Abstract

We review the kinematic explanation of the Sagnac effect in fiber gyroscopes and recall that the index of the dielectric medium does not have any influence. Furthermore, we present a novel electrodynamic approach that confirms in more detail that the Sagnac phase shift of a ring-waveguide interferometer is the same as for the original Sagnac experiment with plane waves in a vacuum.

© 1981 Optical Society of America

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References

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  1. H. Fizeau, “Sur les hypothèses relatives à l’éther lumineux, et sur une expérience qui parait démontrer que le mouvement des corps change la vitesse avec laquelle la lumière se propage dans leur intérieur,” C. R. Acad. Sci. 33, 349–354 (1851).
  2. G. Sagnac, “L’éther lumineux démontré par l’effet du vent relatif d’éther dans un interféromètre en rotation uniforme,” C. R. Acad. Sci. 95, 708–710 (1913).
  3. E. J. Post, “Sagnac effect,” Rev. Mod. Phys. 39, 475–494 (1967).
    [CrossRef]
  4. V. Vali, R. W. Shorthill, M. F. Berg, “Fresnel–Fizeau effect in a rotating optical fiber ring interferometer,” Appl. Opt. 16, 2605–2607 (1977).
    [CrossRef] [PubMed]
  5. W. R. Leeb, G. Schiffner, E. Scheiterer, “Optical fiber gyroscopes: Sagnac or Fizeau effect?” Appl. Opt. 18, 1293–1295 (1979).
    [CrossRef] [PubMed]
  6. See, for example, M. A. Tonnelat, Principles de la théorie electromagnétique et de la relativité (Masson, Paris, 1959) [Principles of Electromagnetic Theory and Relativity (Gordon and Breach, London, 1966)].
  7. F. Haress, “Die Geschw. d. Lichtes in bewegten Körpern,” Thesis Dissertation (University of Jena, Erfurt, Germany, 1912).
  8. H. C. Lefèvre, “Gyromètre interférométrique à fibre optique,” Doctoral Thesis (University of Paris-Orsay, 1979).
  9. H. J. Arditty, H. C. Lefèvre, “Electromagnétisme des milieux dielectriques linéaires en rotation et application à la propagation d’ondes guidées,” to be published.
  10. J. L. Anderson, J. W. Ryon, “Electromagnetic radiation in accelerated systems,” Phys. Rev. 181, 1765–1775 (1969).
    [CrossRef]
  11. T. Shiozawa, “Phenomenological and electron-theoretical study of the electrodynamics of rotating systems,” Proc. IEEE 61, 1694–1702 (1973).
    [CrossRef]
  12. K. Petermann, “Fundamental mode microbending loss in graded-index and W fibres,” Opt. Quantum Electron. 9, 167–175 (1977).
    [CrossRef]
  13. W. A. Gambling, H. Matsumura, C. M. Ragdale, “Field deformation in a curved single mode fibre,” Electron. Lett. 14, 130–132 (1978).
    [CrossRef]
  14. D. Marcuse, “Loss-analysis of single-mode fiber splices,” Bell Syst. Tech. J. 56, 703–718 (1977).
  15. H. J. Arditty, H. J. Shaw, M. Chodorow, R. Kompfner, “Re-entrant fiber optic approach to rotation sensing,” Proc. Soc. Photo-Opt. Instrum. Eng. 157, 138–148 (1978).
  16. C. C. Cutler, S. A. Newton, H. J. Shaw, “Limitation of rotation sensing by scattering,” Opt. Lett. 5, 488–490 (1980).
    [CrossRef] [PubMed]

1980 (1)

1979 (1)

1978 (2)

H. J. Arditty, H. J. Shaw, M. Chodorow, R. Kompfner, “Re-entrant fiber optic approach to rotation sensing,” Proc. Soc. Photo-Opt. Instrum. Eng. 157, 138–148 (1978).

W. A. Gambling, H. Matsumura, C. M. Ragdale, “Field deformation in a curved single mode fibre,” Electron. Lett. 14, 130–132 (1978).
[CrossRef]

1977 (3)

D. Marcuse, “Loss-analysis of single-mode fiber splices,” Bell Syst. Tech. J. 56, 703–718 (1977).

K. Petermann, “Fundamental mode microbending loss in graded-index and W fibres,” Opt. Quantum Electron. 9, 167–175 (1977).
[CrossRef]

V. Vali, R. W. Shorthill, M. F. Berg, “Fresnel–Fizeau effect in a rotating optical fiber ring interferometer,” Appl. Opt. 16, 2605–2607 (1977).
[CrossRef] [PubMed]

1973 (1)

T. Shiozawa, “Phenomenological and electron-theoretical study of the electrodynamics of rotating systems,” Proc. IEEE 61, 1694–1702 (1973).
[CrossRef]

1969 (1)

J. L. Anderson, J. W. Ryon, “Electromagnetic radiation in accelerated systems,” Phys. Rev. 181, 1765–1775 (1969).
[CrossRef]

1967 (1)

E. J. Post, “Sagnac effect,” Rev. Mod. Phys. 39, 475–494 (1967).
[CrossRef]

1913 (1)

G. Sagnac, “L’éther lumineux démontré par l’effet du vent relatif d’éther dans un interféromètre en rotation uniforme,” C. R. Acad. Sci. 95, 708–710 (1913).

1851 (1)

H. Fizeau, “Sur les hypothèses relatives à l’éther lumineux, et sur une expérience qui parait démontrer que le mouvement des corps change la vitesse avec laquelle la lumière se propage dans leur intérieur,” C. R. Acad. Sci. 33, 349–354 (1851).

Anderson, J. L.

J. L. Anderson, J. W. Ryon, “Electromagnetic radiation in accelerated systems,” Phys. Rev. 181, 1765–1775 (1969).
[CrossRef]

Arditty, H. J.

H. J. Arditty, H. J. Shaw, M. Chodorow, R. Kompfner, “Re-entrant fiber optic approach to rotation sensing,” Proc. Soc. Photo-Opt. Instrum. Eng. 157, 138–148 (1978).

H. J. Arditty, H. C. Lefèvre, “Electromagnétisme des milieux dielectriques linéaires en rotation et application à la propagation d’ondes guidées,” to be published.

Berg, M. F.

Chodorow, M.

H. J. Arditty, H. J. Shaw, M. Chodorow, R. Kompfner, “Re-entrant fiber optic approach to rotation sensing,” Proc. Soc. Photo-Opt. Instrum. Eng. 157, 138–148 (1978).

Cutler, C. C.

Fizeau, H.

H. Fizeau, “Sur les hypothèses relatives à l’éther lumineux, et sur une expérience qui parait démontrer que le mouvement des corps change la vitesse avec laquelle la lumière se propage dans leur intérieur,” C. R. Acad. Sci. 33, 349–354 (1851).

Gambling, W. A.

W. A. Gambling, H. Matsumura, C. M. Ragdale, “Field deformation in a curved single mode fibre,” Electron. Lett. 14, 130–132 (1978).
[CrossRef]

Haress, F.

F. Haress, “Die Geschw. d. Lichtes in bewegten Körpern,” Thesis Dissertation (University of Jena, Erfurt, Germany, 1912).

Kompfner, R.

H. J. Arditty, H. J. Shaw, M. Chodorow, R. Kompfner, “Re-entrant fiber optic approach to rotation sensing,” Proc. Soc. Photo-Opt. Instrum. Eng. 157, 138–148 (1978).

Leeb, W. R.

Lefèvre, H. C.

H. C. Lefèvre, “Gyromètre interférométrique à fibre optique,” Doctoral Thesis (University of Paris-Orsay, 1979).

H. J. Arditty, H. C. Lefèvre, “Electromagnétisme des milieux dielectriques linéaires en rotation et application à la propagation d’ondes guidées,” to be published.

Marcuse, D.

D. Marcuse, “Loss-analysis of single-mode fiber splices,” Bell Syst. Tech. J. 56, 703–718 (1977).

Matsumura, H.

W. A. Gambling, H. Matsumura, C. M. Ragdale, “Field deformation in a curved single mode fibre,” Electron. Lett. 14, 130–132 (1978).
[CrossRef]

Newton, S. A.

Petermann, K.

K. Petermann, “Fundamental mode microbending loss in graded-index and W fibres,” Opt. Quantum Electron. 9, 167–175 (1977).
[CrossRef]

Post, E. J.

E. J. Post, “Sagnac effect,” Rev. Mod. Phys. 39, 475–494 (1967).
[CrossRef]

Ragdale, C. M.

W. A. Gambling, H. Matsumura, C. M. Ragdale, “Field deformation in a curved single mode fibre,” Electron. Lett. 14, 130–132 (1978).
[CrossRef]

Ryon, J. W.

J. L. Anderson, J. W. Ryon, “Electromagnetic radiation in accelerated systems,” Phys. Rev. 181, 1765–1775 (1969).
[CrossRef]

Sagnac, G.

G. Sagnac, “L’éther lumineux démontré par l’effet du vent relatif d’éther dans un interféromètre en rotation uniforme,” C. R. Acad. Sci. 95, 708–710 (1913).

Scheiterer, E.

Schiffner, G.

Shaw, H. J.

C. C. Cutler, S. A. Newton, H. J. Shaw, “Limitation of rotation sensing by scattering,” Opt. Lett. 5, 488–490 (1980).
[CrossRef] [PubMed]

H. J. Arditty, H. J. Shaw, M. Chodorow, R. Kompfner, “Re-entrant fiber optic approach to rotation sensing,” Proc. Soc. Photo-Opt. Instrum. Eng. 157, 138–148 (1978).

Shiozawa, T.

T. Shiozawa, “Phenomenological and electron-theoretical study of the electrodynamics of rotating systems,” Proc. IEEE 61, 1694–1702 (1973).
[CrossRef]

Shorthill, R. W.

Tonnelat, M. A.

See, for example, M. A. Tonnelat, Principles de la théorie electromagnétique et de la relativité (Masson, Paris, 1959) [Principles of Electromagnetic Theory and Relativity (Gordon and Breach, London, 1966)].

Vali, V.

Appl. Opt. (2)

Bell Syst. Tech. J. (1)

D. Marcuse, “Loss-analysis of single-mode fiber splices,” Bell Syst. Tech. J. 56, 703–718 (1977).

C. R. Acad. Sci. (2)

H. Fizeau, “Sur les hypothèses relatives à l’éther lumineux, et sur une expérience qui parait démontrer que le mouvement des corps change la vitesse avec laquelle la lumière se propage dans leur intérieur,” C. R. Acad. Sci. 33, 349–354 (1851).

G. Sagnac, “L’éther lumineux démontré par l’effet du vent relatif d’éther dans un interféromètre en rotation uniforme,” C. R. Acad. Sci. 95, 708–710 (1913).

Electron. Lett. (1)

W. A. Gambling, H. Matsumura, C. M. Ragdale, “Field deformation in a curved single mode fibre,” Electron. Lett. 14, 130–132 (1978).
[CrossRef]

Opt. Lett. (1)

Opt. Quantum Electron. (1)

K. Petermann, “Fundamental mode microbending loss in graded-index and W fibres,” Opt. Quantum Electron. 9, 167–175 (1977).
[CrossRef]

Phys. Rev. (1)

J. L. Anderson, J. W. Ryon, “Electromagnetic radiation in accelerated systems,” Phys. Rev. 181, 1765–1775 (1969).
[CrossRef]

Proc. IEEE (1)

T. Shiozawa, “Phenomenological and electron-theoretical study of the electrodynamics of rotating systems,” Proc. IEEE 61, 1694–1702 (1973).
[CrossRef]

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

H. J. Arditty, H. J. Shaw, M. Chodorow, R. Kompfner, “Re-entrant fiber optic approach to rotation sensing,” Proc. Soc. Photo-Opt. Instrum. Eng. 157, 138–148 (1978).

Rev. Mod. Phys. (1)

E. J. Post, “Sagnac effect,” Rev. Mod. Phys. 39, 475–494 (1967).
[CrossRef]

Other (4)

See, for example, M. A. Tonnelat, Principles de la théorie electromagnétique et de la relativité (Masson, Paris, 1959) [Principles of Electromagnetic Theory and Relativity (Gordon and Breach, London, 1966)].

F. Haress, “Die Geschw. d. Lichtes in bewegten Körpern,” Thesis Dissertation (University of Jena, Erfurt, Germany, 1912).

H. C. Lefèvre, “Gyromètre interférométrique à fibre optique,” Doctoral Thesis (University of Paris-Orsay, 1979).

H. J. Arditty, H. C. Lefèvre, “Electromagnétisme des milieux dielectriques linéaires en rotation et application à la propagation d’ondes guidées,” to be published.

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Figures (1)

Fig. 1
Fig. 1

Simplified Sagnac ring interferometer, (a) Interferometer at rest, (b) vacuum interferometer in rotation, (c) dielectric medium interferometer in rotation.

Equations (5)

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Δ t M = 4 π R 2 Ω c υ 2 n 2 ( 1 α ) .
c MM = c υ n ( ω P ) + ( 1 1 n 2 ) υ
c MM = c υ n ( ω 0 ) + ( 1 1 n 2 ω 0 n d n d ω ) υ .
2 E r R 2 + 1 r R 2 2 E θ R 2 + 2 E z R 2 + n 2 ω 2 c υ 2 E + 2 i ω c υ 2 × Ω × E θ R = 0 ,
2 β R ( ω Ω c υ 2 Δ K r R 2 ) + ( d A / d r R ) ( d Δ A / d r R ) A ( r R , z R ) + d 2 A d r R 2 = 0 .

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