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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 A.V. Gaponov-Grekhov 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.

Fulltext pdf (476 KB)
Fulltext is also available at DOI: 10.3367/UFNe.0184.201407g.0775
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/
000343769200006
2-s2.0-84907893519
2014PhyU...57..714M
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)
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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 (25) Similar articles (20)

  1. Sagnac M G C.R. Acad. Sci. 157 708 (1913)
  2. Sagnac M G C.R. Acad. Sci. 157 1410 (1913)
  3. Malykin G B Usp. Fiz. Nauk 167 337 (1997); Malykin G B Phys. Usp. 40 317 (1997)
  4. Malykin G B Usp. Fiz. Nauk 170 1325 (2000); Malykin G B Phys. Usp. 43 1229 (2000)
  5. Vugal’ter G A, Malykin G B Izv. Vuzov Radiofizika 42 373 (1999); Vugal’ter G A, Malykin G B Radiophys. Quantum Electron. 42 333 (1999)
  6. Malykin G B Usp. Fiz. Nauk 172 969 (2002); Malykin G B Phys. Usp. 45 907 (2002)
  7. Witte H Verhandl. Deutsch. Phys. Gesell. 16 142 (1914)
  8. Langevin P C.R. Acad. Sci. 173 831 (1921)
  9. Logunov A A, Chugreev Yu V Usp. Fiz. Nauk 156 137 (1988); Logunov A A, Chugreev Yu V Sov. Phys. Usp. 31 861 (1988)
  10. Andronova I A, Malykin G B Usp. Fiz. Nauk 172 849 (2002); Andronova I A, Malykin G B Phys. Usp. 45 793 (2002)
  11. Stedman G E, Schreiber K U, Bilger H R Class. Quantum Grav. 20 2527 (2003)
  12. Stedman G E, Hurst R B, Schreiber K U Opt. Commun. 279 124 (2007)
  13. Schreiber K U et al. Phys. Rev. Lett. 107 173904 (2011)
  14. Bosi F et al. Phys. Rev. D 84 122002 (2011)
  15. Rosenthal A H J. Opt. Soc. Am. 52 1143 (1962)
  16. Macek W M, Davis D T M (Jr.) Appl. Phys. Lett. 2 67 (1963)
  17. Kravtsov N V, Lariontsev E G Kvantovaya Elektronika 36 192 (2006); Kravtsov N V, Lariontsev E G Quantum Electron. 36 192 (2006)
  18. Melnikov L A, Plotnikov P K Inertial Sensors and Systems. Symp. Gyro Technology 2011, Karlsruhe, Germany, September 20 - 21, 2011 (Ed. G F Trommer) p. 6
  19. Letokhov V S, Chebotaev V P Nelineinaya Lazernaya Spektroskopiya Sverkhvysokogo Razresheniya (M.: Nauka, 1990)
  20. Kravtsov N V, Shelaev A N "Lazernyi giroskop" Fizicheskaya Entsiklopediya Vol. 2 (M.: Sov. entsiklopediya, 1990) p. 558
  21. Wilkinson J R Prog. Quantum Electron. 11 1 (1987)
  22. Sunada S, Harayama T Phys. Rev. A 74 021801(R) (2006)
  23. Harayama T, Sunada S, Miyasaka T Phys. Rev. E 76 016212 (2007)
  24. Scheuer J Opt. Express 15 15053 (2007)
  25. Sunada S, Harayama T Opt. Express 15 16245 (2007)
  26. Sarma R, Noh H, Cao H J. Opt. Soc. Am. B 29 1648 (2012)
  27. Cheo P K, Heer C V Appl. Opt. 3 788 (1964)
  28. Heer C V Phys. Rev. 134 A799 (1964)
  29. Khromykh A M Zh. Eksp. Teor. Fiz. 50 281 (1966); Khromykh A M Sov. Phys. JETP 23 185 (1966)
  30. Post E J Rev. Mod. Phys. 39 475 (1967)
  31. Privalov V E, Fridrikhov S A Usp. Fiz. Nauk 97 377 (1969); Privalov V E, Fridrikhov S A Sov. Phys. Usp. 12 153 (1969)
  32. Lianis G, Whicker D Arch. Ration. Mech. Anal. 57 325 (1975)
  33. Privalov V E, Filatov Yu V Kvantovaya Elektronika 4 1418 (1977); Privalov V E, Filatov Yu V Sov. J. Quantum Electron. 7 802 (1977)
  34. Privalov V E Gazorazryadnye Lazery v Sudovykh Izmeritel’nykh Kompleksakh (L.: Sudostroenie, 1977)
  35. Korostelev A A, Fateev V F Optika Spektroskopiya 45 132 (1978); Korostelev A A, Fateev V F Opt. Spectrosc. 45 73 (1978)
  36. Shpak I V, Solomin A V Optika Spektroskopiya 46 133 (1979); Shpak I V, Solomin A V Opt. Spectrosc. 46 72 (1979)
  37. Shpak I V i dr. Zh. Eksp. Teor. Fiz. 79 2057 (1980); Shpak I V et al. Sov. Phys. JETP 52 1038 (1980)
  38. Fateev V F Optika Spektroskopiya 50 30 (1981); Fateev V F Opt. Spectrosc. 50 14 (1981)
  39. Schröder W et al. Fiber Optics Gyro. 10th Anniversary Conf., 24 - 26 September 1986, Cambridge, Massachusetts, USA; Schröder W et al. Proc. SPIE 719 162 (1986)
  40. Carroll R et al. Fiber Optics Gyro. 10th Anniversary Conf., 24 - 26 September 1986, Cambridge, Massachusetts, USA (1986); Carroll R et al. Proc. SPIE 719 169 (1986)
  41. Privalov V E Gazorazryadnye Lazery v Izmeritel’nykh Kompleksakh (L.: Sudostroenie, 1989)
  42. Liaw Ch-Y, Zhow Y, Lam Y-L IEEE J. Quantum Electron. 12 1777 (1999)
  43. Volk C H et al. RTO AGARDograph 339 (Eds D Loukianov et al.) (Neuilly-sur-Seine Cedex, France: North Atlantic Treaty Org., Research and Technology Org., 1999) p. 4-1; Volk C H et al. http://www.dtic.mil/dtic/tr/fulltext/u2/a363917.pdf
  44. Ivanov V V, Novikov M A, Gelikonov V M Kvantovaya Elektronika 30 119 (2000); Ivanov V V, Novikov M A, Gelikonov V M Quantum Electron. 30 119 (2000)
  45. Eliseev P G Kvantovaya Elektronika 36 738 (2006); Eliseev P G Quantum Electron. 36 738 (2006)
  46. Steinberg B Z, Shamir A, Boag A Phys. Rev. E 74 016608 (2006)
  47. Schwartz S et al. Phys. Rev. Lett. 97 093902 (2006)
  48. Sunada S et al. Phys. Rev. A 78 053822 (2008)
  49. Sakharov V K, Duraev V P "Tverdotel’nyi lazernyi giroskop" Patent RU 2421689 S1. 12.11.2009
  50. Prokof’eva L, Sakharov V, Shcherbakov V Fotonika (5) 12 (2010)
  51. Akparov V V i dr. Kvantovaya Elektronika 40 851 (2010); Akparov V V et al. Quantum Electron. 40 851 (2010)
  52. Sakharov V K Zh. Tekh. Fiz. 71 (8) 76 (2011); Sakharov V K Tech. Phys. 56 1135 (2011)
  53. Novitski R, Steinberg B Z, Scheuer J Phys. Rev. A 85 023813 (2012)
  54. Post E J, Yildiz A Phys. Rev. Lett. 15 177 (1965)
  55. Yildiz A, Tang C H Phys. Rev. 146 947 (1966)
  56. Gersht E P Kvantovo-generatornye (lazernye i Yadernye) Giroskopy (L.: Leningr. voen. inzh. krasnoznam. akad. im. A F Mozhaiskogo, 1967)
  57. Bakalyar A I, Luk’yanov D P Osnovy Teorii Lazernykh Giroskopov i Ikh Primenenie v Navigatsionnykh Kompleksakh (L.: Leningr. voen. inzh. krasnoznam. akad. im. A F Mozhaiskogo, 1967)
  58. Fedorov B F, Sheremet’ev A G, Umnikov V N Opticheskii Kvantovyi Giroskop (M.: Mashinostroenie, 1973)
  59. Bychkov S I, Luk’yanov D P, Bakalyar A I Lazernyi Giroskop (M.: Sov. radio, 1975)
  60. Shupe D M Appl. Opt. 20 286 (1981)
  61. Sanders G A, Prentiss M G, Ezekiel S Opt. Lett. 6 569 (1981)
  62. Pavlath G A, Shaw H J Fiber-Optic Rotation Sensors (Eds S Ezekiel, H J Arditty) (Berlin: Springer-Verlag, 1982) p. 364
  63. Meyer R E et al. Opt. Lett. 8 644 (1983)
  64. Zarinetchi F et al. Proc. SPIE 478 122 (1984)
  65. Heer C V Proc. SPIE 487 2 (1984)
  66. Chow W W et al. Rev. Mod. Phys. 57 61 (1985)
  67. Donati S, Giuliani G, Sorel M Riv. Elletronica 6 (9) 61 (1997)
  68. Taguchi K et al. Opt. Quantum Electron. 31 1219 (1999)
  69. Taguchi K et al. IEEE Trans. Instrum. Measur. 48 1314 (1999)
  70. Taguchi K et al. Electr. Engen. Jpn. 132 (4) 73 (2000)
  71. Filatov Yu V Opticheskie Giroskopy (SPb.: GNTs RF TsNII "Elektropribor", 2005)
  72. Shvarts S i dr. "Tverdotel’nyi lazernyi giroskop s mekhanicheski aktiviruemoi usilivayushchei sredoi" Patent RU 2437062 S2. 17.08.2007
  73. Dmitriev V i dr. Fotonika (4) 18 (2008)
  74. Rabeendran A Thesis of Master of Science (Christchurch, New Zealand: Univ. Canterbury, 2008)
  75. Mignot A et al. Opt. Lett. 34 97 (2009)
  76. Anderson J L, Ryon J W Phys. Rev. 181 1765 (1969)
  77. Volkov A M, Kiselev V A Optika Spektroskopiya 29 365 (1970)
  78. Ohtsuka Y J. Lightwave Tech. 3 378 (1985)
  79. Sardyko V I Optika Spektroskopiya 82 598 (1997); Sardyko V I Opt. Spectrosc. 82 552 (1997)
  80. Numai T J. Appl. Phys 89 1537 (2001)
  81. Scheuer J, Yariv A Phys. Rev. Lett. 96 053901 (2006)
  82. Michelson A A Philos. Mag. 6 8 716 (1904)
  83. Pogány B Ann. Physik 85 244 (1928)
  84. Fabry Ch, Pérot A G C.R. Acad. Sci. 126 34 (1898)
  85. Prokof’eva L P, Sakharov V K, Shcherbakov V V Kvantovaya Elektronika 44 362 (2014); Prokof’eva L P, Sakharov V K, Shcherbakov V V Quantum. Electron. 44 362 (2014)

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