Abstract

Large ring lasers have exceeded the performance of navigational gyroscopes by several orders of magnitude and have become useful tools for geodesy. In order to apply them to tests in fundamental physics, remaining systematic errors have to be significantly reduced. We derive a modified expression for the Sagnac frequency of a square ring laser gyro under Earth rotation. The modifications include corrections for dispersion (of both the gain medium and the mirrors), for the Goos–Hänchen effect in the mirrors, and for refractive index of the gas filling the cavity. The corrections were measured and calculated for the 16  m2 Grossring laser located at the Geodetic Observatory Wettzell. The optical frequency and the free spectral range of this laser were measured, allowing unique determination of the longitudinal mode number, and measurement of the dispersion. Ultimately we find that the absolute scale factor of the gyroscope can be estimated to an accuracy of approximately 1 part in 108.

© 2017 Optical Society of America

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References

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    [Crossref]
  2. K. U. Schreiber, T. Klügel, J.-P. R. Wells, R. B. Hurst, and A. Gebauer, “How to detect the chandler and the annual wobble of the earth with a large ring laser gyroscope,” Phys. Rev. Lett. 107, 173904 (2011).
    [Crossref]
  3. K. U. Schreiber, A. Velikoseltsev, M. Rothacher, T. Klügel, G. Stedman, and D. L. Wiltshire, “Direct measurement of diurnal polar motion by ring laser gyroscopes,” J. Geophys. Res. Solid Earth 109, B06405 (2004).
    [Crossref]
  4. F. Bosi, G. Cella, A. Di Virgilio, A. Ortolan, A. Porzio, S. Solimeno, M. Cerdonio, J. P. Zendri, M. Allegrini, M. Allegrini, J. Belfi, N. Beverini, B. Bouhadef, G. Carelli, I. Ferrante, E. Maccioni, R. Passaquieti, F. Stefani, M. L. Ruggiero, A. Tartaglia, K. U. Schreiber, A. Gebauer, and J.-P. R. Wells, “Measuring gravitomagnetic effects by a multi-ring-laser gyroscope,” Phys. Rev. D 84, 122002 (2011).
    [Crossref]
  5. R. B. Hurst, N. Rabeendran, K. U. Schreiber, and J.-P. R. Wells, “Correction of backscatter-induced systematic errors in ring laser gyroscopes,” Appl. Opt. 53, 7610–7618 (2014).
    [Crossref]
  6. K. U. Schreiber and J.-P. R. Wells, “Invited review article: large ring lasers for rotation sensing,” Rev. Sci. Instrum. 84, 041101 (2013).
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    [Crossref]
  12. J. Holdaway, R. B. Hurst, R. Graham, N. Rabeendran, K. U. Schreiber, and J.-P. R. Wells, “Self-locked operation of large He-Ne ring laser gyroscopes,” Metrologia 49, 209–212 (2012).
    [Crossref]
  13. K. U. Schreiber, A. Gebauer, and J.-P. R. Wells, “Closed-loop locking of an optical frequency comb to a large ring laser,” Opt. Lett. 38, 3574–3577 (2013).
    [Crossref]
  14. R. B. Hurst, R. W. Dunn, K. U. Schreiber, R. J. Thirkettle, and G. MacDonald, “Mode behavior in ultralarge ring lasers,” Appl. Opt. 43, 2337–2346 (2004).
    [Crossref]
  15. D. H. Foster, A. K. Cook, and J. U. Nöckel, “Goos-Hänchen induced vector eigenmodes in a dome cavity,” Opt. Lett. 32, 1764–1766 (2007).
    [Crossref]
  16. R. B. Hurst, J.-P. R. Wells, and G. Stedman, “An elementary proof of the geometrical dependence of the Sagnac effect,” J. Opt. A 9, 838–841 (2007).
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    [Crossref]
  18. D. Cuccato, A. Beghi, J. Belfi, N. Beverini, and A. Ortolan, “Controlling the non-linear intracavity dynamics of large He–Ne laser gyroscopes,” Metrologia 51, 97–107 (2014).
  19. K. U. Schreiber, A. Gebauer, and J.-P. R. Wells, “Long-term frequency stabilization of a 16  m2 ring laser gyroscope,” Opt. Lett. 37, 1925–1927 (2012).
    [Crossref]
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  21. R. W. Dunn, H. H. Mahdi, H. J. Al-Shukri, and H. J. Al-Shukri, “Design of a relatively inexpensive ring laser seismic detector,” Bull. Seismol. Soc. Am. 99, 1437–1442 (2009).
    [Crossref]
  22. P. W. Smith, “The effect of cross relaxation on the behavior of gas laser oscillators,” IEEE J. Quantum Electron. QE-8, 704–709 (1972).

2014 (2)

D. Cuccato, A. Beghi, J. Belfi, N. Beverini, and A. Ortolan, “Controlling the non-linear intracavity dynamics of large He–Ne laser gyroscopes,” Metrologia 51, 97–107 (2014).

R. B. Hurst, N. Rabeendran, K. U. Schreiber, and J.-P. R. Wells, “Correction of backscatter-induced systematic errors in ring laser gyroscopes,” Appl. Opt. 53, 7610–7618 (2014).
[Crossref]

2013 (2)

K. U. Schreiber, A. Gebauer, and J.-P. R. Wells, “Closed-loop locking of an optical frequency comb to a large ring laser,” Opt. Lett. 38, 3574–3577 (2013).
[Crossref]

K. U. Schreiber and J.-P. R. Wells, “Invited review article: large ring lasers for rotation sensing,” Rev. Sci. Instrum. 84, 041101 (2013).

2012 (2)

J. Holdaway, R. B. Hurst, R. Graham, N. Rabeendran, K. U. Schreiber, and J.-P. R. Wells, “Self-locked operation of large He-Ne ring laser gyroscopes,” Metrologia 49, 209–212 (2012).
[Crossref]

K. U. Schreiber, A. Gebauer, and J.-P. R. Wells, “Long-term frequency stabilization of a 16  m2 ring laser gyroscope,” Opt. Lett. 37, 1925–1927 (2012).
[Crossref]

2011 (2)

K. U. Schreiber, T. Klügel, J.-P. R. Wells, R. B. Hurst, and A. Gebauer, “How to detect the chandler and the annual wobble of the earth with a large ring laser gyroscope,” Phys. Rev. Lett. 107, 173904 (2011).
[Crossref]

F. Bosi, G. Cella, A. Di Virgilio, A. Ortolan, A. Porzio, S. Solimeno, M. Cerdonio, J. P. Zendri, M. Allegrini, M. Allegrini, J. Belfi, N. Beverini, B. Bouhadef, G. Carelli, I. Ferrante, E. Maccioni, R. Passaquieti, F. Stefani, M. L. Ruggiero, A. Tartaglia, K. U. Schreiber, A. Gebauer, and J.-P. R. Wells, “Measuring gravitomagnetic effects by a multi-ring-laser gyroscope,” Phys. Rev. D 84, 122002 (2011).
[Crossref]

2009 (3)

K. U. Schreiber, T. Klügel, A. Velikoseltsev, W. Schlüter, G. Stedman, and J.-P. R. Wells, “The large ring laser G for continuous earth rotation monitoring,” Pure Appl. Geophys. 166, 1485–1498 (2009).
[Crossref]

R. W. Dunn, H. H. Mahdi, H. J. Al-Shukri, and H. J. Al-Shukri, “Design of a relatively inexpensive ring laser seismic detector,” Bull. Seismol. Soc. Am. 99, 1437–1442 (2009).
[Crossref]

R. B. Hurst, G. Stedman, K. U. Schreiber, R. J. Thirkettle, R. Graham, N. Rabeendran, and J.-P. R. Wells, “Experiments with an 834  m2 ring laser interferometer,” J. Appl. Phys. 105, 113115 (2009).
[Crossref]

2007 (2)

D. H. Foster, A. K. Cook, and J. U. Nöckel, “Goos-Hänchen induced vector eigenmodes in a dome cavity,” Opt. Lett. 32, 1764–1766 (2007).
[Crossref]

R. B. Hurst, J.-P. R. Wells, and G. Stedman, “An elementary proof of the geometrical dependence of the Sagnac effect,” J. Opt. A 9, 838–841 (2007).
[Crossref]

2004 (3)

J. Stone and A. Stejskal, “Using helium as a standard of refractive index: correcting errors in a gas refractometer,” Metrologia 41, 189–197 (2004).
[Crossref]

K. U. Schreiber, A. Velikoseltsev, M. Rothacher, T. Klügel, G. Stedman, and D. L. Wiltshire, “Direct measurement of diurnal polar motion by ring laser gyroscopes,” J. Geophys. Res. Solid Earth 109, B06405 (2004).
[Crossref]

R. B. Hurst, R. W. Dunn, K. U. Schreiber, R. J. Thirkettle, and G. MacDonald, “Mode behavior in ultralarge ring lasers,” Appl. Opt. 43, 2337–2346 (2004).
[Crossref]

1991 (1)

1972 (1)

P. W. Smith, “The effect of cross relaxation on the behavior of gas laser oscillators,” IEEE J. Quantum Electron. QE-8, 704–709 (1972).

1967 (1)

E. J. Post, “Sagnac effect,” Rev. Modern Phys. 39, 475–493 (1967).
[Crossref]

Allegrini, M.

F. Bosi, G. Cella, A. Di Virgilio, A. Ortolan, A. Porzio, S. Solimeno, M. Cerdonio, J. P. Zendri, M. Allegrini, M. Allegrini, J. Belfi, N. Beverini, B. Bouhadef, G. Carelli, I. Ferrante, E. Maccioni, R. Passaquieti, F. Stefani, M. L. Ruggiero, A. Tartaglia, K. U. Schreiber, A. Gebauer, and J.-P. R. Wells, “Measuring gravitomagnetic effects by a multi-ring-laser gyroscope,” Phys. Rev. D 84, 122002 (2011).
[Crossref]

F. Bosi, G. Cella, A. Di Virgilio, A. Ortolan, A. Porzio, S. Solimeno, M. Cerdonio, J. P. Zendri, M. Allegrini, M. Allegrini, J. Belfi, N. Beverini, B. Bouhadef, G. Carelli, I. Ferrante, E. Maccioni, R. Passaquieti, F. Stefani, M. L. Ruggiero, A. Tartaglia, K. U. Schreiber, A. Gebauer, and J.-P. R. Wells, “Measuring gravitomagnetic effects by a multi-ring-laser gyroscope,” Phys. Rev. D 84, 122002 (2011).
[Crossref]

Al-Shukri, H. J.

R. W. Dunn, H. H. Mahdi, H. J. Al-Shukri, and H. J. Al-Shukri, “Design of a relatively inexpensive ring laser seismic detector,” Bull. Seismol. Soc. Am. 99, 1437–1442 (2009).
[Crossref]

R. W. Dunn, H. H. Mahdi, H. J. Al-Shukri, and H. J. Al-Shukri, “Design of a relatively inexpensive ring laser seismic detector,” Bull. Seismol. Soc. Am. 99, 1437–1442 (2009).
[Crossref]

Beghi, A.

D. Cuccato, A. Beghi, J. Belfi, N. Beverini, and A. Ortolan, “Controlling the non-linear intracavity dynamics of large He–Ne laser gyroscopes,” Metrologia 51, 97–107 (2014).

Belfi, J.

D. Cuccato, A. Beghi, J. Belfi, N. Beverini, and A. Ortolan, “Controlling the non-linear intracavity dynamics of large He–Ne laser gyroscopes,” Metrologia 51, 97–107 (2014).

F. Bosi, G. Cella, A. Di Virgilio, A. Ortolan, A. Porzio, S. Solimeno, M. Cerdonio, J. P. Zendri, M. Allegrini, M. Allegrini, J. Belfi, N. Beverini, B. Bouhadef, G. Carelli, I. Ferrante, E. Maccioni, R. Passaquieti, F. Stefani, M. L. Ruggiero, A. Tartaglia, K. U. Schreiber, A. Gebauer, and J.-P. R. Wells, “Measuring gravitomagnetic effects by a multi-ring-laser gyroscope,” Phys. Rev. D 84, 122002 (2011).
[Crossref]

Beverini, N.

D. Cuccato, A. Beghi, J. Belfi, N. Beverini, and A. Ortolan, “Controlling the non-linear intracavity dynamics of large He–Ne laser gyroscopes,” Metrologia 51, 97–107 (2014).

F. Bosi, G. Cella, A. Di Virgilio, A. Ortolan, A. Porzio, S. Solimeno, M. Cerdonio, J. P. Zendri, M. Allegrini, M. Allegrini, J. Belfi, N. Beverini, B. Bouhadef, G. Carelli, I. Ferrante, E. Maccioni, R. Passaquieti, F. Stefani, M. L. Ruggiero, A. Tartaglia, K. U. Schreiber, A. Gebauer, and J.-P. R. Wells, “Measuring gravitomagnetic effects by a multi-ring-laser gyroscope,” Phys. Rev. D 84, 122002 (2011).
[Crossref]

Birch, K. P.

Bosi, F.

F. Bosi, G. Cella, A. Di Virgilio, A. Ortolan, A. Porzio, S. Solimeno, M. Cerdonio, J. P. Zendri, M. Allegrini, M. Allegrini, J. Belfi, N. Beverini, B. Bouhadef, G. Carelli, I. Ferrante, E. Maccioni, R. Passaquieti, F. Stefani, M. L. Ruggiero, A. Tartaglia, K. U. Schreiber, A. Gebauer, and J.-P. R. Wells, “Measuring gravitomagnetic effects by a multi-ring-laser gyroscope,” Phys. Rev. D 84, 122002 (2011).
[Crossref]

Bouhadef, B.

F. Bosi, G. Cella, A. Di Virgilio, A. Ortolan, A. Porzio, S. Solimeno, M. Cerdonio, J. P. Zendri, M. Allegrini, M. Allegrini, J. Belfi, N. Beverini, B. Bouhadef, G. Carelli, I. Ferrante, E. Maccioni, R. Passaquieti, F. Stefani, M. L. Ruggiero, A. Tartaglia, K. U. Schreiber, A. Gebauer, and J.-P. R. Wells, “Measuring gravitomagnetic effects by a multi-ring-laser gyroscope,” Phys. Rev. D 84, 122002 (2011).
[Crossref]

Carelli, G.

F. Bosi, G. Cella, A. Di Virgilio, A. Ortolan, A. Porzio, S. Solimeno, M. Cerdonio, J. P. Zendri, M. Allegrini, M. Allegrini, J. Belfi, N. Beverini, B. Bouhadef, G. Carelli, I. Ferrante, E. Maccioni, R. Passaquieti, F. Stefani, M. L. Ruggiero, A. Tartaglia, K. U. Schreiber, A. Gebauer, and J.-P. R. Wells, “Measuring gravitomagnetic effects by a multi-ring-laser gyroscope,” Phys. Rev. D 84, 122002 (2011).
[Crossref]

Cella, G.

F. Bosi, G. Cella, A. Di Virgilio, A. Ortolan, A. Porzio, S. Solimeno, M. Cerdonio, J. P. Zendri, M. Allegrini, M. Allegrini, J. Belfi, N. Beverini, B. Bouhadef, G. Carelli, I. Ferrante, E. Maccioni, R. Passaquieti, F. Stefani, M. L. Ruggiero, A. Tartaglia, K. U. Schreiber, A. Gebauer, and J.-P. R. Wells, “Measuring gravitomagnetic effects by a multi-ring-laser gyroscope,” Phys. Rev. D 84, 122002 (2011).
[Crossref]

Cerdonio, M.

F. Bosi, G. Cella, A. Di Virgilio, A. Ortolan, A. Porzio, S. Solimeno, M. Cerdonio, J. P. Zendri, M. Allegrini, M. Allegrini, J. Belfi, N. Beverini, B. Bouhadef, G. Carelli, I. Ferrante, E. Maccioni, R. Passaquieti, F. Stefani, M. L. Ruggiero, A. Tartaglia, K. U. Schreiber, A. Gebauer, and J.-P. R. Wells, “Measuring gravitomagnetic effects by a multi-ring-laser gyroscope,” Phys. Rev. D 84, 122002 (2011).
[Crossref]

Cook, A. K.

Cuccato, D.

D. Cuccato, A. Beghi, J. Belfi, N. Beverini, and A. Ortolan, “Controlling the non-linear intracavity dynamics of large He–Ne laser gyroscopes,” Metrologia 51, 97–107 (2014).

Di Virgilio, A.

F. Bosi, G. Cella, A. Di Virgilio, A. Ortolan, A. Porzio, S. Solimeno, M. Cerdonio, J. P. Zendri, M. Allegrini, M. Allegrini, J. Belfi, N. Beverini, B. Bouhadef, G. Carelli, I. Ferrante, E. Maccioni, R. Passaquieti, F. Stefani, M. L. Ruggiero, A. Tartaglia, K. U. Schreiber, A. Gebauer, and J.-P. R. Wells, “Measuring gravitomagnetic effects by a multi-ring-laser gyroscope,” Phys. Rev. D 84, 122002 (2011).
[Crossref]

Dobrowolski, J. A.

J. A. Dobrowolski, Handbook of Optics, 2nd ed. (McGraw-Hill, 1985), Vol. 1.

Dunn, R. W.

R. W. Dunn, H. H. Mahdi, H. J. Al-Shukri, and H. J. Al-Shukri, “Design of a relatively inexpensive ring laser seismic detector,” Bull. Seismol. Soc. Am. 99, 1437–1442 (2009).
[Crossref]

R. B. Hurst, R. W. Dunn, K. U. Schreiber, R. J. Thirkettle, and G. MacDonald, “Mode behavior in ultralarge ring lasers,” Appl. Opt. 43, 2337–2346 (2004).
[Crossref]

Ferrante, I.

F. Bosi, G. Cella, A. Di Virgilio, A. Ortolan, A. Porzio, S. Solimeno, M. Cerdonio, J. P. Zendri, M. Allegrini, M. Allegrini, J. Belfi, N. Beverini, B. Bouhadef, G. Carelli, I. Ferrante, E. Maccioni, R. Passaquieti, F. Stefani, M. L. Ruggiero, A. Tartaglia, K. U. Schreiber, A. Gebauer, and J.-P. R. Wells, “Measuring gravitomagnetic effects by a multi-ring-laser gyroscope,” Phys. Rev. D 84, 122002 (2011).
[Crossref]

Foster, D. H.

Gebauer, A.

K. U. Schreiber, A. Gebauer, and J.-P. R. Wells, “Closed-loop locking of an optical frequency comb to a large ring laser,” Opt. Lett. 38, 3574–3577 (2013).
[Crossref]

K. U. Schreiber, A. Gebauer, and J.-P. R. Wells, “Long-term frequency stabilization of a 16  m2 ring laser gyroscope,” Opt. Lett. 37, 1925–1927 (2012).
[Crossref]

F. Bosi, G. Cella, A. Di Virgilio, A. Ortolan, A. Porzio, S. Solimeno, M. Cerdonio, J. P. Zendri, M. Allegrini, M. Allegrini, J. Belfi, N. Beverini, B. Bouhadef, G. Carelli, I. Ferrante, E. Maccioni, R. Passaquieti, F. Stefani, M. L. Ruggiero, A. Tartaglia, K. U. Schreiber, A. Gebauer, and J.-P. R. Wells, “Measuring gravitomagnetic effects by a multi-ring-laser gyroscope,” Phys. Rev. D 84, 122002 (2011).
[Crossref]

K. U. Schreiber, T. Klügel, J.-P. R. Wells, R. B. Hurst, and A. Gebauer, “How to detect the chandler and the annual wobble of the earth with a large ring laser gyroscope,” Phys. Rev. Lett. 107, 173904 (2011).
[Crossref]

Graham, R.

J. Holdaway, R. B. Hurst, R. Graham, N. Rabeendran, K. U. Schreiber, and J.-P. R. Wells, “Self-locked operation of large He-Ne ring laser gyroscopes,” Metrologia 49, 209–212 (2012).
[Crossref]

R. B. Hurst, G. Stedman, K. U. Schreiber, R. J. Thirkettle, R. Graham, N. Rabeendran, and J.-P. R. Wells, “Experiments with an 834  m2 ring laser interferometer,” J. Appl. Phys. 105, 113115 (2009).
[Crossref]

Holdaway, J.

J. Holdaway, R. B. Hurst, R. Graham, N. Rabeendran, K. U. Schreiber, and J.-P. R. Wells, “Self-locked operation of large He-Ne ring laser gyroscopes,” Metrologia 49, 209–212 (2012).
[Crossref]

Hurst, R. B.

R. B. Hurst, N. Rabeendran, K. U. Schreiber, and J.-P. R. Wells, “Correction of backscatter-induced systematic errors in ring laser gyroscopes,” Appl. Opt. 53, 7610–7618 (2014).
[Crossref]

J. Holdaway, R. B. Hurst, R. Graham, N. Rabeendran, K. U. Schreiber, and J.-P. R. Wells, “Self-locked operation of large He-Ne ring laser gyroscopes,” Metrologia 49, 209–212 (2012).
[Crossref]

K. U. Schreiber, T. Klügel, J.-P. R. Wells, R. B. Hurst, and A. Gebauer, “How to detect the chandler and the annual wobble of the earth with a large ring laser gyroscope,” Phys. Rev. Lett. 107, 173904 (2011).
[Crossref]

R. B. Hurst, G. Stedman, K. U. Schreiber, R. J. Thirkettle, R. Graham, N. Rabeendran, and J.-P. R. Wells, “Experiments with an 834  m2 ring laser interferometer,” J. Appl. Phys. 105, 113115 (2009).
[Crossref]

R. B. Hurst, J.-P. R. Wells, and G. Stedman, “An elementary proof of the geometrical dependence of the Sagnac effect,” J. Opt. A 9, 838–841 (2007).
[Crossref]

R. B. Hurst, R. W. Dunn, K. U. Schreiber, R. J. Thirkettle, and G. MacDonald, “Mode behavior in ultralarge ring lasers,” Appl. Opt. 43, 2337–2346 (2004).
[Crossref]

Klügel, T.

K. U. Schreiber, T. Klügel, J.-P. R. Wells, R. B. Hurst, and A. Gebauer, “How to detect the chandler and the annual wobble of the earth with a large ring laser gyroscope,” Phys. Rev. Lett. 107, 173904 (2011).
[Crossref]

K. U. Schreiber, T. Klügel, A. Velikoseltsev, W. Schlüter, G. Stedman, and J.-P. R. Wells, “The large ring laser G for continuous earth rotation monitoring,” Pure Appl. Geophys. 166, 1485–1498 (2009).
[Crossref]

K. U. Schreiber, A. Velikoseltsev, M. Rothacher, T. Klügel, G. Stedman, and D. L. Wiltshire, “Direct measurement of diurnal polar motion by ring laser gyroscopes,” J. Geophys. Res. Solid Earth 109, B06405 (2004).
[Crossref]

Maccioni, E.

F. Bosi, G. Cella, A. Di Virgilio, A. Ortolan, A. Porzio, S. Solimeno, M. Cerdonio, J. P. Zendri, M. Allegrini, M. Allegrini, J. Belfi, N. Beverini, B. Bouhadef, G. Carelli, I. Ferrante, E. Maccioni, R. Passaquieti, F. Stefani, M. L. Ruggiero, A. Tartaglia, K. U. Schreiber, A. Gebauer, and J.-P. R. Wells, “Measuring gravitomagnetic effects by a multi-ring-laser gyroscope,” Phys. Rev. D 84, 122002 (2011).
[Crossref]

MacDonald, G.

Mahdi, H. H.

R. W. Dunn, H. H. Mahdi, H. J. Al-Shukri, and H. J. Al-Shukri, “Design of a relatively inexpensive ring laser seismic detector,” Bull. Seismol. Soc. Am. 99, 1437–1442 (2009).
[Crossref]

Nöckel, J. U.

Ortolan, A.

D. Cuccato, A. Beghi, J. Belfi, N. Beverini, and A. Ortolan, “Controlling the non-linear intracavity dynamics of large He–Ne laser gyroscopes,” Metrologia 51, 97–107 (2014).

F. Bosi, G. Cella, A. Di Virgilio, A. Ortolan, A. Porzio, S. Solimeno, M. Cerdonio, J. P. Zendri, M. Allegrini, M. Allegrini, J. Belfi, N. Beverini, B. Bouhadef, G. Carelli, I. Ferrante, E. Maccioni, R. Passaquieti, F. Stefani, M. L. Ruggiero, A. Tartaglia, K. U. Schreiber, A. Gebauer, and J.-P. R. Wells, “Measuring gravitomagnetic effects by a multi-ring-laser gyroscope,” Phys. Rev. D 84, 122002 (2011).
[Crossref]

Passaquieti, R.

F. Bosi, G. Cella, A. Di Virgilio, A. Ortolan, A. Porzio, S. Solimeno, M. Cerdonio, J. P. Zendri, M. Allegrini, M. Allegrini, J. Belfi, N. Beverini, B. Bouhadef, G. Carelli, I. Ferrante, E. Maccioni, R. Passaquieti, F. Stefani, M. L. Ruggiero, A. Tartaglia, K. U. Schreiber, A. Gebauer, and J.-P. R. Wells, “Measuring gravitomagnetic effects by a multi-ring-laser gyroscope,” Phys. Rev. D 84, 122002 (2011).
[Crossref]

Porzio, A.

F. Bosi, G. Cella, A. Di Virgilio, A. Ortolan, A. Porzio, S. Solimeno, M. Cerdonio, J. P. Zendri, M. Allegrini, M. Allegrini, J. Belfi, N. Beverini, B. Bouhadef, G. Carelli, I. Ferrante, E. Maccioni, R. Passaquieti, F. Stefani, M. L. Ruggiero, A. Tartaglia, K. U. Schreiber, A. Gebauer, and J.-P. R. Wells, “Measuring gravitomagnetic effects by a multi-ring-laser gyroscope,” Phys. Rev. D 84, 122002 (2011).
[Crossref]

Post, E. J.

E. J. Post, “Sagnac effect,” Rev. Modern Phys. 39, 475–493 (1967).
[Crossref]

Rabeendran, N.

R. B. Hurst, N. Rabeendran, K. U. Schreiber, and J.-P. R. Wells, “Correction of backscatter-induced systematic errors in ring laser gyroscopes,” Appl. Opt. 53, 7610–7618 (2014).
[Crossref]

J. Holdaway, R. B. Hurst, R. Graham, N. Rabeendran, K. U. Schreiber, and J.-P. R. Wells, “Self-locked operation of large He-Ne ring laser gyroscopes,” Metrologia 49, 209–212 (2012).
[Crossref]

R. B. Hurst, G. Stedman, K. U. Schreiber, R. J. Thirkettle, R. Graham, N. Rabeendran, and J.-P. R. Wells, “Experiments with an 834  m2 ring laser interferometer,” J. Appl. Phys. 105, 113115 (2009).
[Crossref]

Rothacher, M.

K. U. Schreiber, A. Velikoseltsev, M. Rothacher, T. Klügel, G. Stedman, and D. L. Wiltshire, “Direct measurement of diurnal polar motion by ring laser gyroscopes,” J. Geophys. Res. Solid Earth 109, B06405 (2004).
[Crossref]

Ruggiero, M. L.

F. Bosi, G. Cella, A. Di Virgilio, A. Ortolan, A. Porzio, S. Solimeno, M. Cerdonio, J. P. Zendri, M. Allegrini, M. Allegrini, J. Belfi, N. Beverini, B. Bouhadef, G. Carelli, I. Ferrante, E. Maccioni, R. Passaquieti, F. Stefani, M. L. Ruggiero, A. Tartaglia, K. U. Schreiber, A. Gebauer, and J.-P. R. Wells, “Measuring gravitomagnetic effects by a multi-ring-laser gyroscope,” Phys. Rev. D 84, 122002 (2011).
[Crossref]

Sampas, N. M.

N. M. Sampas, “A ring laser gyroscope with optical subtraction,” Ph.D. thesis (University of Colorado, 1990).

Schlüter, W.

K. U. Schreiber, T. Klügel, A. Velikoseltsev, W. Schlüter, G. Stedman, and J.-P. R. Wells, “The large ring laser G for continuous earth rotation monitoring,” Pure Appl. Geophys. 166, 1485–1498 (2009).
[Crossref]

Schreiber, K. U.

R. B. Hurst, N. Rabeendran, K. U. Schreiber, and J.-P. R. Wells, “Correction of backscatter-induced systematic errors in ring laser gyroscopes,” Appl. Opt. 53, 7610–7618 (2014).
[Crossref]

K. U. Schreiber, A. Gebauer, and J.-P. R. Wells, “Closed-loop locking of an optical frequency comb to a large ring laser,” Opt. Lett. 38, 3574–3577 (2013).
[Crossref]

K. U. Schreiber and J.-P. R. Wells, “Invited review article: large ring lasers for rotation sensing,” Rev. Sci. Instrum. 84, 041101 (2013).

J. Holdaway, R. B. Hurst, R. Graham, N. Rabeendran, K. U. Schreiber, and J.-P. R. Wells, “Self-locked operation of large He-Ne ring laser gyroscopes,” Metrologia 49, 209–212 (2012).
[Crossref]

K. U. Schreiber, A. Gebauer, and J.-P. R. Wells, “Long-term frequency stabilization of a 16  m2 ring laser gyroscope,” Opt. Lett. 37, 1925–1927 (2012).
[Crossref]

F. Bosi, G. Cella, A. Di Virgilio, A. Ortolan, A. Porzio, S. Solimeno, M. Cerdonio, J. P. Zendri, M. Allegrini, M. Allegrini, J. Belfi, N. Beverini, B. Bouhadef, G. Carelli, I. Ferrante, E. Maccioni, R. Passaquieti, F. Stefani, M. L. Ruggiero, A. Tartaglia, K. U. Schreiber, A. Gebauer, and J.-P. R. Wells, “Measuring gravitomagnetic effects by a multi-ring-laser gyroscope,” Phys. Rev. D 84, 122002 (2011).
[Crossref]

K. U. Schreiber, T. Klügel, J.-P. R. Wells, R. B. Hurst, and A. Gebauer, “How to detect the chandler and the annual wobble of the earth with a large ring laser gyroscope,” Phys. Rev. Lett. 107, 173904 (2011).
[Crossref]

K. U. Schreiber, T. Klügel, A. Velikoseltsev, W. Schlüter, G. Stedman, and J.-P. R. Wells, “The large ring laser G for continuous earth rotation monitoring,” Pure Appl. Geophys. 166, 1485–1498 (2009).
[Crossref]

R. B. Hurst, G. Stedman, K. U. Schreiber, R. J. Thirkettle, R. Graham, N. Rabeendran, and J.-P. R. Wells, “Experiments with an 834  m2 ring laser interferometer,” J. Appl. Phys. 105, 113115 (2009).
[Crossref]

K. U. Schreiber, A. Velikoseltsev, M. Rothacher, T. Klügel, G. Stedman, and D. L. Wiltshire, “Direct measurement of diurnal polar motion by ring laser gyroscopes,” J. Geophys. Res. Solid Earth 109, B06405 (2004).
[Crossref]

R. B. Hurst, R. W. Dunn, K. U. Schreiber, R. J. Thirkettle, and G. MacDonald, “Mode behavior in ultralarge ring lasers,” Appl. Opt. 43, 2337–2346 (2004).
[Crossref]

Siegman, A. E.

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

Smith, P. W.

P. W. Smith, “The effect of cross relaxation on the behavior of gas laser oscillators,” IEEE J. Quantum Electron. QE-8, 704–709 (1972).

Solimeno, S.

F. Bosi, G. Cella, A. Di Virgilio, A. Ortolan, A. Porzio, S. Solimeno, M. Cerdonio, J. P. Zendri, M. Allegrini, M. Allegrini, J. Belfi, N. Beverini, B. Bouhadef, G. Carelli, I. Ferrante, E. Maccioni, R. Passaquieti, F. Stefani, M. L. Ruggiero, A. Tartaglia, K. U. Schreiber, A. Gebauer, and J.-P. R. Wells, “Measuring gravitomagnetic effects by a multi-ring-laser gyroscope,” Phys. Rev. D 84, 122002 (2011).
[Crossref]

Stedman, G.

K. U. Schreiber, T. Klügel, A. Velikoseltsev, W. Schlüter, G. Stedman, and J.-P. R. Wells, “The large ring laser G for continuous earth rotation monitoring,” Pure Appl. Geophys. 166, 1485–1498 (2009).
[Crossref]

R. B. Hurst, G. Stedman, K. U. Schreiber, R. J. Thirkettle, R. Graham, N. Rabeendran, and J.-P. R. Wells, “Experiments with an 834  m2 ring laser interferometer,” J. Appl. Phys. 105, 113115 (2009).
[Crossref]

R. B. Hurst, J.-P. R. Wells, and G. Stedman, “An elementary proof of the geometrical dependence of the Sagnac effect,” J. Opt. A 9, 838–841 (2007).
[Crossref]

K. U. Schreiber, A. Velikoseltsev, M. Rothacher, T. Klügel, G. Stedman, and D. L. Wiltshire, “Direct measurement of diurnal polar motion by ring laser gyroscopes,” J. Geophys. Res. Solid Earth 109, B06405 (2004).
[Crossref]

Stefani, F.

F. Bosi, G. Cella, A. Di Virgilio, A. Ortolan, A. Porzio, S. Solimeno, M. Cerdonio, J. P. Zendri, M. Allegrini, M. Allegrini, J. Belfi, N. Beverini, B. Bouhadef, G. Carelli, I. Ferrante, E. Maccioni, R. Passaquieti, F. Stefani, M. L. Ruggiero, A. Tartaglia, K. U. Schreiber, A. Gebauer, and J.-P. R. Wells, “Measuring gravitomagnetic effects by a multi-ring-laser gyroscope,” Phys. Rev. D 84, 122002 (2011).
[Crossref]

Stejskal, A.

J. Stone and A. Stejskal, “Using helium as a standard of refractive index: correcting errors in a gas refractometer,” Metrologia 41, 189–197 (2004).
[Crossref]

Stone, J.

J. Stone and A. Stejskal, “Using helium as a standard of refractive index: correcting errors in a gas refractometer,” Metrologia 41, 189–197 (2004).
[Crossref]

Tartaglia, A.

F. Bosi, G. Cella, A. Di Virgilio, A. Ortolan, A. Porzio, S. Solimeno, M. Cerdonio, J. P. Zendri, M. Allegrini, M. Allegrini, J. Belfi, N. Beverini, B. Bouhadef, G. Carelli, I. Ferrante, E. Maccioni, R. Passaquieti, F. Stefani, M. L. Ruggiero, A. Tartaglia, K. U. Schreiber, A. Gebauer, and J.-P. R. Wells, “Measuring gravitomagnetic effects by a multi-ring-laser gyroscope,” Phys. Rev. D 84, 122002 (2011).
[Crossref]

Thirkettle, R. J.

R. B. Hurst, G. Stedman, K. U. Schreiber, R. J. Thirkettle, R. Graham, N. Rabeendran, and J.-P. R. Wells, “Experiments with an 834  m2 ring laser interferometer,” J. Appl. Phys. 105, 113115 (2009).
[Crossref]

R. B. Hurst, R. W. Dunn, K. U. Schreiber, R. J. Thirkettle, and G. MacDonald, “Mode behavior in ultralarge ring lasers,” Appl. Opt. 43, 2337–2346 (2004).
[Crossref]

Velikoseltsev, A.

K. U. Schreiber, T. Klügel, A. Velikoseltsev, W. Schlüter, G. Stedman, and J.-P. R. Wells, “The large ring laser G for continuous earth rotation monitoring,” Pure Appl. Geophys. 166, 1485–1498 (2009).
[Crossref]

K. U. Schreiber, A. Velikoseltsev, M. Rothacher, T. Klügel, G. Stedman, and D. L. Wiltshire, “Direct measurement of diurnal polar motion by ring laser gyroscopes,” J. Geophys. Res. Solid Earth 109, B06405 (2004).
[Crossref]

Wells, J.-P. R.

R. B. Hurst, N. Rabeendran, K. U. Schreiber, and J.-P. R. Wells, “Correction of backscatter-induced systematic errors in ring laser gyroscopes,” Appl. Opt. 53, 7610–7618 (2014).
[Crossref]

K. U. Schreiber, A. Gebauer, and J.-P. R. Wells, “Closed-loop locking of an optical frequency comb to a large ring laser,” Opt. Lett. 38, 3574–3577 (2013).
[Crossref]

K. U. Schreiber and J.-P. R. Wells, “Invited review article: large ring lasers for rotation sensing,” Rev. Sci. Instrum. 84, 041101 (2013).

J. Holdaway, R. B. Hurst, R. Graham, N. Rabeendran, K. U. Schreiber, and J.-P. R. Wells, “Self-locked operation of large He-Ne ring laser gyroscopes,” Metrologia 49, 209–212 (2012).
[Crossref]

K. U. Schreiber, A. Gebauer, and J.-P. R. Wells, “Long-term frequency stabilization of a 16  m2 ring laser gyroscope,” Opt. Lett. 37, 1925–1927 (2012).
[Crossref]

K. U. Schreiber, T. Klügel, J.-P. R. Wells, R. B. Hurst, and A. Gebauer, “How to detect the chandler and the annual wobble of the earth with a large ring laser gyroscope,” Phys. Rev. Lett. 107, 173904 (2011).
[Crossref]

F. Bosi, G. Cella, A. Di Virgilio, A. Ortolan, A. Porzio, S. Solimeno, M. Cerdonio, J. P. Zendri, M. Allegrini, M. Allegrini, J. Belfi, N. Beverini, B. Bouhadef, G. Carelli, I. Ferrante, E. Maccioni, R. Passaquieti, F. Stefani, M. L. Ruggiero, A. Tartaglia, K. U. Schreiber, A. Gebauer, and J.-P. R. Wells, “Measuring gravitomagnetic effects by a multi-ring-laser gyroscope,” Phys. Rev. D 84, 122002 (2011).
[Crossref]

K. U. Schreiber, T. Klügel, A. Velikoseltsev, W. Schlüter, G. Stedman, and J.-P. R. Wells, “The large ring laser G for continuous earth rotation monitoring,” Pure Appl. Geophys. 166, 1485–1498 (2009).
[Crossref]

R. B. Hurst, G. Stedman, K. U. Schreiber, R. J. Thirkettle, R. Graham, N. Rabeendran, and J.-P. R. Wells, “Experiments with an 834  m2 ring laser interferometer,” J. Appl. Phys. 105, 113115 (2009).
[Crossref]

R. B. Hurst, J.-P. R. Wells, and G. Stedman, “An elementary proof of the geometrical dependence of the Sagnac effect,” J. Opt. A 9, 838–841 (2007).
[Crossref]

Wiltshire, D. L.

K. U. Schreiber, A. Velikoseltsev, M. Rothacher, T. Klügel, G. Stedman, and D. L. Wiltshire, “Direct measurement of diurnal polar motion by ring laser gyroscopes,” J. Geophys. Res. Solid Earth 109, B06405 (2004).
[Crossref]

Zendri, J. P.

F. Bosi, G. Cella, A. Di Virgilio, A. Ortolan, A. Porzio, S. Solimeno, M. Cerdonio, J. P. Zendri, M. Allegrini, M. Allegrini, J. Belfi, N. Beverini, B. Bouhadef, G. Carelli, I. Ferrante, E. Maccioni, R. Passaquieti, F. Stefani, M. L. Ruggiero, A. Tartaglia, K. U. Schreiber, A. Gebauer, and J.-P. R. Wells, “Measuring gravitomagnetic effects by a multi-ring-laser gyroscope,” Phys. Rev. D 84, 122002 (2011).
[Crossref]

Appl. Opt. (2)

Bull. Seismol. Soc. Am. (1)

R. W. Dunn, H. H. Mahdi, H. J. Al-Shukri, and H. J. Al-Shukri, “Design of a relatively inexpensive ring laser seismic detector,” Bull. Seismol. Soc. Am. 99, 1437–1442 (2009).
[Crossref]

IEEE J. Quantum Electron. (1)

P. W. Smith, “The effect of cross relaxation on the behavior of gas laser oscillators,” IEEE J. Quantum Electron. QE-8, 704–709 (1972).

J. Appl. Phys. (1)

R. B. Hurst, G. Stedman, K. U. Schreiber, R. J. Thirkettle, R. Graham, N. Rabeendran, and J.-P. R. Wells, “Experiments with an 834  m2 ring laser interferometer,” J. Appl. Phys. 105, 113115 (2009).
[Crossref]

J. Geophys. Res. Solid Earth (1)

K. U. Schreiber, A. Velikoseltsev, M. Rothacher, T. Klügel, G. Stedman, and D. L. Wiltshire, “Direct measurement of diurnal polar motion by ring laser gyroscopes,” J. Geophys. Res. Solid Earth 109, B06405 (2004).
[Crossref]

J. Opt. A (1)

R. B. Hurst, J.-P. R. Wells, and G. Stedman, “An elementary proof of the geometrical dependence of the Sagnac effect,” J. Opt. A 9, 838–841 (2007).
[Crossref]

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

Metrologia (3)

D. Cuccato, A. Beghi, J. Belfi, N. Beverini, and A. Ortolan, “Controlling the non-linear intracavity dynamics of large He–Ne laser gyroscopes,” Metrologia 51, 97–107 (2014).

J. Holdaway, R. B. Hurst, R. Graham, N. Rabeendran, K. U. Schreiber, and J.-P. R. Wells, “Self-locked operation of large He-Ne ring laser gyroscopes,” Metrologia 49, 209–212 (2012).
[Crossref]

J. Stone and A. Stejskal, “Using helium as a standard of refractive index: correcting errors in a gas refractometer,” Metrologia 41, 189–197 (2004).
[Crossref]

Opt. Lett. (3)

Phys. Rev. D (1)

F. Bosi, G. Cella, A. Di Virgilio, A. Ortolan, A. Porzio, S. Solimeno, M. Cerdonio, J. P. Zendri, M. Allegrini, M. Allegrini, J. Belfi, N. Beverini, B. Bouhadef, G. Carelli, I. Ferrante, E. Maccioni, R. Passaquieti, F. Stefani, M. L. Ruggiero, A. Tartaglia, K. U. Schreiber, A. Gebauer, and J.-P. R. Wells, “Measuring gravitomagnetic effects by a multi-ring-laser gyroscope,” Phys. Rev. D 84, 122002 (2011).
[Crossref]

Phys. Rev. Lett. (1)

K. U. Schreiber, T. Klügel, J.-P. R. Wells, R. B. Hurst, and A. Gebauer, “How to detect the chandler and the annual wobble of the earth with a large ring laser gyroscope,” Phys. Rev. Lett. 107, 173904 (2011).
[Crossref]

Pure Appl. Geophys. (1)

K. U. Schreiber, T. Klügel, A. Velikoseltsev, W. Schlüter, G. Stedman, and J.-P. R. Wells, “The large ring laser G for continuous earth rotation monitoring,” Pure Appl. Geophys. 166, 1485–1498 (2009).
[Crossref]

Rev. Modern Phys. (1)

E. J. Post, “Sagnac effect,” Rev. Modern Phys. 39, 475–493 (1967).
[Crossref]

Rev. Sci. Instrum. (1)

K. U. Schreiber and J.-P. R. Wells, “Invited review article: large ring lasers for rotation sensing,” Rev. Sci. Instrum. 84, 041101 (2013).

Other (3)

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

J. A. Dobrowolski, Handbook of Optics, 2nd ed. (McGraw-Hill, 1985), Vol. 1.

N. M. Sampas, “A ring laser gyroscope with optical subtraction,” Ph.D. thesis (University of Colorado, 1990).

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Figures (2)

Fig. 1.
Fig. 1. One arm of a square RLG, illustrating the realignment of the beams caused by the GH effect.
Fig. 2.
Fig. 2. Sagnac frequency data from G between 3 February and 27 February 2016. (a) Raw data with no corrections applied; (b) the same data after corrections for backscatter perturbations, diurnal polar motion, tidally induced tilts and present pole position are applied. Each data point corresponds to a 4 h average.

Tables (1)

Tables Icon

Table 1. Correction Factors for Eq. (26), for the G Ring Laser a

Equations (27)

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

f s = 4 A · Ω λ P ,
f s = N 4 Ω .
ϕ P = 2 π P / λ = 2 π P n / λ vac ,
ϕ G = 2 [ arccos ( 1 L 2 / R ) + arccos ( 1 L / R 2 ) ] .
ϕ M = ϕ M 0 + Δ f ϕ M f ,
ϕ K = ϕ K 0 + Δ f ϕ K f ,
ϕ P ϕ G 4 ϕ M ϕ K = 2 π N .
f opt = c n P ( N + ( ϕ G + 4 ϕ M + ϕ K ) / 2 π ) .
f opt * = f opt c n P ( ϕ G + 4 ϕ M + ϕ K ) / 2 π ,
F = c n P [ 1 + F ϕ D f / 2 π ] .
F * = c n P = F [ 1 F ϕ D f / 2 π ] ,
N = f opt * / F * .
f opt * = 473612701.08 ± 0.15    MHz .
F * = 18734385.26 ± 0.2    Hz .
F * = 18734385.425    Hz .
P = 16.00225212    m .
D = 1 F ϕ D f / 2 π .
γ = λ 2 π d ϕ d θ ,
A = L 2 + 4 L γ / 2 = L 2 ( 1 + 2 γ / L ) .
A = P 2 16 ( 1 + 8 γ / P ) .
Δ τ 12 = 2 A 12 Ω / c 2 ,
ϕ S 1 = 4 π A Ω f opt 1 c 2 and ϕ S 2 = 4 π A Ω f opt 2 c 2 .
f opt 1 f opt 2 = c 2 π n P [ ( f opt 1 f opt 2 ) ϕ D f + 8 π A Ω f opt c 2 ] .
Ω = f s c n P D 4 A f opt ,
f s = 4 A Ω f opt c n P D = 4 A Ω n λ vac P D .
f s = N Ω 4 ( 1 + 8 γ / P ) n 2 D [ 1 + ϕ G + ϕ D 2 π N ] .
f s = N 4 Ω ( 1 7.854 × 10 7 ) .

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