Abstract

We demonstrate an active power stabilization of a Nd:YAG laser employing the optical ac-coupling scheme and derive its fundamental quantum limit. This limit is 3dB better than the one encountered in traditional power stabilization schemes. In our experiment, the optical ac coupling improved the shot-noise-limited sensitivity of the stabilization photodetector by a factor of 11.2. With an independent photodetector, we measured a relative power stability of 3.7×109Hz1/2 at frequencies of around 200kHz. A detailed investigation of the performance limit of our experiment revealed a novel noise source that disturbed the fundamental mode field in the optical resonator. This effect could be of relevance to many precision experiments using optical resonators.

© 2009 Optical Society of America

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References

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  1. S. Rowan and J. Hough, “Gravitational wave detection by interferometry (ground and space),” Living Rev. Relativity 3 (2000), http://www.livingreviews.org/lrr-2000-3.
  2. K. Somiya, Y. Chen, S. Kawamura, and N. Mio, “Frequency noise and intensity noise of next-generation gravitational-wave detectors with RF/DC readout schemes,” Phys. Rev. D 73, 122005 (2006).
    [CrossRef]
  3. B. Willke, K. Danzmann, M. Frede, P. King, D. Kracht, P. Kwee, O. Punken, R. Savage, B. Schulz, F. Seifert, C. Veltkamp, S. Wagner, P. Weßels, and L. Winkelmann, “Stabilized high power lasers for advanced gravitational wave detectors,” Class. Quantum Grav. 25, 114040 (2008).
    [CrossRef]
  4. F. Seifert, P. Kwee, M. Heurs, B. Willke, and K. Danzmann, “Laser power stabilization for second-generation gravitational wave detectors,” Opt. Lett. 31, 2000-2002 (2006).
    [CrossRef] [PubMed]
  5. J. Rollins, D. Ottaway, M. Zucker, R. Weiss, and R. Abbott, “Solid-state laser intensity stabilization at the 10−8 level,” Opt. Lett. 29, 1876-1878 (2004).
    [CrossRef] [PubMed]
  6. N. Mio, H. Takahashi, and S. Moriwaki, “High-power photo-detection system for next-generation gravitational wave detectors,” J. Phys. Conf. Ser. 122, 012014 (2008).
    [CrossRef]
  7. P. Kwee, B. Willke, and K. Danzmann, “Optical ac coupling to overcome limitations in the detection of optical power fluctuations,” Opt. Lett. 33, 1509-1511 (2008).
    [CrossRef] [PubMed]
  8. T. Klaassen, J. de Jong, M. van Exter, and J. Woerdman, “Transverse mode coupling in an optical resonator,” Opt. Lett. 30, 1959-1961 (2005).
    [CrossRef] [PubMed]
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  10. M. Taubman, H. Wiseman, D. McClelland, and H. Bachor, “Intensity feedback effects on quantum-limited noise,” J. Opt. Soc. Am. B 12, 1792-1800 (1995).
    [CrossRef]
  11. A. E. Siegman, Lasers (University Science, 1986), Chap. 11.
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    [CrossRef]
  13. E. D. Black, “An introduction to Pound-Drever-Hall laser frequency stabilization,” Am. J. Phys. 69, 79-87(2001).
    [CrossRef]
  14. 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]
  15. B. Willke, N. Uehara, E. Gustafson, R. L. Byer, P. J. King, S. U. Seel, and R. L. Savage, “Spatial and temporal filtering of a 10 w Nd:Yag laser with a Fabry-Perot ring-cavity premode cleaner,” Opt. Lett. 23, 1704-1706 (1998).
    [CrossRef]
  16. T. Hansch and B. Couillaud, “Laser frequency stabilization by polarization spectroscopy of a reflecting reference cavity,” Opt. Commun. 35, 441-444 (1980).
    [CrossRef]
  17. N. Uehara, E. K. Gustafson, M. M. Fejer, and R. L. Byer, “Modeling of efficient mode-matching and thermal-lensing effect on a laser-beam coupling into a mode-cleaner cavity,” Proc. SPIE 2989, 57-68 (1997).
    [CrossRef]
  18. T. Klaassen, M. van Exter, and J. Woerdman, “Characterization of scattering in an optical Fabry-Perot resonator,” Appl. Opt. 46, 5210-5215 (2007).
    [CrossRef] [PubMed]
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    [CrossRef]

2008 (3)

B. Willke, K. Danzmann, M. Frede, P. King, D. Kracht, P. Kwee, O. Punken, R. Savage, B. Schulz, F. Seifert, C. Veltkamp, S. Wagner, P. Weßels, and L. Winkelmann, “Stabilized high power lasers for advanced gravitational wave detectors,” Class. Quantum Grav. 25, 114040 (2008).
[CrossRef]

N. Mio, H. Takahashi, and S. Moriwaki, “High-power photo-detection system for next-generation gravitational wave detectors,” J. Phys. Conf. Ser. 122, 012014 (2008).
[CrossRef]

P. Kwee, B. Willke, and K. Danzmann, “Optical ac coupling to overcome limitations in the detection of optical power fluctuations,” Opt. Lett. 33, 1509-1511 (2008).
[CrossRef] [PubMed]

2007 (1)

2006 (2)

F. Seifert, P. Kwee, M. Heurs, B. Willke, and K. Danzmann, “Laser power stabilization for second-generation gravitational wave detectors,” Opt. Lett. 31, 2000-2002 (2006).
[CrossRef] [PubMed]

K. Somiya, Y. Chen, S. Kawamura, and N. Mio, “Frequency noise and intensity noise of next-generation gravitational-wave detectors with RF/DC readout schemes,” Phys. Rev. D 73, 122005 (2006).
[CrossRef]

2005 (1)

2004 (1)

2003 (1)

P. Fritschel, “Second generation instruments for the Laser Interferometer Gravitational Wave Observatory (LIGO),” Proc. SPIE 4856, 282-291 (2003).
[CrossRef]

2001 (1)

E. D. Black, “An introduction to Pound-Drever-Hall laser frequency stabilization,” Am. J. Phys. 69, 79-87(2001).
[CrossRef]

2000 (1)

S. Rowan and J. Hough, “Gravitational wave detection by interferometry (ground and space),” Living Rev. Relativity 3 (2000), http://www.livingreviews.org/lrr-2000-3.

1998 (1)

1997 (1)

N. Uehara, E. K. Gustafson, M. M. Fejer, and R. L. Byer, “Modeling of efficient mode-matching and thermal-lensing effect on a laser-beam coupling into a mode-cleaner cavity,” Proc. SPIE 2989, 57-68 (1997).
[CrossRef]

1995 (2)

I. Freitag, A. Tünnermann, and H. Welling, “Power scaling of diode-pumped monolithic Nd:YAG lasers to output powers of several watts,” Opt. Commun. 115, 511-515 (1995).
[CrossRef]

M. Taubman, H. Wiseman, D. McClelland, and H. Bachor, “Intensity feedback effects on quantum-limited noise,” J. Opt. Soc. Am. B 12, 1792-1800 (1995).
[CrossRef]

1983 (1)

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]

1980 (1)

T. Hansch and B. Couillaud, “Laser frequency stabilization by polarization spectroscopy of a reflecting reference cavity,” Opt. Commun. 35, 441-444 (1980).
[CrossRef]

Abbott, R.

Bachor, H.

Bachor, H.-A.

H.-A. Bachor and T. C. Ralph, A Guide to Experiments in Quantum Optics (Wiley-VCH, 2004), Chap. 8.3.
[CrossRef]

Black, E. D.

E. D. Black, “An introduction to Pound-Drever-Hall laser frequency stabilization,” Am. J. Phys. 69, 79-87(2001).
[CrossRef]

Byer, R. L.

B. Willke, N. Uehara, E. Gustafson, R. L. Byer, P. J. King, S. U. Seel, and R. L. Savage, “Spatial and temporal filtering of a 10 w Nd:Yag laser with a Fabry-Perot ring-cavity premode cleaner,” Opt. Lett. 23, 1704-1706 (1998).
[CrossRef]

N. Uehara, E. K. Gustafson, M. M. Fejer, and R. L. Byer, “Modeling of efficient mode-matching and thermal-lensing effect on a laser-beam coupling into a mode-cleaner cavity,” Proc. SPIE 2989, 57-68 (1997).
[CrossRef]

Chen, Y.

K. Somiya, Y. Chen, S. Kawamura, and N. Mio, “Frequency noise and intensity noise of next-generation gravitational-wave detectors with RF/DC readout schemes,” Phys. Rev. D 73, 122005 (2006).
[CrossRef]

Couillaud, B.

T. Hansch and B. Couillaud, “Laser frequency stabilization by polarization spectroscopy of a reflecting reference cavity,” Opt. Commun. 35, 441-444 (1980).
[CrossRef]

Danzmann, K.

B. Willke, K. Danzmann, M. Frede, P. King, D. Kracht, P. Kwee, O. Punken, R. Savage, B. Schulz, F. Seifert, C. Veltkamp, S. Wagner, P. Weßels, and L. Winkelmann, “Stabilized high power lasers for advanced gravitational wave detectors,” Class. Quantum Grav. 25, 114040 (2008).
[CrossRef]

P. Kwee, B. Willke, and K. Danzmann, “Optical ac coupling to overcome limitations in the detection of optical power fluctuations,” Opt. Lett. 33, 1509-1511 (2008).
[CrossRef] [PubMed]

F. Seifert, P. Kwee, M. Heurs, B. Willke, and K. Danzmann, “Laser power stabilization for second-generation gravitational wave detectors,” Opt. Lett. 31, 2000-2002 (2006).
[CrossRef] [PubMed]

de Jong, J.

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]

Fejer, M. M.

N. Uehara, E. K. Gustafson, M. M. Fejer, and R. L. Byer, “Modeling of efficient mode-matching and thermal-lensing effect on a laser-beam coupling into a mode-cleaner cavity,” Proc. SPIE 2989, 57-68 (1997).
[CrossRef]

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]

Frede, M.

B. Willke, K. Danzmann, M. Frede, P. King, D. Kracht, P. Kwee, O. Punken, R. Savage, B. Schulz, F. Seifert, C. Veltkamp, S. Wagner, P. Weßels, and L. Winkelmann, “Stabilized high power lasers for advanced gravitational wave detectors,” Class. Quantum Grav. 25, 114040 (2008).
[CrossRef]

Freitag, I.

I. Freitag, A. Tünnermann, and H. Welling, “Power scaling of diode-pumped monolithic Nd:YAG lasers to output powers of several watts,” Opt. Commun. 115, 511-515 (1995).
[CrossRef]

Fritschel, P.

P. Fritschel, “Second generation instruments for the Laser Interferometer Gravitational Wave Observatory (LIGO),” Proc. SPIE 4856, 282-291 (2003).
[CrossRef]

Gustafson, E.

Gustafson, E. K.

N. Uehara, E. K. Gustafson, M. M. Fejer, and R. L. Byer, “Modeling of efficient mode-matching and thermal-lensing effect on a laser-beam coupling into a mode-cleaner cavity,” Proc. SPIE 2989, 57-68 (1997).
[CrossRef]

Hall, J. L.

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]

Hansch, T.

T. Hansch and B. Couillaud, “Laser frequency stabilization by polarization spectroscopy of a reflecting reference cavity,” Opt. Commun. 35, 441-444 (1980).
[CrossRef]

Heurs, M.

Hough, J.

S. Rowan and J. Hough, “Gravitational wave detection by interferometry (ground and space),” Living Rev. Relativity 3 (2000), http://www.livingreviews.org/lrr-2000-3.

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]

Kawamura, S.

K. Somiya, Y. Chen, S. Kawamura, and N. Mio, “Frequency noise and intensity noise of next-generation gravitational-wave detectors with RF/DC readout schemes,” Phys. Rev. D 73, 122005 (2006).
[CrossRef]

King, P.

B. Willke, K. Danzmann, M. Frede, P. King, D. Kracht, P. Kwee, O. Punken, R. Savage, B. Schulz, F. Seifert, C. Veltkamp, S. Wagner, P. Weßels, and L. Winkelmann, “Stabilized high power lasers for advanced gravitational wave detectors,” Class. Quantum Grav. 25, 114040 (2008).
[CrossRef]

King, P. J.

Klaassen, T.

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]

Kracht, D.

B. Willke, K. Danzmann, M. Frede, P. King, D. Kracht, P. Kwee, O. Punken, R. Savage, B. Schulz, F. Seifert, C. Veltkamp, S. Wagner, P. Weßels, and L. Winkelmann, “Stabilized high power lasers for advanced gravitational wave detectors,” Class. Quantum Grav. 25, 114040 (2008).
[CrossRef]

Kwee, P.

B. Willke, K. Danzmann, M. Frede, P. King, D. Kracht, P. Kwee, O. Punken, R. Savage, B. Schulz, F. Seifert, C. Veltkamp, S. Wagner, P. Weßels, and L. Winkelmann, “Stabilized high power lasers for advanced gravitational wave detectors,” Class. Quantum Grav. 25, 114040 (2008).
[CrossRef]

P. Kwee, B. Willke, and K. Danzmann, “Optical ac coupling to overcome limitations in the detection of optical power fluctuations,” Opt. Lett. 33, 1509-1511 (2008).
[CrossRef] [PubMed]

F. Seifert, P. Kwee, M. Heurs, B. Willke, and K. Danzmann, “Laser power stabilization for second-generation gravitational wave detectors,” Opt. Lett. 31, 2000-2002 (2006).
[CrossRef] [PubMed]

McClelland, D.

Mio, N.

N. Mio, H. Takahashi, and S. Moriwaki, “High-power photo-detection system for next-generation gravitational wave detectors,” J. Phys. Conf. Ser. 122, 012014 (2008).
[CrossRef]

K. Somiya, Y. Chen, S. Kawamura, and N. Mio, “Frequency noise and intensity noise of next-generation gravitational-wave detectors with RF/DC readout schemes,” Phys. Rev. D 73, 122005 (2006).
[CrossRef]

Moriwaki, S.

N. Mio, H. Takahashi, and S. Moriwaki, “High-power photo-detection system for next-generation gravitational wave detectors,” J. Phys. Conf. Ser. 122, 012014 (2008).
[CrossRef]

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]

Ottaway, D.

Punken, O.

B. Willke, K. Danzmann, M. Frede, P. King, D. Kracht, P. Kwee, O. Punken, R. Savage, B. Schulz, F. Seifert, C. Veltkamp, S. Wagner, P. Weßels, and L. Winkelmann, “Stabilized high power lasers for advanced gravitational wave detectors,” Class. Quantum Grav. 25, 114040 (2008).
[CrossRef]

Ralph, T. C.

H.-A. Bachor and T. C. Ralph, A Guide to Experiments in Quantum Optics (Wiley-VCH, 2004), Chap. 8.3.
[CrossRef]

Rollins, J.

Rowan, S.

S. Rowan and J. Hough, “Gravitational wave detection by interferometry (ground and space),” Living Rev. Relativity 3 (2000), http://www.livingreviews.org/lrr-2000-3.

Savage, R.

B. Willke, K. Danzmann, M. Frede, P. King, D. Kracht, P. Kwee, O. Punken, R. Savage, B. Schulz, F. Seifert, C. Veltkamp, S. Wagner, P. Weßels, and L. Winkelmann, “Stabilized high power lasers for advanced gravitational wave detectors,” Class. Quantum Grav. 25, 114040 (2008).
[CrossRef]

Savage, R. L.

Schulz, B.

B. Willke, K. Danzmann, M. Frede, P. King, D. Kracht, P. Kwee, O. Punken, R. Savage, B. Schulz, F. Seifert, C. Veltkamp, S. Wagner, P. Weßels, and L. Winkelmann, “Stabilized high power lasers for advanced gravitational wave detectors,” Class. Quantum Grav. 25, 114040 (2008).
[CrossRef]

Seel, S. U.

Seifert, F.

B. Willke, K. Danzmann, M. Frede, P. King, D. Kracht, P. Kwee, O. Punken, R. Savage, B. Schulz, F. Seifert, C. Veltkamp, S. Wagner, P. Weßels, and L. Winkelmann, “Stabilized high power lasers for advanced gravitational wave detectors,” Class. Quantum Grav. 25, 114040 (2008).
[CrossRef]

F. Seifert, P. Kwee, M. Heurs, B. Willke, and K. Danzmann, “Laser power stabilization for second-generation gravitational wave detectors,” Opt. Lett. 31, 2000-2002 (2006).
[CrossRef] [PubMed]

Siegman, A. E.

A. E. Siegman, Lasers (University Science, 1986), Chap. 11.

Somiya, K.

K. Somiya, Y. Chen, S. Kawamura, and N. Mio, “Frequency noise and intensity noise of next-generation gravitational-wave detectors with RF/DC readout schemes,” Phys. Rev. D 73, 122005 (2006).
[CrossRef]

Takahashi, H.

N. Mio, H. Takahashi, and S. Moriwaki, “High-power photo-detection system for next-generation gravitational wave detectors,” J. Phys. Conf. Ser. 122, 012014 (2008).
[CrossRef]

Taubman, M.

Tünnermann, A.

I. Freitag, A. Tünnermann, and H. Welling, “Power scaling of diode-pumped monolithic Nd:YAG lasers to output powers of several watts,” Opt. Commun. 115, 511-515 (1995).
[CrossRef]

Uehara, N.

B. Willke, N. Uehara, E. Gustafson, R. L. Byer, P. J. King, S. U. Seel, and R. L. Savage, “Spatial and temporal filtering of a 10 w Nd:Yag laser with a Fabry-Perot ring-cavity premode cleaner,” Opt. Lett. 23, 1704-1706 (1998).
[CrossRef]

N. Uehara, E. K. Gustafson, M. M. Fejer, and R. L. Byer, “Modeling of efficient mode-matching and thermal-lensing effect on a laser-beam coupling into a mode-cleaner cavity,” Proc. SPIE 2989, 57-68 (1997).
[CrossRef]

van Exter, M.

Veltkamp, C.

B. Willke, K. Danzmann, M. Frede, P. King, D. Kracht, P. Kwee, O. Punken, R. Savage, B. Schulz, F. Seifert, C. Veltkamp, S. Wagner, P. Weßels, and L. Winkelmann, “Stabilized high power lasers for advanced gravitational wave detectors,” Class. Quantum Grav. 25, 114040 (2008).
[CrossRef]

Wagner, S.

B. Willke, K. Danzmann, M. Frede, P. King, D. Kracht, P. Kwee, O. Punken, R. Savage, B. Schulz, F. Seifert, C. Veltkamp, S. Wagner, P. Weßels, and L. Winkelmann, “Stabilized high power lasers for advanced gravitational wave detectors,” Class. Quantum Grav. 25, 114040 (2008).
[CrossRef]

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]

Weiss, R.

Welling, H.

I. Freitag, A. Tünnermann, and H. Welling, “Power scaling of diode-pumped monolithic Nd:YAG lasers to output powers of several watts,” Opt. Commun. 115, 511-515 (1995).
[CrossRef]

Weßels, P.

B. Willke, K. Danzmann, M. Frede, P. King, D. Kracht, P. Kwee, O. Punken, R. Savage, B. Schulz, F. Seifert, C. Veltkamp, S. Wagner, P. Weßels, and L. Winkelmann, “Stabilized high power lasers for advanced gravitational wave detectors,” Class. Quantum Grav. 25, 114040 (2008).
[CrossRef]

Willke, B.

Winkelmann, L.

B. Willke, K. Danzmann, M. Frede, P. King, D. Kracht, P. Kwee, O. Punken, R. Savage, B. Schulz, F. Seifert, C. Veltkamp, S. Wagner, P. Weßels, and L. Winkelmann, “Stabilized high power lasers for advanced gravitational wave detectors,” Class. Quantum Grav. 25, 114040 (2008).
[CrossRef]

Wiseman, H.

Woerdman, J.

Zucker, M.

Am. J. Phys. (1)

E. D. Black, “An introduction to Pound-Drever-Hall laser frequency stabilization,” Am. J. Phys. 69, 79-87(2001).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. B (1)

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]

Class. Quantum Grav. (1)

B. Willke, K. Danzmann, M. Frede, P. King, D. Kracht, P. Kwee, O. Punken, R. Savage, B. Schulz, F. Seifert, C. Veltkamp, S. Wagner, P. Weßels, and L. Winkelmann, “Stabilized high power lasers for advanced gravitational wave detectors,” Class. Quantum Grav. 25, 114040 (2008).
[CrossRef]

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

J. Phys. Conf. Ser. (1)

N. Mio, H. Takahashi, and S. Moriwaki, “High-power photo-detection system for next-generation gravitational wave detectors,” J. Phys. Conf. Ser. 122, 012014 (2008).
[CrossRef]

Living Rev. Relativity (1)

S. Rowan and J. Hough, “Gravitational wave detection by interferometry (ground and space),” Living Rev. Relativity 3 (2000), http://www.livingreviews.org/lrr-2000-3.

Opt. Commun. (2)

T. Hansch and B. Couillaud, “Laser frequency stabilization by polarization spectroscopy of a reflecting reference cavity,” Opt. Commun. 35, 441-444 (1980).
[CrossRef]

I. Freitag, A. Tünnermann, and H. Welling, “Power scaling of diode-pumped monolithic Nd:YAG lasers to output powers of several watts,” Opt. Commun. 115, 511-515 (1995).
[CrossRef]

Opt. Lett. (5)

Phys. Rev. D (1)

K. Somiya, Y. Chen, S. Kawamura, and N. Mio, “Frequency noise and intensity noise of next-generation gravitational-wave detectors with RF/DC readout schemes,” Phys. Rev. D 73, 122005 (2006).
[CrossRef]

Proc. SPIE (2)

N. Uehara, E. K. Gustafson, M. M. Fejer, and R. L. Byer, “Modeling of efficient mode-matching and thermal-lensing effect on a laser-beam coupling into a mode-cleaner cavity,” Proc. SPIE 2989, 57-68 (1997).
[CrossRef]

P. Fritschel, “Second generation instruments for the Laser Interferometer Gravitational Wave Observatory (LIGO),” Proc. SPIE 4856, 282-291 (2003).
[CrossRef]

Other (2)

H.-A. Bachor and T. C. Ralph, A Guide to Experiments in Quantum Optics (Wiley-VCH, 2004), Chap. 8.3.
[CrossRef]

A. E. Siegman, Lasers (University Science, 1986), Chap. 11.

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Figures (7)

Fig. 1
Fig. 1

Models used for calculating the quantum noise limit of three different power stabilization schemes: (a) traditional power stabilization, (b) traditional power stabilization with additional resonator in the out-of-loop path, and (c) power stabilization with optical ac coupling. The relative power noise of the out-of-loop fields A ool , a , A ool , b , and A ool , c were calculated as functions of the input field A las and the vacuum fields A vac .

Fig. 2
Fig. 2

Shot-noise limit for different power stabilization schemes. The limits are given in relation to the relative shot noise of the original beam. Traditional power stabilizations are always 3 to 6 dB above this reference. A stabilization with optical ac coupling is very close to the relative shot noise of the original beam for Fourier frequencies above the resonator bandwidth.

Fig. 3
Fig. 3

Resonator model used to simulate the complex field amplitudes inside and outside the resonator. To simplify matters, only two possible modes and a coupling between them are considered.

Fig. 4
Fig. 4

Experimental setup. The laser (NPRO) was filtered by a mode cleaner (MC) and locked to the ac-coupling cavity (ACC). The power noise was measured with detector LPD in reflection of the ACC for the power stabilization control loop. Detector HPD was used as an out-of-loop detector to independently measure the power noise in front of the ACC. Details of the purpose of the other components are given in Section 3. EOM, electro-optic phase modulator; EOAM, electro-optic amplitude modulator; FI, Faraday isolator; PBS, polarizing beam splitter; IPD, servo control filters; λ / 2 , λ / 4 , wave plates.

Fig. 5
Fig. 5

Typical out-of-loop power noise measurements performed with the HPD detector. Scattering to higher- order modes (curve a) or into the countercirculating fundamental mode (curve b) limited the power stability. The expected limits without any scattering are shown as smooth solid curve (curves a * , b * ). For the case of scattering to the countercirculating fundamental mode, a projection of the power noise due to scattering is shown (curve c, see Subsection 4B).

Fig. 6
Fig. 6

Excitation of higher-order transverse modes by resonator internal scattering. The resonance frequencies of the modes changed with the input power due to a radius of curvature change of the cavity mirrors caused by absorption of a fraction of the circulating power. When a higher-order mode came into resonance, the power in reflection of the ACC was increased. The higher-order modes have been effectively suppressed by a resonator internal aperture.

Fig. 7
Fig. 7

Out-of-loop measured power noise (HPD) using different power stabilization schemes. The results are close to their shot noise limits. With optical ac coupling (OAC) the power stability (curve c) achieved is significantly better than with the equivalent traditional stabilization scheme (curve b).

Equations (11)

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G ( f ) = g ( g 1 ) h ( f ) ,
h ( f ) = 1 1 + i f / f 0 .
U in = U 0 · exp ( i Ω t + i m cos ( ω t ) ) U 0 · ( 1 + i m 2 e i ω t + i m 2 e i ω t ) · e i Ω t ,
U circ U 0 ( h ( ϵ ) + i m 2 e i ω t h ( f + ϵ ) + i m 2 e i ω t h ( f + ϵ ) ) .
N F ( f ) = 2 ϵ g 2 f 0 2 h ( f ) .
U in = U 0 · ( 1 | U 1 | 2 | U 0 | 2 m e i ω t ) + U 1 · ( 1 + m e i ω t ) .
N M ( f ) = | U 1 | 2 | U 0 | 2 / g 2 + | U 1 | 2 .
a = ( a 0 a 1 ) ,
a = S · P · a .
P = ( r 0 e i ϕ 0 0 0 r 1 e i ϕ 1 ) .
S = ( 1 C 2 i C i C 1 C 2 ) .

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