Abstract

The electromagnetically induced transparency- (EIT)-like phenomenon, called coupled-resonator-induced transparency (CRIT), could occur through a classical mean in a coupled resonator structure, due to classical destructive interference. We propose to utilize this property to construct a miniature highly sensitive gyroscope. We analyze the Sagnac effect in the CRIT structure and point out that the Sagnac phase shift contributed by the whole structure is notably enhanced due to its highly dispersive property. An explicit expression of the phase shift is derived and discussed. To realize the implementation of the CRIT-structure-based gyroscope, issues that ought to be considered are fully discussed here, such as the fabrication possibility, linewidth, shot-noise-limit sensitivity, and integration.

© 2007 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. E. J. Post, "Sagnac effect," Rev. Mod. Phys. 39, 475-493 (1967).
    [CrossRef]
  2. H. J. Arditty and H. C. Lefevre, "Sagnac effect in fiber gyroscopes," Opt. Lett. 6, 401-403 (1981).
    [CrossRef] [PubMed]
  3. R. A. Bergh, H. C. Lefevre, and H. J. Shaw, "An overview of fiber-optic gyroscopes," J. Lightwave Technol. 2, 91-107 (1984).
    [CrossRef]
  4. H. C. Lefevre, The Fiber-Optic Gyroscope (Artech House Publishers, 1993).
  5. U. Leonhardt and P. Piwnitski, "Ultrahigh sensitivity of slow-light gyroscope," Phys. Rev. A. 62, 055801 (2000).
    [CrossRef]
  6. B. Z. Steinberg, "Rotating photonic crystals: A medium for compact optical gyroscopes," Phys. Rev. E. 71, 056621 (2005).
    [CrossRef]
  7. B. Z. Steinberg and A. Boag, "Splitting of microcavity degenerate modes in rotating photonic crystals—the miniature optical gyroscopes," J. Opt. Soc. Am. B. 24, 142-151 (2006).
    [CrossRef]
  8. B. Matsko, A. A. Savchenkov, V. S. Ilchenko, and L. Maleki, "Optical gyroscope with whispering gallery mode optical cavities," Opt. Commun. 233, 107-112 (2004).
    [CrossRef]
  9. J. Scheuer and A. Yariv, "Sagnac effect in coupled-resonator slow-light waveguide structures," Phys. Rev. Lett. 96, 053901 (2006).
    [CrossRef] [PubMed]
  10. V. Vali, R. W. Shorthill, and M. F. Berg, "Fresnel-Fizeau effect in a rotating optical fiber ring interferometer," Appl. Opt. 16, 2605-2607 (1977).
    [CrossRef] [PubMed]
  11. V. Vali and R. W. Shorthill, "Fiber ring interferometer," Appl. Opt. 15, 1099-1100 (1976).
    [CrossRef] [PubMed]
  12. W. R. Leeb, G. Schiffner, and E. Scheiterer, "Optical fiber gyroscopes: Sagnac or Fizeau effect," Appl. Opt. 18, 1293-1295 (1979).
    [CrossRef] [PubMed]
  13. G. B. Malykin, "The Sagnac effect: correct and incorrect explanations," Physics-Uspekhi 43, 1229-1252 (2000).
    [CrossRef]
  14. C. Peng, Z. Li, and A. Xu, "Rotation sensing based on a slow light resonating structure with high group dispersion," Appl. Opt. (to be published).
    [PubMed]
  15. D. Smith, H. Chang, K. A. Fuller, A. T. Rosenberger, and R. W. Boyd, "Coupled-resonator-induced transparency," Phys. Rev. A 69, 063804 (2004).
    [CrossRef]
  16. Y. Li and M. Xiao, "Observation of quantum interference between dressed states in an electromagnetically induced transparency," Phys. Rev. A 51, 4959-4962 (1995).
    [CrossRef] [PubMed]
  17. D. Smith, H. Chang, and K. A. Fuller, "Whispering-gallery mode splitting in coupled microresonators," J. Opt. Soc. Am. B 20, 1967-1974 (2003).
    [CrossRef]
  18. Q. Xu, S. Sandhu, M. L. Povinelli, J. Shakya, S. Fan, and M. Lipson, "Experimental realization of an on-chip all-optical analogue to electromagnetically induced transparency," Phys. Rev. Lett. 96, 123901 (2006).
    [CrossRef] [PubMed]

2006

B. Z. Steinberg and A. Boag, "Splitting of microcavity degenerate modes in rotating photonic crystals—the miniature optical gyroscopes," J. Opt. Soc. Am. B. 24, 142-151 (2006).
[CrossRef]

J. Scheuer and A. Yariv, "Sagnac effect in coupled-resonator slow-light waveguide structures," Phys. Rev. Lett. 96, 053901 (2006).
[CrossRef] [PubMed]

Q. Xu, S. Sandhu, M. L. Povinelli, J. Shakya, S. Fan, and M. Lipson, "Experimental realization of an on-chip all-optical analogue to electromagnetically induced transparency," Phys. Rev. Lett. 96, 123901 (2006).
[CrossRef] [PubMed]

2005

B. Z. Steinberg, "Rotating photonic crystals: A medium for compact optical gyroscopes," Phys. Rev. E. 71, 056621 (2005).
[CrossRef]

2004

D. Smith, H. Chang, K. A. Fuller, A. T. Rosenberger, and R. W. Boyd, "Coupled-resonator-induced transparency," Phys. Rev. A 69, 063804 (2004).
[CrossRef]

B. Matsko, A. A. Savchenkov, V. S. Ilchenko, and L. Maleki, "Optical gyroscope with whispering gallery mode optical cavities," Opt. Commun. 233, 107-112 (2004).
[CrossRef]

2003

2000

G. B. Malykin, "The Sagnac effect: correct and incorrect explanations," Physics-Uspekhi 43, 1229-1252 (2000).
[CrossRef]

U. Leonhardt and P. Piwnitski, "Ultrahigh sensitivity of slow-light gyroscope," Phys. Rev. A. 62, 055801 (2000).
[CrossRef]

1995

Y. Li and M. Xiao, "Observation of quantum interference between dressed states in an electromagnetically induced transparency," Phys. Rev. A 51, 4959-4962 (1995).
[CrossRef] [PubMed]

1984

R. A. Bergh, H. C. Lefevre, and H. J. Shaw, "An overview of fiber-optic gyroscopes," J. Lightwave Technol. 2, 91-107 (1984).
[CrossRef]

1981

1979

1977

1976

1967

E. J. Post, "Sagnac effect," Rev. Mod. Phys. 39, 475-493 (1967).
[CrossRef]

Arditty, H. J.

Berg, M. F.

Bergh, R. A.

R. A. Bergh, H. C. Lefevre, and H. J. Shaw, "An overview of fiber-optic gyroscopes," J. Lightwave Technol. 2, 91-107 (1984).
[CrossRef]

Boag, A.

B. Z. Steinberg and A. Boag, "Splitting of microcavity degenerate modes in rotating photonic crystals—the miniature optical gyroscopes," J. Opt. Soc. Am. B. 24, 142-151 (2006).
[CrossRef]

Boyd, R. W.

D. Smith, H. Chang, K. A. Fuller, A. T. Rosenberger, and R. W. Boyd, "Coupled-resonator-induced transparency," Phys. Rev. A 69, 063804 (2004).
[CrossRef]

Chang, H.

D. Smith, H. Chang, K. A. Fuller, A. T. Rosenberger, and R. W. Boyd, "Coupled-resonator-induced transparency," Phys. Rev. A 69, 063804 (2004).
[CrossRef]

D. Smith, H. Chang, and K. A. Fuller, "Whispering-gallery mode splitting in coupled microresonators," J. Opt. Soc. Am. B 20, 1967-1974 (2003).
[CrossRef]

Fan, S.

Q. Xu, S. Sandhu, M. L. Povinelli, J. Shakya, S. Fan, and M. Lipson, "Experimental realization of an on-chip all-optical analogue to electromagnetically induced transparency," Phys. Rev. Lett. 96, 123901 (2006).
[CrossRef] [PubMed]

Fuller, K. A.

D. Smith, H. Chang, K. A. Fuller, A. T. Rosenberger, and R. W. Boyd, "Coupled-resonator-induced transparency," Phys. Rev. A 69, 063804 (2004).
[CrossRef]

D. Smith, H. Chang, and K. A. Fuller, "Whispering-gallery mode splitting in coupled microresonators," J. Opt. Soc. Am. B 20, 1967-1974 (2003).
[CrossRef]

Ilchenko, V. S.

B. Matsko, A. A. Savchenkov, V. S. Ilchenko, and L. Maleki, "Optical gyroscope with whispering gallery mode optical cavities," Opt. Commun. 233, 107-112 (2004).
[CrossRef]

Leeb, W. R.

Lefevre, H. C.

R. A. Bergh, H. C. Lefevre, and H. J. Shaw, "An overview of fiber-optic gyroscopes," J. Lightwave Technol. 2, 91-107 (1984).
[CrossRef]

H. J. Arditty and H. C. Lefevre, "Sagnac effect in fiber gyroscopes," Opt. Lett. 6, 401-403 (1981).
[CrossRef] [PubMed]

Leonhardt, U.

U. Leonhardt and P. Piwnitski, "Ultrahigh sensitivity of slow-light gyroscope," Phys. Rev. A. 62, 055801 (2000).
[CrossRef]

Li, Y.

Y. Li and M. Xiao, "Observation of quantum interference between dressed states in an electromagnetically induced transparency," Phys. Rev. A 51, 4959-4962 (1995).
[CrossRef] [PubMed]

Li, Z.

C. Peng, Z. Li, and A. Xu, "Rotation sensing based on a slow light resonating structure with high group dispersion," Appl. Opt. (to be published).
[PubMed]

Lipson, M.

Q. Xu, S. Sandhu, M. L. Povinelli, J. Shakya, S. Fan, and M. Lipson, "Experimental realization of an on-chip all-optical analogue to electromagnetically induced transparency," Phys. Rev. Lett. 96, 123901 (2006).
[CrossRef] [PubMed]

Maleki, L.

B. Matsko, A. A. Savchenkov, V. S. Ilchenko, and L. Maleki, "Optical gyroscope with whispering gallery mode optical cavities," Opt. Commun. 233, 107-112 (2004).
[CrossRef]

Malykin, G. B.

G. B. Malykin, "The Sagnac effect: correct and incorrect explanations," Physics-Uspekhi 43, 1229-1252 (2000).
[CrossRef]

Matsko, B.

B. Matsko, A. A. Savchenkov, V. S. Ilchenko, and L. Maleki, "Optical gyroscope with whispering gallery mode optical cavities," Opt. Commun. 233, 107-112 (2004).
[CrossRef]

Peng, C.

C. Peng, Z. Li, and A. Xu, "Rotation sensing based on a slow light resonating structure with high group dispersion," Appl. Opt. (to be published).
[PubMed]

Piwnitski, P.

U. Leonhardt and P. Piwnitski, "Ultrahigh sensitivity of slow-light gyroscope," Phys. Rev. A. 62, 055801 (2000).
[CrossRef]

Post, E. J.

E. J. Post, "Sagnac effect," Rev. Mod. Phys. 39, 475-493 (1967).
[CrossRef]

Povinelli, M. L.

Q. Xu, S. Sandhu, M. L. Povinelli, J. Shakya, S. Fan, and M. Lipson, "Experimental realization of an on-chip all-optical analogue to electromagnetically induced transparency," Phys. Rev. Lett. 96, 123901 (2006).
[CrossRef] [PubMed]

Rosenberger, A. T.

D. Smith, H. Chang, K. A. Fuller, A. T. Rosenberger, and R. W. Boyd, "Coupled-resonator-induced transparency," Phys. Rev. A 69, 063804 (2004).
[CrossRef]

Sandhu, S.

Q. Xu, S. Sandhu, M. L. Povinelli, J. Shakya, S. Fan, and M. Lipson, "Experimental realization of an on-chip all-optical analogue to electromagnetically induced transparency," Phys. Rev. Lett. 96, 123901 (2006).
[CrossRef] [PubMed]

Savchenkov, A. A.

B. Matsko, A. A. Savchenkov, V. S. Ilchenko, and L. Maleki, "Optical gyroscope with whispering gallery mode optical cavities," Opt. Commun. 233, 107-112 (2004).
[CrossRef]

Scheiterer, E.

Scheuer, J.

J. Scheuer and A. Yariv, "Sagnac effect in coupled-resonator slow-light waveguide structures," Phys. Rev. Lett. 96, 053901 (2006).
[CrossRef] [PubMed]

Schiffner, G.

Shakya, J.

Q. Xu, S. Sandhu, M. L. Povinelli, J. Shakya, S. Fan, and M. Lipson, "Experimental realization of an on-chip all-optical analogue to electromagnetically induced transparency," Phys. Rev. Lett. 96, 123901 (2006).
[CrossRef] [PubMed]

Shaw, H. J.

R. A. Bergh, H. C. Lefevre, and H. J. Shaw, "An overview of fiber-optic gyroscopes," J. Lightwave Technol. 2, 91-107 (1984).
[CrossRef]

Shorthill, R. W.

Smith, D.

D. Smith, H. Chang, K. A. Fuller, A. T. Rosenberger, and R. W. Boyd, "Coupled-resonator-induced transparency," Phys. Rev. A 69, 063804 (2004).
[CrossRef]

D. Smith, H. Chang, and K. A. Fuller, "Whispering-gallery mode splitting in coupled microresonators," J. Opt. Soc. Am. B 20, 1967-1974 (2003).
[CrossRef]

Steinberg, B. Z.

B. Z. Steinberg and A. Boag, "Splitting of microcavity degenerate modes in rotating photonic crystals—the miniature optical gyroscopes," J. Opt. Soc. Am. B. 24, 142-151 (2006).
[CrossRef]

B. Z. Steinberg, "Rotating photonic crystals: A medium for compact optical gyroscopes," Phys. Rev. E. 71, 056621 (2005).
[CrossRef]

Vali, V.

Xiao, M.

Y. Li and M. Xiao, "Observation of quantum interference between dressed states in an electromagnetically induced transparency," Phys. Rev. A 51, 4959-4962 (1995).
[CrossRef] [PubMed]

Xu, A.

C. Peng, Z. Li, and A. Xu, "Rotation sensing based on a slow light resonating structure with high group dispersion," Appl. Opt. (to be published).
[PubMed]

Xu, Q.

Q. Xu, S. Sandhu, M. L. Povinelli, J. Shakya, S. Fan, and M. Lipson, "Experimental realization of an on-chip all-optical analogue to electromagnetically induced transparency," Phys. Rev. Lett. 96, 123901 (2006).
[CrossRef] [PubMed]

Yariv, A.

J. Scheuer and A. Yariv, "Sagnac effect in coupled-resonator slow-light waveguide structures," Phys. Rev. Lett. 96, 053901 (2006).
[CrossRef] [PubMed]

Appl. Opt.

J. Lightwave Technol.

R. A. Bergh, H. C. Lefevre, and H. J. Shaw, "An overview of fiber-optic gyroscopes," J. Lightwave Technol. 2, 91-107 (1984).
[CrossRef]

J. Opt. Soc. Am. B

J. Opt. Soc. Am. B.

B. Z. Steinberg and A. Boag, "Splitting of microcavity degenerate modes in rotating photonic crystals—the miniature optical gyroscopes," J. Opt. Soc. Am. B. 24, 142-151 (2006).
[CrossRef]

Opt. Commun.

B. Matsko, A. A. Savchenkov, V. S. Ilchenko, and L. Maleki, "Optical gyroscope with whispering gallery mode optical cavities," Opt. Commun. 233, 107-112 (2004).
[CrossRef]

Opt. Lett.

Phys. Rev. A

D. Smith, H. Chang, K. A. Fuller, A. T. Rosenberger, and R. W. Boyd, "Coupled-resonator-induced transparency," Phys. Rev. A 69, 063804 (2004).
[CrossRef]

Y. Li and M. Xiao, "Observation of quantum interference between dressed states in an electromagnetically induced transparency," Phys. Rev. A 51, 4959-4962 (1995).
[CrossRef] [PubMed]

Phys. Rev. A.

U. Leonhardt and P. Piwnitski, "Ultrahigh sensitivity of slow-light gyroscope," Phys. Rev. A. 62, 055801 (2000).
[CrossRef]

Phys. Rev. E.

B. Z. Steinberg, "Rotating photonic crystals: A medium for compact optical gyroscopes," Phys. Rev. E. 71, 056621 (2005).
[CrossRef]

Phys. Rev. Lett.

J. Scheuer and A. Yariv, "Sagnac effect in coupled-resonator slow-light waveguide structures," Phys. Rev. Lett. 96, 053901 (2006).
[CrossRef] [PubMed]

Q. Xu, S. Sandhu, M. L. Povinelli, J. Shakya, S. Fan, and M. Lipson, "Experimental realization of an on-chip all-optical analogue to electromagnetically induced transparency," Phys. Rev. Lett. 96, 123901 (2006).
[CrossRef] [PubMed]

Physics-Uspekhi

G. B. Malykin, "The Sagnac effect: correct and incorrect explanations," Physics-Uspekhi 43, 1229-1252 (2000).
[CrossRef]

Rev. Mod. Phys.

E. J. Post, "Sagnac effect," Rev. Mod. Phys. 39, 475-493 (1967).
[CrossRef]

Other

H. C. Lefevre, The Fiber-Optic Gyroscope (Artech House Publishers, 1993).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1.
Fig. 1.

Typical-energy-level diagram for the observation of degenerated three-level EIT.

Fig. 2.
Fig. 2.

CRIT configuration with N coupled optical resonators.

Fig. 3.
Fig. 3.

Two-identical-rings CRIT configuration, analogous to the degenerated two-level EIT: a1 = 0.9999, a2 = 0.88; r1 = 0.999, r2 = 0.8; and four-identical rings CRIT configuration, analogous to the multilevel EIT:

Fig. 4.
Fig. 4.

Sagnac-effect-induced normalized phase shift versus single-pass phase shift for the two-rings configuration: a1 = 0.9999, a2 = 0.88; r1 = 0.999, r2 = 0.8. The results that follow the dispersion relation of the structure (dashed curve) and straightforward numerical calculation from transfer function (solid curve) are plotted. The Sagnac-effect-induced normalized phase shift versus single-pass phase shift for the single-resonator configuration: a1 = 0.9999, r1 = 0.8(red, dotted curve).

Fig. 5.
Fig. 5.

Sagnac-effect-induced normalized phase shift at resonance as a function of the reflection coefficients for the two-rings configuration: a 1 = 0.9999 , a 2 = 0.88 . The numerical result from transfer function and theoretic result from explicit expression Eq. (14).

Fig. 6.
Fig. 6.

CRIT linewidth versus the reflection coefficients r 1and r 2, for the two-rings configuration: a 1 = 0.9999, a 2 = 0.88.

Equations (18)

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

W ( Δ ) = Ω p 2 Γ 1 + 4 Γ 2 [ Δ ( Ω c 2 ) 2 Δ ] 2 [ Ω p 2 Γ ] K ( Δ ) ,
τ ˜ j ( ϕ j , ϕ j 1 , , ϕ 1 ) = E ˜ 4 ( j 1 ) + 2 E ˜ 4 ( j 1 ) = r j a j τ ˜ j 1 e j 1 r j a j τ ˜ j 1 e j ,
A ˜ j ( ϕ j , ϕ j 1 , , ϕ 1 ) 1 T ˜ j = A ˜ j ( env ) 1 + F ˜ j sin 2 ( ϕ ˜ j 1 ( eff ) + ϕ j 2 ) ,
A ˜ 2 ( δ ) = A ˜ 2 ( env ) 1 + 4 γ 2 [ δ ( Δω 2 ) 2 δ ] 2 A ˜ 2 ( env ) κ ( δ ) .
Δϕ = 4 ωA c 2 Ω ,
Δ ϕ ˜ j ( eff ) = ϕ ˜ j , + ( eff ) ( ϕ j + Δϕ j , ϕ j 1 + Δϕ j 1 , , ϕ 1 + Δϕ 1 )
ϕ ˜ j , ( eff ) ( ϕ j Δϕ j , ϕ j 1 Δϕ j 1 , , ϕ 1 Δϕ 1 ) ,
Δ ϕ ˜ j ( eff ) = ϕ ˜ j ( eff ) ∂ϕ Δ ϕ .
d τ ˜ j = τ ˜ j ϕ j d ϕ j + τ ˜ j τ ˜ j 1 d τ ˜ j 1 .
κ ˜ j = a j t ˜ j 2 e i ϕ j ( 1 r j a j τ ˜ j 1 e j ) 2 .
d τ ˜ j = i τ ˜ j 1 κ ˜ j d ϕ j + i τ ˜ j 2 κ ˜ j κ ˜ j 1 d ϕ j 1 + + i ( 1 ) j τ ˜ 0 κ ˜ j κ ˜ j 1 κ ˜ 1 d ϕ 1 .
Δ ϕ ˜ j ( eff ) ϕ = 0 = arg ( τ ˜ j + d τ ˜ j ) arg ( τ ˜ j ) = arg ( τ ˜ j + d τ ˜ j ) .
Δ ϕ ˜ j ( eff ) ϕ = 0 = d τ ˜ j τ ˜ j .
Δ ϕ ˜ 2 ( eff ) ϕ = 0 = ( τ ˜ 1 τ ˜ 2 κ ˜ 2 ) d ϕ 2 + ( 1 τ ˜ 2 κ ˜ 2 κ ˜ 1 ) d ϕ 1 ϕ = 0 .
Δϕ̃ 2 ( eff ) = a 2 ( 1 r 2 2 ) ( 1 + r 2 a 2 ) ( r 2 + a 2 ) [ 1 + r 1 1 r 1 1 + 2 ] = 1 r 2 2 ( 1 + r 2 a 2 ) ( r 2 + a 2 ) 2 r 1 a 2 1 r 1 .
δ FWHM = Δ ω 2 γ = 4 ( 1 r 1 ) r 2 a 2 r 1 ( 1 r 2 a 2 ) τ R .
Δ ϕ min > σ Δϕ = ησ P P = 2 ħω Pt M η ,
Ω min = c 2 4 ω A ( 1 + r 2 a 2 ) ( r 2 + a 2 ) 1 r 2 2 1 r 1 2 r 1 a 2 2 ħω Pt M η .

Metrics