Abstract

We present a simple technique to actively stabilize the optical path length in an optical fiber. A part of the fiber is coated with a thin, electrically conductive layer, which acts as a heater. The optical path length is thus modified by temperature-dependent changes in the refractive index and the mechanical length of the fiber. For the first time, we measure the dynamic response of the optical path length to the periodic changes of temperature and find it to be in agreement with our former theoretical prediction. The fiber’s response to the temperature changes is determined by the speed of sound in quartz rather than by slow thermal diffusion. Making use of this fact, we succeeded in actively stabilizing the optical path length with a closed-loop bandwidth of 3.8kHz.

© 2009 Optical Society of America

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2006 (1)

H. Müller, A. Peters, and C. Braxmaier, “Optical fibers with interferometric path length stability by controlled heating for transmission of optical signals and as components in frequency standards,” Appl. Phys. B 84, 401-408 (2006).
[Crossref]

2005 (2)

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]

2002 (1)

T. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature 416, 233-237 (2002).
[Crossref] [PubMed]

1999 (2)

B. C. Young, F. C. Cruz, W. M. Itano, and J. C. Bergquist, “Visible lasers with subhertz linewidths,” Phys. Rev. Lett. 82, 3799-3802 (1999).
[Crossref]

K. Imai, Y. Zhao, M. Kourogi, B. Widiyatmoko, and M. Ohtsu, “Accuracy of optical comb generation in optical fiber,” Opt. Lett. 24, 214-216 (1999).
[Crossref]

1997 (1)

M. J. Matthewson, C. R. Kurkjian, and J. R. Hamblin, “Acid stripping of fused silica optical fibers without strength degradation,” J. Lightwave Technol. 15, 490-497 (1997).
[Crossref]

1994 (1)

1983 (2)

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97-105 (1983).
[Crossref]

L. S. Schuetz, J. H. Cole, J. Jarzynski, N. Lagakos, and J. A. Bucaro, “Dynamic thermal response of single-mode optical fiber for interferometric sensors,” Appl. Opt. 22, 478-483 (1983).
[Crossref] [PubMed]

1982 (2)

T. Musha, J. Kamimura, and M. Nakazawa, “Optical phase fluctuations thermally induced in a single-mode optical fiber,” Appl. Opt. 21, 694-698 (1982).
[Crossref] [PubMed]

S. J. Petuchowski, G. H. Sigel, and T. G. Giallorenzi, “Single-mode-fibre point and extended temperature sensors,” Electron. Lett. 18, 814-815 (1982).
[Crossref]

1980 (1)

1977 (1)

Bergquist, J. C.

B. C. Young, F. C. Cruz, W. M. Itano, and J. C. Bergquist, “Visible lasers with subhertz linewidths,” Phys. Rev. Lett. 82, 3799-3802 (1999).
[Crossref]

Braxmaier, C.

H. Müller, A. Peters, and C. Braxmaier, “Optical fibers with interferometric path length stability by controlled heating for transmission of optical signals and as components in frequency standards,” Appl. Phys. B 84, 401-408 (2006).
[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]

Bucaro, J. A.

Carome, E. F.

Cole, J. H.

Cruz, F. C.

B. C. Young, F. C. Cruz, W. M. Itano, and J. C. Bergquist, “Visible lasers with subhertz linewidths,” Phys. Rev. Lett. 82, 3799-3802 (1999).
[Crossref]

Dardy, H. D.

Drever, R. W. P.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97-105 (1983).
[Crossref]

Eichenseer, M.

Ford, G. M.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97-105 (1983).
[Crossref]

Giallorenzi, T. G.

S. J. Petuchowski, G. H. Sigel, and T. G. Giallorenzi, “Single-mode-fibre point and extended temperature sensors,” Electron. Lett. 18, 814-815 (1982).
[Crossref]

Hall, J. L.

Hamblin, J. R.

M. J. Matthewson, C. R. Kurkjian, and J. R. Hamblin, “Acid stripping of fused silica optical fibers without strength degradation,” J. Lightwave Technol. 15, 490-497 (1997).
[Crossref]

Hänsch, T. W.

T. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature 416, 233-237 (2002).
[Crossref] [PubMed]

Herrmann, 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]

Holzwarth, R.

T. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature 416, 233-237 (2002).
[Crossref] [PubMed]

Hough, J.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97-105 (1983).
[Crossref]

Hughes, R.

Imai, K.

Itano, W. M.

B. C. Young, F. C. Cruz, W. M. Itano, and J. C. Bergquist, “Visible lasers with subhertz linewidths,” Phys. Rev. Lett. 82, 3799-3802 (1999).
[Crossref]

Jarzynski, J.

Jungner, P.

Kamimura, J.

Kourogi, M.

Kowalski, F. V.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97-105 (1983).
[Crossref]

Kurkjian, C. R.

M. J. Matthewson, C. R. Kurkjian, and J. R. Hamblin, “Acid stripping of fused silica optical fibers without strength degradation,” J. Lightwave Technol. 15, 490-497 (1997).
[Crossref]

Lagakos, N.

Ma, L.-S.

Matthewson, M. J.

M. J. Matthewson, C. R. Kurkjian, and J. R. Hamblin, “Acid stripping of fused silica optical fibers without strength degradation,” J. Lightwave Technol. 15, 490-497 (1997).
[Crossref]

Müller, H.

H. Müller, A. Peters, and C. Braxmaier, “Optical fibers with interferometric path length stability by controlled heating for transmission of optical signals and as components in frequency standards,” Appl. Phys. B 84, 401-408 (2006).
[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]

Munley, A. J.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97-105 (1983).
[Crossref]

Musha, T.

Nakazawa, M.

Notcutt, M.

Ohtsu, M.

Peters, A.

H. Müller, A. Peters, and C. Braxmaier, “Optical fibers with interferometric path length stability by controlled heating for transmission of optical signals and as components in frequency standards,” Appl. Phys. B 84, 401-408 (2006).
[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]

Petuchowski, S. J.

S. J. Petuchowski, G. H. Sigel, and T. G. Giallorenzi, “Single-mode-fibre point and extended temperature sensors,” Electron. Lett. 18, 814-815 (1982).
[Crossref]

Priest, R.

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]

Schuetz, L. S.

Sigel, G. H.

S. J. Petuchowski, G. H. Sigel, and T. G. Giallorenzi, “Single-mode-fibre point and extended temperature sensors,” Electron. Lett. 18, 814-815 (1982).
[Crossref]

Udem, T.

T. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature 416, 233-237 (2002).
[Crossref] [PubMed]

Walther, H.

Ward, H.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97-105 (1983).
[Crossref]

Widiyatmoko, B.

Ye, J.

Young, B. C.

B. C. Young, F. C. Cruz, W. M. Itano, and J. C. Bergquist, “Visible lasers with subhertz linewidths,” Phys. Rev. Lett. 82, 3799-3802 (1999).
[Crossref]

Zanthier, J. V.

Zhao, Y.

Appl. Opt. (4)

Appl. Phys. B (2)

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97-105 (1983).
[Crossref]

H. Müller, A. Peters, and C. Braxmaier, “Optical fibers with interferometric path length stability by controlled heating for transmission of optical signals and as components in frequency standards,” Appl. Phys. B 84, 401-408 (2006).
[Crossref]

Electron. Lett. (1)

S. J. Petuchowski, G. H. Sigel, and T. G. Giallorenzi, “Single-mode-fibre point and extended temperature sensors,” Electron. Lett. 18, 814-815 (1982).
[Crossref]

J. Lightwave Technol. (1)

M. J. Matthewson, C. R. Kurkjian, and J. R. Hamblin, “Acid stripping of fused silica optical fibers without strength degradation,” J. Lightwave Technol. 15, 490-497 (1997).
[Crossref]

Nature (1)

T. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature 416, 233-237 (2002).
[Crossref] [PubMed]

Opt. Lett. (4)

Phys. Rev. Lett. (2)

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]

B. C. Young, F. C. Cruz, W. M. Itano, and J. C. Bergquist, “Visible lasers with subhertz linewidths,” Phys. Rev. Lett. 82, 3799-3802 (1999).
[Crossref]

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Figures (4)

Fig. 1
Fig. 1

Experimental setup.

Fig. 2
Fig. 2

Frequency response (transfer function) of the fiber core length to the heating of the outer copper coating: theoretical prediction (dashed) and measurement (solid). The amplitude is shown in micrometers of the fiber length per 1 W of the heating power deposited in 1 m of the heater. 1 / f decay of the amplitude and phase change of less than 180 ° ensures a good closed-loop performance for the frequencies in the lower kilohertz domain. An acoustic resonance at 20 kHz limits the lock bandwidth.

Fig. 3
Fig. 3

Closed-loop gain of the active stabilization. The unity gain point is at 3.8 kHz , and the phase at this point does not exceed its critical value of 180 ° .

Fig. 4
Fig. 4

Sine of the phase fluctuations induced in the optical fiber (DC output from the mixer) free running (left) and with the active length stabilization (right). Acoustic noise at 20 and 200 Hz dominates. Without stabilization, the phase fluctuation easily exceeds 2 π for longer measurement times. With active stabilization, the residual phase fluctuations are of the order of microradians, which corresponds to the absolute length stability better than λ / 150 .

Equations (1)

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ϕ = 2 π n L λ ,

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