Abstract

Temperature dependent structural distortion at the contacted mirrors of low-expansion glass cavities can introduce changes to the cavity length independent of the length of the spacer. There are resulting temperature sensitivities of the path (m/K) at each end of a cavity that are proportional to the difference of the coefficient of thermal expansion (α) at the contact. The temperature sensitivity of the resonant frequency can be a minimum at a temperature TC if the product of length times α(TC) of the spacer approximately offsets the combined sensitivities of the ends, even if α(TC) of the spacer is significantly nonzero.

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  1. Ch. Eisele, M. Okhapkin, A. Yu. Nevsky, and S. Schiller, “A crossed optical cavities apparatus for a precision test of the isotropy of light propagation,” Opt. Commun. 281(5), 1189–1196 (2008).
    [CrossRef]
  2. 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 1x10(-15).,” Opt. Lett. 32(6), 641–643 (2007).
    [CrossRef] [PubMed]
  3. ULE and TSG are trademarks of Corning Inc., and mention here is for technical clarity only and does not imply endorsement.
  4. 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]
  5. N. M. Sampas, E. K. Gustafson, and R. L. Byer, “Long-term stability of two diode-laser-pumped nonplanar ring lasers independently stabilized to two Fabry-Perot interferometers,” Opt. Lett. 18(12), 947–949 (1993).
    [CrossRef] [PubMed]
  6. N. Poli, R. E. Drullinger, G. Ferrari, M. Prevedelli, F. Sorrentino, M. G. Tarallo, and G. M. Tino, “Prospect for a compact strontium optical lattice clock,” Proc. SPIE 6673 (2007).
  7. J. Alnis, A. Matveev, N. Kolachevsky, T. Wilken, Th. 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]
  8. S. F. Jacobs, J. W. Berthold, and J. Osmundsen, “Ultraprecise measurement of thermal expansion coefficients – recent progress,” AIP conf. Proceedings, New York (1970).
  9. 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), 1807–1810 (1995).
    [CrossRef]
  10. K. Numata, A. Kemery, and J. Camp, “Thermal-noise limit in the frequency stabilization of lasers with rigid cavities,” Phys. Rev. Lett. 93(25), 250602 (2004).
    [CrossRef]
  11. J. W. Berthold and S. F. Jacobs, “Ultraprecise thermal expansion measurements of seven low expansion materials,” Appl. Opt. 15(10), 2344–2347 (1976).
    [CrossRef]
  12. S. F. Jacobs, “Dimensional stability of materials useful in optical engineering,” Opt. Acta (Lond.) 33(11), 1377–1388 (1986).
    [CrossRef]
  13. H. Takashashi, “Temperature stability of thin-film narrow-bandpass filters produced by ion-assisted deposition,” Appl. Opt. 34(4), 667–675 (1995).
    [CrossRef] [PubMed]
  14. Based on the slope of the phase of the Ta2O5-SiO2 coatings used here, 10 mr/nm, and a spectral shift of such coatings on low expansion glass of Δν/ν ~−10−5 K−1 [13].
  15. A. E. Siegman, Lasers, (University Research Books, 1986).
  16. M. Fukuhara and A. Sampei, “Effects on high-temperature-elastic properties on α-/β-quartz phase transition of fused quartz,” J. Mater. Sci. Lett. 18(10), 751–753 (1999).
    [CrossRef]
  17. R. R. VanBrocklin, M. J. Edwards, and B. Wells, “Review of Corning’s capabilities for ULE mirror blank manufacturing for an extremely large telescope,” Proc. SPIE 6273–01, 1–11 (2006).
  18. Fused Silica CTE from 5 − 35 C adapted from the expression in SRM 739: http://ts.nist.gov/MeasurementServices/ReferenceMaterials/archived_certificates/739.pdf
  19. ULE and TSG Product Information Sheets, Corning Advanced Optics, 334 County Rt., 16, Canton, New York 13617 (2006). http://www.corning.com/docs/specialtymaterials/pisheets/TSGBro91106.pdf http://www.corning.com/docs/specialtymaterials/pisheets/UleBro91106.pdf
  20. M. Edwards, Corning Inc., private communication, α(T) = K0 + 2.21T - 0.0122T2 + 1.88e-5T3 ppb/K, T in Celsius (2006).
  21. R. W. Fox, “Fabry-Perot temperature dependence and surface-mounted optical cavities,” Proc. SPIE 7099 (2008). (available as arXiv:0807.0656v1 [physics.optics]).
  22. Ansys Workbench Simulation, V11.0. Mentioned only for technical clarity, no endorsement implied.
  23. D. Coyne, “Beamsplitter coating strain induced radius of curvature,” LIGO document LIGO-T050057–00-D (2005).
  24. M. Okaji, N. Yamada, K. Nara, and H. Kato, “Laser interferometric dilatometer at low temperatures: application to fused silica SRM 739,” Cryogenics 35(12), 887–891 (1995).
    [CrossRef]

2008 (3)

Ch. Eisele, M. Okhapkin, A. Yu. Nevsky, and S. Schiller, “A crossed optical cavities apparatus for a precision test of the isotropy of light propagation,” Opt. Commun. 281(5), 1189–1196 (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]

J. Alnis, A. Matveev, N. Kolachevsky, T. Wilken, Th. 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]

2007 (1)

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(25), 250602 (2004).
[CrossRef]

1999 (1)

M. Fukuhara and A. Sampei, “Effects on high-temperature-elastic properties on α-/β-quartz phase transition of fused quartz,” J. Mater. Sci. Lett. 18(10), 751–753 (1999).
[CrossRef]

1995 (3)

M. Okaji, N. Yamada, K. Nara, and H. Kato, “Laser interferometric dilatometer at low temperatures: application to fused silica SRM 739,” Cryogenics 35(12), 887–891 (1995).
[CrossRef]

H. Takashashi, “Temperature stability of thin-film narrow-bandpass filters produced by ion-assisted deposition,” Appl. Opt. 34(4), 667–675 (1995).
[CrossRef] [PubMed]

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), 1807–1810 (1995).
[CrossRef]

1993 (1)

1986 (1)

S. F. Jacobs, “Dimensional stability of materials useful in optical engineering,” Opt. Acta (Lond.) 33(11), 1377–1388 (1986).
[CrossRef]

1976 (1)

Alnis, J.

J. Alnis, A. Matveev, N. Kolachevsky, T. Wilken, Th. 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]

Berthold, J. W.

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), 1807–1810 (1995).
[CrossRef]

Blatt, S.

Boyd, M. M.

Byer, R. L.

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(25), 250602 (2004).
[CrossRef]

Eisele, Ch.

Ch. Eisele, M. Okhapkin, A. Yu. Nevsky, and S. Schiller, “A crossed optical cavities apparatus for a precision test of the isotropy of light propagation,” Opt. Commun. 281(5), 1189–1196 (2008).
[CrossRef]

Foreman, S. M.

Fukuhara, M.

M. Fukuhara and A. Sampei, “Effects on high-temperature-elastic properties on α-/β-quartz phase transition of fused quartz,” J. Mater. Sci. Lett. 18(10), 751–753 (1999).
[CrossRef]

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]

Gustafson, E. K.

Hänsch, T. W.

J. Alnis, A. Matveev, N. Kolachevsky, T. Wilken, Th. 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]

Huang, X.

Jacobs, S. F.

S. F. Jacobs, “Dimensional stability of materials useful in optical engineering,” Opt. Acta (Lond.) 33(11), 1377–1388 (1986).
[CrossRef]

J. W. Berthold and S. F. Jacobs, “Ultraprecise thermal expansion measurements of seven low expansion materials,” Appl. Opt. 15(10), 2344–2347 (1976).
[CrossRef]

Kato, H.

M. Okaji, N. Yamada, K. Nara, and H. Kato, “Laser interferometric dilatometer at low temperatures: application to fused silica SRM 739,” Cryogenics 35(12), 887–891 (1995).
[CrossRef]

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(25), 250602 (2004).
[CrossRef]

Kolachevsky, N.

J. Alnis, A. Matveev, N. Kolachevsky, T. Wilken, Th. 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]

Ludlow, A. D.

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), 1807–1810 (1995).
[CrossRef]

Matveev, A.

J. Alnis, A. Matveev, N. Kolachevsky, T. Wilken, Th. 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]

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]

Nara, K.

M. Okaji, N. Yamada, K. Nara, and H. Kato, “Laser interferometric dilatometer at low temperatures: application to fused silica SRM 739,” Cryogenics 35(12), 887–891 (1995).
[CrossRef]

Nevsky, A. Yu.

Ch. Eisele, M. Okhapkin, A. Yu. Nevsky, and S. Schiller, “A crossed optical cavities apparatus for a precision test of the isotropy of light propagation,” Opt. Commun. 281(5), 1189–1196 (2008).
[CrossRef]

Notcutt, M.

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 1x10(-15).,” Opt. Lett. 32(6), 641–643 (2007).
[CrossRef] [PubMed]

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), 1807–1810 (1995).
[CrossRef]

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(25), 250602 (2004).
[CrossRef]

Okaji, M.

M. Okaji, N. Yamada, K. Nara, and H. Kato, “Laser interferometric dilatometer at low temperatures: application to fused silica SRM 739,” Cryogenics 35(12), 887–891 (1995).
[CrossRef]

Okhapkin, M.

Ch. Eisele, M. Okhapkin, A. Yu. Nevsky, and S. Schiller, “A crossed optical cavities apparatus for a precision test of the isotropy of light propagation,” Opt. Commun. 281(5), 1189–1196 (2008).
[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]

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]

Sampas, N. M.

Sampei, A.

M. Fukuhara and A. Sampei, “Effects on high-temperature-elastic properties on α-/β-quartz phase transition of fused quartz,” J. Mater. Sci. Lett. 18(10), 751–753 (1999).
[CrossRef]

Schiller, S.

Ch. Eisele, M. Okhapkin, A. Yu. Nevsky, and S. Schiller, “A crossed optical cavities apparatus for a precision test of the isotropy of light propagation,” Opt. Commun. 281(5), 1189–1196 (2008).
[CrossRef]

Takashashi, H.

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), 1807–1810 (1995).
[CrossRef]

Udem, Th.

J. Alnis, A. Matveev, N. Kolachevsky, T. Wilken, Th. 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]

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]

Wilken, T.

J. Alnis, A. Matveev, N. Kolachevsky, T. Wilken, Th. 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]

Yamada, N.

M. Okaji, N. Yamada, K. Nara, and H. Kato, “Laser interferometric dilatometer at low temperatures: application to fused silica SRM 739,” Cryogenics 35(12), 887–891 (1995).
[CrossRef]

Ye, J.

Zanon-Willette, T.

Appl. Opt. (2)

Cryogenics (1)

M. Okaji, N. Yamada, K. Nara, and H. Kato, “Laser interferometric dilatometer at low temperatures: application to fused silica SRM 739,” Cryogenics 35(12), 887–891 (1995).
[CrossRef]

J. Mater. Sci. Lett. (1)

M. Fukuhara and A. Sampei, “Effects on high-temperature-elastic properties on α-/β-quartz phase transition of fused quartz,” J. Mater. Sci. Lett. 18(10), 751–753 (1999).
[CrossRef]

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), 1807–1810 (1995).
[CrossRef]

Opt. Acta (Lond.) (1)

S. F. Jacobs, “Dimensional stability of materials useful in optical engineering,” Opt. Acta (Lond.) 33(11), 1377–1388 (1986).
[CrossRef]

Opt. Commun. (1)

Ch. Eisele, M. Okhapkin, A. Yu. Nevsky, and S. Schiller, “A crossed optical cavities apparatus for a precision test of the isotropy of light propagation,” Opt. Commun. 281(5), 1189–1196 (2008).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. A (2)

J. Alnis, A. Matveev, N. Kolachevsky, T. Wilken, Th. 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]

Phys. Rev. Lett. (1)

K. Numata, A. Kemery, and J. Camp, “Thermal-noise limit in the frequency stabilization of lasers with rigid cavities,” Phys. Rev. Lett. 93(25), 250602 (2004).
[CrossRef]

Other (12)

Based on the slope of the phase of the Ta2O5-SiO2 coatings used here, 10 mr/nm, and a spectral shift of such coatings on low expansion glass of Δν/ν ~−10−5 K−1 [13].

A. E. Siegman, Lasers, (University Research Books, 1986).

N. Poli, R. E. Drullinger, G. Ferrari, M. Prevedelli, F. Sorrentino, M. G. Tarallo, and G. M. Tino, “Prospect for a compact strontium optical lattice clock,” Proc. SPIE 6673 (2007).

ULE and TSG are trademarks of Corning Inc., and mention here is for technical clarity only and does not imply endorsement.

R. R. VanBrocklin, M. J. Edwards, and B. Wells, “Review of Corning’s capabilities for ULE mirror blank manufacturing for an extremely large telescope,” Proc. SPIE 6273–01, 1–11 (2006).

Fused Silica CTE from 5 − 35 C adapted from the expression in SRM 739: http://ts.nist.gov/MeasurementServices/ReferenceMaterials/archived_certificates/739.pdf

ULE and TSG Product Information Sheets, Corning Advanced Optics, 334 County Rt., 16, Canton, New York 13617 (2006). http://www.corning.com/docs/specialtymaterials/pisheets/TSGBro91106.pdf http://www.corning.com/docs/specialtymaterials/pisheets/UleBro91106.pdf

M. Edwards, Corning Inc., private communication, α(T) = K0 + 2.21T - 0.0122T2 + 1.88e-5T3 ppb/K, T in Celsius (2006).

R. W. Fox, “Fabry-Perot temperature dependence and surface-mounted optical cavities,” Proc. SPIE 7099 (2008). (available as arXiv:0807.0656v1 [physics.optics]).

Ansys Workbench Simulation, V11.0. Mentioned only for technical clarity, no endorsement implied.

D. Coyne, “Beamsplitter coating strain induced radius of curvature,” LIGO document LIGO-T050057–00-D (2005).

S. F. Jacobs, J. W. Berthold, and J. Osmundsen, “Ultraprecise measurement of thermal expansion coefficients – recent progress,” AIP conf. Proceedings, New York (1970).

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Figures (5)

Fig. 1
Fig. 1

(Top) Nominal CTE of fused silica per NIST Standard Reference Material 739 [18]. (Lower) CTE bounds of ULE (dashed) and TSG. The ULE(TSG) glass specifications state that within the range of 5 to 35 C, the mean value of the CTE is within the limits of ± 30 ( ± 100) ppb/K [19]. The nominal temperature dependence, which is given graphically in references [12] and [19], is approximately α(T) = K0 + 2.21T – 0.0122T 2 ppb/K [20] over this limited temperature range shown. No data concerning the statistical variability of the higher-order coefficients of the CTE was found during this work.

Fig. 2
Fig. 2

(Left) A cross section of the 98.04 mm long spacer. (Right) Red: optical frequency versus temperature of a cavity mode with fused silica mirrors contacted. Blue: frequency of a cavity mode with ULE mirrors contacted to the same spacer. The missing data are times when the laser is unlocked.

Fig. 3
Fig. 3

The FEA graphical results of deformation in the direction of the optical axis caused by a + 1 K temperature change for the case of a 5.75 mm thick fused silica mirror contacted to the one inch diameter spacer, with αS = 0 ppb/K and αM = 520 ppb/K. The range of the color bar is + 3.5 nm to −2.5 nm, with positive numbers indicating an elongation of the cavity. (Left) The coated mirror with the spacer hidden. The center of the coating moves + 3.2 nm/K in the z direction, while the contacted area (outside the white ring) distorts in the opposite direction. (Right) The end of the spacer with the coating and substrate hidden.

Fig. 4
Fig. 4

The temperature sensitivity of one end of a cavity as a function of the CTE difference between a fused silica mirror and the TSG spacer shown in Fig. 2. Red dots, calculated ln values for the case of a 25.4 mm diameter, 5.75 mm thick mirror with the geometry and coating described in the text. A linear fit, and the fit residuals (crosses, right axis) are also shown.

Fig. 5
Fig. 5

The spacer CTE as deduced from a fit to the frequency data of Fig. 2 using Eq. (4) and the FEA calculations of end distortion. The expansivity, or curvature of the spacer’s CTE is assumed as given in Fig. 1 and only the absolute value (y-intercept) is solved for. The band between the red traces is the range of the spacer CTE resulting from a fit to the cavity data with fused silica mirrors contacted. Similarly, the band between the blue traces is the range of the spacer CTE resulting from a fit to the cavity data with ULE mirrors contacted. In both cases the width of the uncertainty band is due to the mirror CTE uncertainty. Consistent with both measurements are CTE curves that cross zero CTE between 17 and 19 C (cross hatched).

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

ν=mc2l,
ν=νo(1Δllo).
ν=c2l(m+2ϕ2π).
ν(T)=νo(11loToT[lSαS(T)+l1(T)+l2(T)]dT)+c2loϕπ(TTo).
ln(T)=A(αMαS)+B.

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