Abstract

We show that temperature compensation based on differential thermal expansion between sapphire and fused silica can be used to create a Fabry–Perot cavity with an exceptionally low coefficient of thermal expansion at low temperatures. We describe the design of such a cavity that utilizes shaped fused silica mirrors and a sapphire spacer. The geometry of the fused silica mirror was designed using a finite element model to have a small platform, giving a frequency temperature turning point of 16.6 K. The measured turning point was 16.2 K and the curvature was 6 × 10−10 K−2, both of which were consistent with the model.

© 1997 Optical Society of America

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  1. Y. Sakai, I. Yokohama, T. Kominato, S. Sudo, “Frequency stabilization of laser diode using a frequency-locked ring resonator to acetylene gas absorption lines,” IEEE Photon. Technol. Lett. 3, 868–870 (1991).
    [CrossRef]
  2. A. Arie, S. Schiller, E. K. Gustafson, R. L. Byer, “Absolute frequency stabilization of diode-laser-pumped Nd:YAG lasers to hyperfine transitions in molecular iodine,” Opt. Lett. 17, 1204–1206 (1992).
    [CrossRef] [PubMed]
  3. E. T. Peng, S. F. Ahmed, C. B. Su, “Frequency stabilization of a travelling wave semiconductor ring laser using a fiber resonator as a frequency reference,” IEEE Photon. Technol. Lett. 6, 334–337 (1994).
    [CrossRef]
  4. N. M. Sampas, E. K. Gustafson, R. L. Byer, “Long-term stability of two diode-laser-pumped nonplanar ring lasers independently stabilized to two Fabry–Perot interferometers,” Opt. Lett. 18, 947–949 (1993).
    [CrossRef] [PubMed]
  5. J. P. Richard, J. J. Hamilton, “Cryogenic monocrystalline silicon Fabry–Perot cavity for the stabilization of laser frequency,” Rev. Sci. Instrum. 62, 2375–2378 (1991).
    [CrossRef]
  6. C. T. Taylor, M. Notcutt, D. G. Blair, “Cryogenic, all-sapphire Fabry–Perot optical frequency reference,” Rev. Sci. Instrum. 66, 955–960 (1995).
    [CrossRef]
  7. D. G. Blair, M. Notcutt, C. T. Taylor, E. K. Wong, C. Walsh, A. Leistner, J. Seckold, J. M. Mackowski, P. Ganau, C. Michel, L. Pinard, “Development of low loss sapphire mirrors,” Appl. Opt. 36, 337–341 (1997).
    [CrossRef] [PubMed]
  8. M. Notcutt, C. T. Taylor, A. G. Mann, D. G. Blair, “Temperature compensation for cryogenic cavity stabilised lasers,” J Phys. D 28, 1807–1810 (1995).
    [CrossRef]
  9. G Care, G Steven, D Kelly, strand6.1 Computer Software (G+D Computing Pty., Ltd., New South Wales, Australia, 1989).
  10. C. T. Taylor, M. Notcutt, E. K. Wong, A. G. Mann, D. G. Blair, “Measurement of the thermal expansion coefficient of an all-sapphire optical cavity,” IEEE Trans. Instrum. Meas. 46, 183–185 (1997).
    [CrossRef]
  11. M. Notcutt, C. T. Taylor, A. G. Mann, R. Gummer, D. G. Blair, “Cryogenic system for a sapphire Fabry–Perot optical frequency standard,” Cryogenics 36, 13–16 (1996).
    [CrossRef]

1997 (2)

D. G. Blair, M. Notcutt, C. T. Taylor, E. K. Wong, C. Walsh, A. Leistner, J. Seckold, J. M. Mackowski, P. Ganau, C. Michel, L. Pinard, “Development of low loss sapphire mirrors,” Appl. Opt. 36, 337–341 (1997).
[CrossRef] [PubMed]

C. T. Taylor, M. Notcutt, E. K. Wong, A. G. Mann, D. G. Blair, “Measurement of the thermal expansion coefficient of an all-sapphire optical cavity,” IEEE Trans. Instrum. Meas. 46, 183–185 (1997).
[CrossRef]

1996 (1)

M. Notcutt, C. T. Taylor, A. G. Mann, R. Gummer, D. G. Blair, “Cryogenic system for a sapphire Fabry–Perot optical frequency standard,” Cryogenics 36, 13–16 (1996).
[CrossRef]

1995 (2)

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

C. T. Taylor, M. Notcutt, D. G. Blair, “Cryogenic, all-sapphire Fabry–Perot optical frequency reference,” Rev. Sci. Instrum. 66, 955–960 (1995).
[CrossRef]

1994 (1)

E. T. Peng, S. F. Ahmed, C. B. Su, “Frequency stabilization of a travelling wave semiconductor ring laser using a fiber resonator as a frequency reference,” IEEE Photon. Technol. Lett. 6, 334–337 (1994).
[CrossRef]

1993 (1)

1992 (1)

1991 (2)

Y. Sakai, I. Yokohama, T. Kominato, S. Sudo, “Frequency stabilization of laser diode using a frequency-locked ring resonator to acetylene gas absorption lines,” IEEE Photon. Technol. Lett. 3, 868–870 (1991).
[CrossRef]

J. P. Richard, J. J. Hamilton, “Cryogenic monocrystalline silicon Fabry–Perot cavity for the stabilization of laser frequency,” Rev. Sci. Instrum. 62, 2375–2378 (1991).
[CrossRef]

Ahmed, S. F.

E. T. Peng, S. F. Ahmed, C. B. Su, “Frequency stabilization of a travelling wave semiconductor ring laser using a fiber resonator as a frequency reference,” IEEE Photon. Technol. Lett. 6, 334–337 (1994).
[CrossRef]

Arie, A.

Blair, D. G.

D. G. Blair, M. Notcutt, C. T. Taylor, E. K. Wong, C. Walsh, A. Leistner, J. Seckold, J. M. Mackowski, P. Ganau, C. Michel, L. Pinard, “Development of low loss sapphire mirrors,” Appl. Opt. 36, 337–341 (1997).
[CrossRef] [PubMed]

C. T. Taylor, M. Notcutt, E. K. Wong, A. G. Mann, D. G. Blair, “Measurement of the thermal expansion coefficient of an all-sapphire optical cavity,” IEEE Trans. Instrum. Meas. 46, 183–185 (1997).
[CrossRef]

M. Notcutt, C. T. Taylor, A. G. Mann, R. Gummer, D. G. Blair, “Cryogenic system for a sapphire Fabry–Perot optical frequency standard,” Cryogenics 36, 13–16 (1996).
[CrossRef]

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

C. T. Taylor, M. Notcutt, D. G. Blair, “Cryogenic, all-sapphire Fabry–Perot optical frequency reference,” Rev. Sci. Instrum. 66, 955–960 (1995).
[CrossRef]

Byer, R. L.

Care, G

G Care, G Steven, D Kelly, strand6.1 Computer Software (G+D Computing Pty., Ltd., New South Wales, Australia, 1989).

Ganau, P.

Gummer, R.

M. Notcutt, C. T. Taylor, A. G. Mann, R. Gummer, D. G. Blair, “Cryogenic system for a sapphire Fabry–Perot optical frequency standard,” Cryogenics 36, 13–16 (1996).
[CrossRef]

Gustafson, E. K.

Hamilton, J. J.

J. P. Richard, J. J. Hamilton, “Cryogenic monocrystalline silicon Fabry–Perot cavity for the stabilization of laser frequency,” Rev. Sci. Instrum. 62, 2375–2378 (1991).
[CrossRef]

Kelly, D

G Care, G Steven, D Kelly, strand6.1 Computer Software (G+D Computing Pty., Ltd., New South Wales, Australia, 1989).

Kominato, T.

Y. Sakai, I. Yokohama, T. Kominato, S. Sudo, “Frequency stabilization of laser diode using a frequency-locked ring resonator to acetylene gas absorption lines,” IEEE Photon. Technol. Lett. 3, 868–870 (1991).
[CrossRef]

Leistner, A.

Mackowski, J. M.

Mann, A. G.

C. T. Taylor, M. Notcutt, E. K. Wong, A. G. Mann, D. G. Blair, “Measurement of the thermal expansion coefficient of an all-sapphire optical cavity,” IEEE Trans. Instrum. Meas. 46, 183–185 (1997).
[CrossRef]

M. Notcutt, C. T. Taylor, A. G. Mann, R. Gummer, D. G. Blair, “Cryogenic system for a sapphire Fabry–Perot optical frequency standard,” Cryogenics 36, 13–16 (1996).
[CrossRef]

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

Michel, C.

Notcutt, M.

D. G. Blair, M. Notcutt, C. T. Taylor, E. K. Wong, C. Walsh, A. Leistner, J. Seckold, J. M. Mackowski, P. Ganau, C. Michel, L. Pinard, “Development of low loss sapphire mirrors,” Appl. Opt. 36, 337–341 (1997).
[CrossRef] [PubMed]

C. T. Taylor, M. Notcutt, E. K. Wong, A. G. Mann, D. G. Blair, “Measurement of the thermal expansion coefficient of an all-sapphire optical cavity,” IEEE Trans. Instrum. Meas. 46, 183–185 (1997).
[CrossRef]

M. Notcutt, C. T. Taylor, A. G. Mann, R. Gummer, D. G. Blair, “Cryogenic system for a sapphire Fabry–Perot optical frequency standard,” Cryogenics 36, 13–16 (1996).
[CrossRef]

C. T. Taylor, M. Notcutt, D. G. Blair, “Cryogenic, all-sapphire Fabry–Perot optical frequency reference,” Rev. Sci. Instrum. 66, 955–960 (1995).
[CrossRef]

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

Peng, E. T.

E. T. Peng, S. F. Ahmed, C. B. Su, “Frequency stabilization of a travelling wave semiconductor ring laser using a fiber resonator as a frequency reference,” IEEE Photon. Technol. Lett. 6, 334–337 (1994).
[CrossRef]

Pinard, L.

Richard, J. P.

J. P. Richard, J. J. Hamilton, “Cryogenic monocrystalline silicon Fabry–Perot cavity for the stabilization of laser frequency,” Rev. Sci. Instrum. 62, 2375–2378 (1991).
[CrossRef]

Sakai, Y.

Y. Sakai, I. Yokohama, T. Kominato, S. Sudo, “Frequency stabilization of laser diode using a frequency-locked ring resonator to acetylene gas absorption lines,” IEEE Photon. Technol. Lett. 3, 868–870 (1991).
[CrossRef]

Sampas, N. M.

Schiller, S.

Seckold, J.

Steven, G

G Care, G Steven, D Kelly, strand6.1 Computer Software (G+D Computing Pty., Ltd., New South Wales, Australia, 1989).

Su, C. B.

E. T. Peng, S. F. Ahmed, C. B. Su, “Frequency stabilization of a travelling wave semiconductor ring laser using a fiber resonator as a frequency reference,” IEEE Photon. Technol. Lett. 6, 334–337 (1994).
[CrossRef]

Sudo, S.

Y. Sakai, I. Yokohama, T. Kominato, S. Sudo, “Frequency stabilization of laser diode using a frequency-locked ring resonator to acetylene gas absorption lines,” IEEE Photon. Technol. Lett. 3, 868–870 (1991).
[CrossRef]

Taylor, C. T.

D. G. Blair, M. Notcutt, C. T. Taylor, E. K. Wong, C. Walsh, A. Leistner, J. Seckold, J. M. Mackowski, P. Ganau, C. Michel, L. Pinard, “Development of low loss sapphire mirrors,” Appl. Opt. 36, 337–341 (1997).
[CrossRef] [PubMed]

C. T. Taylor, M. Notcutt, E. K. Wong, A. G. Mann, D. G. Blair, “Measurement of the thermal expansion coefficient of an all-sapphire optical cavity,” IEEE Trans. Instrum. Meas. 46, 183–185 (1997).
[CrossRef]

M. Notcutt, C. T. Taylor, A. G. Mann, R. Gummer, D. G. Blair, “Cryogenic system for a sapphire Fabry–Perot optical frequency standard,” Cryogenics 36, 13–16 (1996).
[CrossRef]

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

C. T. Taylor, M. Notcutt, D. G. Blair, “Cryogenic, all-sapphire Fabry–Perot optical frequency reference,” Rev. Sci. Instrum. 66, 955–960 (1995).
[CrossRef]

Walsh, C.

Wong, E. K.

D. G. Blair, M. Notcutt, C. T. Taylor, E. K. Wong, C. Walsh, A. Leistner, J. Seckold, J. M. Mackowski, P. Ganau, C. Michel, L. Pinard, “Development of low loss sapphire mirrors,” Appl. Opt. 36, 337–341 (1997).
[CrossRef] [PubMed]

C. T. Taylor, M. Notcutt, E. K. Wong, A. G. Mann, D. G. Blair, “Measurement of the thermal expansion coefficient of an all-sapphire optical cavity,” IEEE Trans. Instrum. Meas. 46, 183–185 (1997).
[CrossRef]

Yokohama, I.

Y. Sakai, I. Yokohama, T. Kominato, S. Sudo, “Frequency stabilization of laser diode using a frequency-locked ring resonator to acetylene gas absorption lines,” IEEE Photon. Technol. Lett. 3, 868–870 (1991).
[CrossRef]

Appl. Opt. (1)

Cryogenics (1)

M. Notcutt, C. T. Taylor, A. G. Mann, R. Gummer, D. G. Blair, “Cryogenic system for a sapphire Fabry–Perot optical frequency standard,” Cryogenics 36, 13–16 (1996).
[CrossRef]

IEEE Photon. Technol. Lett. (2)

Y. Sakai, I. Yokohama, T. Kominato, S. Sudo, “Frequency stabilization of laser diode using a frequency-locked ring resonator to acetylene gas absorption lines,” IEEE Photon. Technol. Lett. 3, 868–870 (1991).
[CrossRef]

E. T. Peng, S. F. Ahmed, C. B. Su, “Frequency stabilization of a travelling wave semiconductor ring laser using a fiber resonator as a frequency reference,” IEEE Photon. Technol. Lett. 6, 334–337 (1994).
[CrossRef]

IEEE Trans. Instrum. Meas. (1)

C. T. Taylor, M. Notcutt, E. K. Wong, A. G. Mann, D. G. Blair, “Measurement of the thermal expansion coefficient of an all-sapphire optical cavity,” IEEE Trans. Instrum. Meas. 46, 183–185 (1997).
[CrossRef]

J Phys. D (1)

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

Opt. Lett. (2)

Rev. Sci. Instrum. (2)

J. P. Richard, J. J. Hamilton, “Cryogenic monocrystalline silicon Fabry–Perot cavity for the stabilization of laser frequency,” Rev. Sci. Instrum. 62, 2375–2378 (1991).
[CrossRef]

C. T. Taylor, M. Notcutt, D. G. Blair, “Cryogenic, all-sapphire Fabry–Perot optical frequency reference,” Rev. Sci. Instrum. 66, 955–960 (1995).
[CrossRef]

Other (1)

G Care, G Steven, D Kelly, strand6.1 Computer Software (G+D Computing Pty., Ltd., New South Wales, Australia, 1989).

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Figures (4)

Fig. 1
Fig. 1

(a) Shape of the curved mirror with platform thickness of tp. The back of the fused silica mirror has antireflection coatings (A-RC). (b) Schematic diagram of the composite optical cavity with a curved mirror (CM) and a flat mirror (FM).

Fig. 2
Fig. 2

CTE of the composite cavity for tp = 0.70 mm (δ = −0.153, —△---); tp = 0.80 mm (δ = −0.147, —■—); tp = 0.90 mm (δ = −0.141, —◇—); and tp = 1.00 mm (δ = −0.136, ----○----) as functions of temperature, showing how the turning point can be tuned.

Fig. 3
Fig. 3

Measurements and finite element model calculations for a platform thickness of 0.90 mm.

Fig. 4
Fig. 4

Beat frequency versus temperature curve of the composite cavity for a temperature sweep from 13 to 22 K. The curve shows that a frequency temperature turning point occurs at 16.2 K.

Equations (4)

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Δ R = R ( α sap - α fs ) Δ T ,
Δ l X = Δ T [ α sap L - α fs t p + δ c R ( α sap - α fs ) ] ,
Δ l Y = Δ T [ α sap L + δ f R ( α sap - α fs ) ] ,
α T = Δ l total 2 L Δ T = α sap - α fs t p 2 L + δ R 2 L ( α sap - α fs ) ,

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