Issues

 / 

2014

 / 

July

  

Methodological notes


Sagnac effect in ring lasers and ring resonators. How does the refraction index of the optical medium influence the sensitivity to rotation?


Federal Research Center Institute of Applied Physics of the Russian Academy of Sciences, ul. Ulyanova 46, Nizhny Novgorod, 603000, Russian Federation

The Sagnac effect in a ring laser (RL) results in that the generation differences of counterpropagating waves differ by an amount proportional to the RL’s angular rotation rate. This paper addresses the question of how an optical medium filling the whole or part of the RL influences the frequency difference of the counterpropagating waves. While the formulas for this difference in a rotating RL abound in the literature, there is no agreement between them as to whether the medium increases, decreases or leaves unchanged this difference. Nor do the available (and often contradictory) experimental data fully clarify the situation. Because the Sagnac effect is a special relativity effect, the relativistic velocity addition law is here used to calculate the frequency difference of counterpropagating waves in an RL. When a homogeneous optical medium fills the entire perimeter of the resonator of the rotating RL, it is shown that the frequency difference of the counterpropagating waves is inversely proportional to the refraction index of the medium. Also, the results obtained can be used to calculate the difference of the resonant frequencies of counterpropagating waves in rotating ring resonators in the presence of an optical medium.

Text can be downloaded in Russian. English translation is available here.
PACS: 03.30.+p, 07.60.−j, 42.60.Da (all)
DOI: 10.3367/UFNe.0184.201407g.0775
URL: https://ufn.ru/en/articles/2014/7/f/
Citation: Malykin G B "Sagnac effect in ring lasers and ring resonators. How does the refraction index of the optical medium influence the sensitivity to rotation?" Phys. Usp. 57 714–720 (2014)
BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks

Received: 23rd, May 2013, 6th, September 2013

Оригинал: Малыкин Г Б «Эффект Саньяка в кольцевых лазерах и кольцевых резонаторах. Влияние показателя преломления оптической среды на чувствительность к вращению» УФН 184 775–781 (2014); DOI: 10.3367/UFNr.0184.201407g.0775

References (85) Cited by (15) Similar articles (20) ↓

  1. G.B. Malykin, V.I. Pozdnyakova “Quadratic Sagnac effect — the influence of the gravitational potential of the Coriolis force on the phase difference between the arms of a rotating Michelson interferometer (an explanation of D C Miller's experimental results 1921—1926)58 398–406 (2015)
  2. G.B. Malykin, V.I. Pozdnyakova “Geometric phases in singlemode fiber lightguides and fiber ring interferometers47 289–308 (2004)
  3. G.B. Malykin “The Sagnac effect: correct and incorrect explanations43 1229 (2000)
  4. G.B. Malykin “Para-Lorentz transformations52 263–266 (2009)
  5. A.A. Logunov, Yu.V. Chugreev “Special theory of relativity and the Sagnac effect31 861–864 (1988)
  6. G.B. Malykin “The relation of Thomas precession to Ishlinskii’s theorem as applied to the rotating image of a relativistically moving body42 505–509 (1999)
  7. B.M. Bolotovskii, S.N. Stolyarov “Reflection of light from a moving mirror and related problems32 813–827 (1989)
  8. V.I. Ritus “On the difference between Wigner’s and Møller’s approaches to the description of Thomas precession50 95–101 (2007)
  9. V.I. Ritus “Lagrange equations of motion of particles and photons in the Schwarzschild field58 1118–1123 (2015)
  10. V.G. Veselago “Formulating Fermat’s principle for light traveling in negative refraction materials45 1097–1099 (2002)
  11. P.B. Ivanov “On relativistic motion of a pair of particles having opposite signs of masses55 1232–1238 (2012)
  12. X.-B. Huang “A rigorous minimum-assumption derivation of the Lorentz transformation54 529–532 (2011)
  13. M.I. Krivoruchenko “Rotation of the swing plane of Foucault’s pendulum and Thomas spin precession: two sides of one coin52 821–829 (2009)
  14. V.P. Makarov, A.A. Rukhadze “Force acting on a substance in an electromagnetic field52 937–943 (2009)
  15. S.I. Blinnikov, L.B. Okun, M.I. Vysotskii “Critical velocities c/sqrt{3} and c/sqrt{2} in the general theory of relativity46 1099–1103 (2003)
  16. J. Gaite “The relativistic virial theorem and scale invariance56 919–931 (2013)
  17. V.A. Aleshkevich “On special relativity teaching using modern experimental data55 1214–1231 (2012)
  18. V.B. Morozov “On the question of the electromagnetic momentum of a charged body54 371–374 (2011)
  19. V.I. Ritus “Permutation asymmetry of the relativistic velocity addition law and non-Euclidean geometry51 709–721 (2008)
  20. A.I. Musienko, L.I. Manevich “Classical mechanical analogs of relativistic effects47 797–820 (2004)

The list is formed automatically.

© 1918–2019 Uspekhi Fizicheskikh Nauk
Email: ufn@ufn.ru Editorial office contacts About the journal Terms and conditions