0.5 mm. Top left: Ultem 1000. Top right: Macor. The vertical dashed lines indicate min. Bottom left: the attenuation of temperature fluctuations at ωc for different support lengths. We set in this calculations ri+1/ri = 0.9 and As/Aj = 0.1. If < min the attenuation is degraded around ωc compared to a system without the supports (the attenuation at ωc is 1 / 2 —horizontal dashed line). Once > min, increasing the length of the supports improves the damping of temperature fluctuations. This improvement reaches an asymptotic value not too far from min. Bottom right: transfer functions as a function of the frequency for two scenarios with different support lengths and the radiative case only.

Fig. 6
Fig. 6

Left: FEM simulation and theoretical results —cf. Eq. (9) for the transfer function of a thermal shield consisting of four aluminum layers (N=3) considering only radiation. The bottom panel shows the ratio between the results. Right: thermal shield model used for the calculations and simulations. The OR (12.5 cm) is not included in the simulations. The mesh is shown in the left figure inset.

Fig. 7
Fig. 7

FEM simulations and analytical results. Left: temperature fluctuations attenuation at ωc for > min (blue) and < min. (red and black). =70 mm for all the simulations. Right: transfer functions for different models —see Table 2, and the ratios between the simulations and the analytical transfer functions, which indicate the good agreement between them. The simulations failed for frequencies higher than 100 μHz due to numerical resolution issues.

Fig. 8
Fig. 8

Left: FEM simulations (solid lines) and theoretical transfer functions (dashed lines) for different values of the supports cross sections and no radiation between the supports and the shields, εs=0. The model agrees with the simulations when the total area of the supports is significantly smaller than the area of the shield (As/Aj ≲ 0.15) as previously stated. The bottom plot shows the ratio between the simulations and the analytical transfer functions. The discrepancies are significant for As/Aj=0.66 at high frequencies. Right: FEM simulations (solid and dashed lines) for different supports emissivities and As/Aj ratios and the theoretical transfer functions (dash-dotted lines) where εs = 0. The difference between the simulations and the model appears for large emissivity values. The bottom plot shows the ratios between the numerical simulations transfer functions and the analytical model.

Fig. 9
Fig. 9

Electrical circuit equivalent to a thermal shield consisting of N shields including the optical resonator. The thermal resistance and heat capacitance are assumed to be the same for all of the layers except the resonator one.

Fig. 10
Fig. 10

Model including the conductive link in a thermal shield layer. Typically, the support cannot be modeled as a thermal resistance since large thermal gradients are present along it. Instead the Fourier heat transfer equation needs to be solved. The model does not include radiative heat transfer from the supports to the shields.

Fig. 11
Fig. 11

Model including the conductive link and the optical resonator for N thermal shields and the OR.

Tables (2)

Tables Icon

Table 1 Properties of the support materials used for the numerical evaluation in Fig. 5.

Tables Icon

Table 2 Properties of the supports used in Fig. 7 (right panel): ρs=1200 kg m3, cs=7200 J kg−1 K−1, = 0.053 m; properties of the layers of the thermal shield: aluminum with h=1.5 mm, ε=0.03, A2=0.06 m2, r2=0.1 m and r1=0.153 m (2r is the length of cube’s edge).

Equations (41)

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δ ν ν = δ = α δ T ,
q ˙ j ( t ) = σ A j [ T i 4 ( t ) T j 4 ( t ) ] β i j ,
q ˙ j ( t ) = m j c j T ˙ j ( t ) ,
4 σ A j T 0 3 β i j [ T i ( t ) T j ( t ) ] = m j c j T ˙ j ( t )
H ˜ i j ( ω ) = T ˜ j ( ω ) T ˜ i ( ω ) = 1 1 + m j c j β i j 4 σ A j T 0 3 i ω ,
ω c = 4 σ A j T 0 3 m j c j β i j .
θ i j = β i j 4 σ A j T 0 3 ,
C j = m j c j
H ˜ ( ω ) = 1 1 + k = 1 N 1 ( 2 k ) ! ( N + k ) ! ( N k ) ! ( i ω τ ) k = ( 1 + 1 4 i ω τ ) 1 / 2 sec [ ( 2 N + 1 ) csc 1 ( 1 + i ω τ / 2 ) ] .
H ˜ ( ω ) = ( 1 + i ω τ ) N .
H ˜ ( ω ) = [ 1 + τ OR τ ( i ω τ ) N + 1 + k = 1 N [ 1 ( 2 k 1 ) ! ( N + k 1 ) ! ( N k ) ! C OR C + 1 ( 2 k 2 ) ! ( N + k 1 ) ! ( N k + 1 ) ! τ OR τ + 1 ( 2 k ) ! ( N + k ) ! ( N k ) ! ] ( i ω τ ) k ] 1 ,
θ N OR 1 4 ε N σ A OR T 0 3 ,
C OR = m OR c OR ,
H ˜ ( ω ) = sinh q s + q s θ κ s A s ( 1 + i ω τ ) sinh q s + q s θ κ s A s cosh q s
q s 2 ρ s c s κ s i ω ,
β i j = 1 ε j + 1 ε i ε i ( r j r i ) 2 , for spheres
β i j = 1 ε j + 1 ε i ε i ( r j r i ) , for ( infinitely long ) cylinders
ω c = 2 ε σ T 0 3 ρ c h ,
τ shield = θ shield C shield 2 π r 2 ρ c κ
τ shield τ = 4 π r 0.1 κ ε σ T 0 3 ,
h B h A = ρ A c A ρ B c B
m A m B = r A 2 c B r B 2 c A .
N log | H ˜ req | log ω / ω c for ω 10 ω c ,
τ s 2 ρ s c s κ s
min ( ρ c h ε σ T 0 3 κ s c s ρ s ) 1 / 2 ,
lim H ( ω c ) = 1 1 + i + ( i ω c ρ s c s κ s ) 1 / 2 1 C j A s .
H ˜ ( ω ) [ sinh q s + q s θ κ s A s ( 1 + i τ ω ) sinh q s + q s θ κ s A s cosh q s ] N .
T ˜ k T ˜ k + 1 θ q 2 k + 1 = 0 , k = 0 N 1
T ˜ k + 1 1 s C q 2 k + 2 = 0 , k = 0 N 1
q 2 k + 1 q 2 k + 2 q 2 k + 3 = 0 , k = 0 N 1
T ˜ N T ˜ OR θ OR q 2 N + 1 = 0
T ˜ OR 1 s C OR q 2 N + 1 = 0 ,
ρ s c s T ( x , t ) t = κ s 2 T ( x , t ) x 2 , x 0 ,
d 2 T ˜ ( x ) d x 2 q s 2 T ˜ ( x ) = 0 ,
T ˜ ( ) = T ˜ 0
κ s A s d T ˜ ( x ) d x | 0 = i ω C T ˜ ( 0 ) + T ˜ ( 0 ) T ˜ ( ) θ ,
d 2 T ˜ k ( x ) d x 2 q s 2 T ˜ k ( x ) = 0 , ( N ( k 1 ) ) x ( N k )
T ˜ 0 ( ( N + 1 ) ) = T ˜ 0
T ˜ k ( ( N k ) ) = T ˜ k + 1 ( ( N k ) )
κ s A s d T ˜ k ( x ) d x | ( N k ) = i ω C T ˜ k ( ( N k ) ) + + T ˜ k ( ( N k ) ) T ˜ k ( ( N k + 1 ) ) θ
κ s A s d T N ˜ ( x ) d x | 0 = i ω C OR T N ˜ ( 0 ) + T N ˜ ( 0 ) T N ˜ ( ) θ OR ,

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