Abstract

Rotation sensitivity of optical gyroscopes with ring resonators and two input/output waveguides in a coplanar add-drop filter configuration is studied. First, the gyroscope with a single resonator is analyzed, which is shown to have slightly higher sensitivity than the one with one waveguide. Next, the sensor with two identical resonators coupled through waveguides is investigated, which turns out to have half the sensitivity of the one with a single resonator when compared for the same footprints. The last point is valid when the resonators have the same coupling coefficients to the waveguides in the sensor with two resonators.

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  1. E. J. Post, “Sagnac effect,” Rev. Mod. Phys. 39(2), 475–493 (1967).
    [CrossRef]
  2. U. Leonhardt and P. Piwnicki, “Ultrahigh sensitivity of slow-light gyroscope,” Phys. Rev. A 62(5), 055801 (2000).
    [CrossRef]
  3. A. B. Matsko, A. A. Savchenkov, V. S. Ilchenko, and L. Maleki, “Optical gyroscope with whispering gallery mode optical cavities,” Opt. Commun. 233(1-3), 107–112 (2004).
    [CrossRef]
  4. B. Z. Steinberg, “Rotating photonic crystals: a medium for compact optical gyroscopes,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(5), 056621 (2005).
    [CrossRef] [PubMed]
  5. J. Scheuer and A. Yariv, “Sagnac effect in coupled-resonator slow-light waveguide structures,” Phys. Rev. Lett. 96(5), 053901 (2006).
    [CrossRef] [PubMed]
  6. M. S. Shahriar, G. S. Pati, R. Tripathi, V. Gopal, M. Messall, and K. Salit, “Ultrahigh enhancement in absolute and relative rotation sensing using fast and slow light,” Phys. Rev. A 75(5), 053807 (2007).
    [CrossRef]
  7. B. Z. Steinberg, J. Scheuer, and A. Boag, “Rotation induced superstructure in slow-light waveguides with mode degeneracy: optical gyroscopes with exponential sensitivity,” J. Opt. Soc. Am. B 24(5), 1216 (2007).
    [CrossRef]
  8. C. Peng, Z. B. Li, and A. S. Xu, “Optical gyroscope based on a coupled resonator with the all-optical analogous property of electromagnetically induced transparency,” Opt. Express 15(7), 3864–3875 (2007).
    [CrossRef] [PubMed]
  9. M. Terrel, M. J. F. Digonnet, and S. Fan, “Performance comparison of slow-light coupled-resonator optical gyroscopes,” Laser Photonics. Rev. 3(5), 452–465 (2009).
    [CrossRef]
  10. Y. Zhang, H. Tian, X. Zhang, N. Wang, J. Zhang, H. Wu, and P. Yuan, “Experimental evidence of enhanced rotation sensing in a slow-light structure,” Opt. Lett. 35(5), 691–693 (2010).
    [CrossRef] [PubMed]
  11. B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15(6), 998–1005 (1997).
    [CrossRef]
  12. J. K. S. Poon, J. Scheuer, S. Mookherjea, G. T. Paloczi, Y. Huang, and A. Yariv, “Matrix analysis of microring coupled-resonator optical waveguides,” Opt. Express 12(1), 90–103 (2004).
    [CrossRef] [PubMed]
  13. R. B. Hurst, J.-P. R. Wells, and G. E. Stedman, “An elementary proof of the geometrical dependence of the Sagnac effect,” J. Opt. A, Pure Appl. Opt. 9(10), 838–841 (2007).
    [CrossRef]

2010

2009

M. Terrel, M. J. F. Digonnet, and S. Fan, “Performance comparison of slow-light coupled-resonator optical gyroscopes,” Laser Photonics. Rev. 3(5), 452–465 (2009).
[CrossRef]

2007

M. S. Shahriar, G. S. Pati, R. Tripathi, V. Gopal, M. Messall, and K. Salit, “Ultrahigh enhancement in absolute and relative rotation sensing using fast and slow light,” Phys. Rev. A 75(5), 053807 (2007).
[CrossRef]

B. Z. Steinberg, J. Scheuer, and A. Boag, “Rotation induced superstructure in slow-light waveguides with mode degeneracy: optical gyroscopes with exponential sensitivity,” J. Opt. Soc. Am. B 24(5), 1216 (2007).
[CrossRef]

C. Peng, Z. B. Li, and A. S. Xu, “Optical gyroscope based on a coupled resonator with the all-optical analogous property of electromagnetically induced transparency,” Opt. Express 15(7), 3864–3875 (2007).
[CrossRef] [PubMed]

R. B. Hurst, J.-P. R. Wells, and G. E. Stedman, “An elementary proof of the geometrical dependence of the Sagnac effect,” J. Opt. A, Pure Appl. Opt. 9(10), 838–841 (2007).
[CrossRef]

2006

J. Scheuer and A. Yariv, “Sagnac effect in coupled-resonator slow-light waveguide structures,” Phys. Rev. Lett. 96(5), 053901 (2006).
[CrossRef] [PubMed]

2005

B. Z. Steinberg, “Rotating photonic crystals: a medium for compact optical gyroscopes,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(5), 056621 (2005).
[CrossRef] [PubMed]

2004

A. B. Matsko, A. A. Savchenkov, V. S. Ilchenko, and L. Maleki, “Optical gyroscope with whispering gallery mode optical cavities,” Opt. Commun. 233(1-3), 107–112 (2004).
[CrossRef]

J. K. S. Poon, J. Scheuer, S. Mookherjea, G. T. Paloczi, Y. Huang, and A. Yariv, “Matrix analysis of microring coupled-resonator optical waveguides,” Opt. Express 12(1), 90–103 (2004).
[CrossRef] [PubMed]

2000

U. Leonhardt and P. Piwnicki, “Ultrahigh sensitivity of slow-light gyroscope,” Phys. Rev. A 62(5), 055801 (2000).
[CrossRef]

1997

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15(6), 998–1005 (1997).
[CrossRef]

1967

E. J. Post, “Sagnac effect,” Rev. Mod. Phys. 39(2), 475–493 (1967).
[CrossRef]

Boag, A.

Chu, S. T.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15(6), 998–1005 (1997).
[CrossRef]

Digonnet, M. J. F.

M. Terrel, M. J. F. Digonnet, and S. Fan, “Performance comparison of slow-light coupled-resonator optical gyroscopes,” Laser Photonics. Rev. 3(5), 452–465 (2009).
[CrossRef]

Fan, S.

M. Terrel, M. J. F. Digonnet, and S. Fan, “Performance comparison of slow-light coupled-resonator optical gyroscopes,” Laser Photonics. Rev. 3(5), 452–465 (2009).
[CrossRef]

Foresi, J.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15(6), 998–1005 (1997).
[CrossRef]

Gopal, V.

M. S. Shahriar, G. S. Pati, R. Tripathi, V. Gopal, M. Messall, and K. Salit, “Ultrahigh enhancement in absolute and relative rotation sensing using fast and slow light,” Phys. Rev. A 75(5), 053807 (2007).
[CrossRef]

Haus, H. A.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15(6), 998–1005 (1997).
[CrossRef]

Huang, Y.

Hurst, R. B.

R. B. Hurst, J.-P. R. Wells, and G. E. Stedman, “An elementary proof of the geometrical dependence of the Sagnac effect,” J. Opt. A, Pure Appl. Opt. 9(10), 838–841 (2007).
[CrossRef]

Ilchenko, V. S.

A. B. Matsko, A. A. Savchenkov, V. S. Ilchenko, and L. Maleki, “Optical gyroscope with whispering gallery mode optical cavities,” Opt. Commun. 233(1-3), 107–112 (2004).
[CrossRef]

Laine, J.-P.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15(6), 998–1005 (1997).
[CrossRef]

Leonhardt, U.

U. Leonhardt and P. Piwnicki, “Ultrahigh sensitivity of slow-light gyroscope,” Phys. Rev. A 62(5), 055801 (2000).
[CrossRef]

Li, Z. B.

Little, B. E.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15(6), 998–1005 (1997).
[CrossRef]

Maleki, L.

A. B. Matsko, A. A. Savchenkov, V. S. Ilchenko, and L. Maleki, “Optical gyroscope with whispering gallery mode optical cavities,” Opt. Commun. 233(1-3), 107–112 (2004).
[CrossRef]

Matsko, A. B.

A. B. Matsko, A. A. Savchenkov, V. S. Ilchenko, and L. Maleki, “Optical gyroscope with whispering gallery mode optical cavities,” Opt. Commun. 233(1-3), 107–112 (2004).
[CrossRef]

Messall, M.

M. S. Shahriar, G. S. Pati, R. Tripathi, V. Gopal, M. Messall, and K. Salit, “Ultrahigh enhancement in absolute and relative rotation sensing using fast and slow light,” Phys. Rev. A 75(5), 053807 (2007).
[CrossRef]

Mookherjea, S.

Paloczi, G. T.

Pati, G. S.

M. S. Shahriar, G. S. Pati, R. Tripathi, V. Gopal, M. Messall, and K. Salit, “Ultrahigh enhancement in absolute and relative rotation sensing using fast and slow light,” Phys. Rev. A 75(5), 053807 (2007).
[CrossRef]

Peng, C.

Piwnicki, P.

U. Leonhardt and P. Piwnicki, “Ultrahigh sensitivity of slow-light gyroscope,” Phys. Rev. A 62(5), 055801 (2000).
[CrossRef]

Poon, J. K. S.

Post, E. J.

E. J. Post, “Sagnac effect,” Rev. Mod. Phys. 39(2), 475–493 (1967).
[CrossRef]

Salit, K.

M. S. Shahriar, G. S. Pati, R. Tripathi, V. Gopal, M. Messall, and K. Salit, “Ultrahigh enhancement in absolute and relative rotation sensing using fast and slow light,” Phys. Rev. A 75(5), 053807 (2007).
[CrossRef]

Savchenkov, A. A.

A. B. Matsko, A. A. Savchenkov, V. S. Ilchenko, and L. Maleki, “Optical gyroscope with whispering gallery mode optical cavities,” Opt. Commun. 233(1-3), 107–112 (2004).
[CrossRef]

Scheuer, J.

Shahriar, M. S.

M. S. Shahriar, G. S. Pati, R. Tripathi, V. Gopal, M. Messall, and K. Salit, “Ultrahigh enhancement in absolute and relative rotation sensing using fast and slow light,” Phys. Rev. A 75(5), 053807 (2007).
[CrossRef]

Stedman, G. E.

R. B. Hurst, J.-P. R. Wells, and G. E. Stedman, “An elementary proof of the geometrical dependence of the Sagnac effect,” J. Opt. A, Pure Appl. Opt. 9(10), 838–841 (2007).
[CrossRef]

Steinberg, B. Z.

Terrel, M.

M. Terrel, M. J. F. Digonnet, and S. Fan, “Performance comparison of slow-light coupled-resonator optical gyroscopes,” Laser Photonics. Rev. 3(5), 452–465 (2009).
[CrossRef]

Tian, H.

Tripathi, R.

M. S. Shahriar, G. S. Pati, R. Tripathi, V. Gopal, M. Messall, and K. Salit, “Ultrahigh enhancement in absolute and relative rotation sensing using fast and slow light,” Phys. Rev. A 75(5), 053807 (2007).
[CrossRef]

Wang, N.

Wells, J.-P. R.

R. B. Hurst, J.-P. R. Wells, and G. E. Stedman, “An elementary proof of the geometrical dependence of the Sagnac effect,” J. Opt. A, Pure Appl. Opt. 9(10), 838–841 (2007).
[CrossRef]

Wu, H.

Xu, A. S.

Yariv, A.

Yuan, P.

Zhang, J.

Zhang, X.

Zhang, Y.

J. Lightwave Technol.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15(6), 998–1005 (1997).
[CrossRef]

J. Opt. A, Pure Appl. Opt.

R. B. Hurst, J.-P. R. Wells, and G. E. Stedman, “An elementary proof of the geometrical dependence of the Sagnac effect,” J. Opt. A, Pure Appl. Opt. 9(10), 838–841 (2007).
[CrossRef]

J. Opt. Soc. Am. B

Laser Photonics. Rev.

M. Terrel, M. J. F. Digonnet, and S. Fan, “Performance comparison of slow-light coupled-resonator optical gyroscopes,” Laser Photonics. Rev. 3(5), 452–465 (2009).
[CrossRef]

Opt. Commun.

A. B. Matsko, A. A. Savchenkov, V. S. Ilchenko, and L. Maleki, “Optical gyroscope with whispering gallery mode optical cavities,” Opt. Commun. 233(1-3), 107–112 (2004).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. A

U. Leonhardt and P. Piwnicki, “Ultrahigh sensitivity of slow-light gyroscope,” Phys. Rev. A 62(5), 055801 (2000).
[CrossRef]

M. S. Shahriar, G. S. Pati, R. Tripathi, V. Gopal, M. Messall, and K. Salit, “Ultrahigh enhancement in absolute and relative rotation sensing using fast and slow light,” Phys. Rev. A 75(5), 053807 (2007).
[CrossRef]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys.

B. Z. Steinberg, “Rotating photonic crystals: a medium for compact optical gyroscopes,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(5), 056621 (2005).
[CrossRef] [PubMed]

Phys. Rev. Lett.

J. Scheuer and A. Yariv, “Sagnac effect in coupled-resonator slow-light waveguide structures,” Phys. Rev. Lett. 96(5), 053901 (2006).
[CrossRef] [PubMed]

Rev. Mod. Phys.

E. J. Post, “Sagnac effect,” Rev. Mod. Phys. 39(2), 475–493 (1967).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

(a) Schematic diagram of an optical gyroscope with a single resonator with two input/output waveguides, which is subject to rotation at an angular rate of Ω. (b) Power at the out port |bout |2 versus ϕring , phase shift during half the roundtrip inside the ring resonator. Ω = 0.

Fig. 2
Fig. 2

(a) Calculated maximum sensitivity Smax versus |κ| for a gyroscope with a single resonator and two waveguides. Curve1: drop port. Curve2: out port. Curve3: combined output with ϕcomb = 0. Curve4: combined output with optimized ϕcomb (or ϕcomb,opt ). Dashed horizontal line: Smax,RFOG of Eq. (6). (b) ϕcomb,opt versus |κ|. R and α values used for the calculation are 5 cm and 0.06 m−1, respectively. Wavelength λ 0 of 700 nm is used throughout the analysis.

Fig. 3
Fig. 3

Maximum sensitivity Smax of a gyroscope with a single resonator and two waveguides at optimized κ, ϕring , and ϕcomb (a) versus α for R = 5 cm, and (b) versus R for α = 0.06 m−1.

Fig. 4
Fig. 4

Schematic diagram of an optical gyroscope with two resonators in a coplanar add-drop filter configuration.

Fig. 5
Fig. 5

(a) Calculated maximum sensitivity Smax versus |κ| for a gyroscope with two resonators and two waveguides when Lwg = 11 cm. Curve1: drop port. Curve2: out port. Curve3: combined output with ϕcomb = 0. Curve4: combined output with ϕcomb = ϕcomb,opt . (b) Calculated Smax versus Lwg . R and α values used for the calculation are 5 cm and 0.06 m−1, respectively.

Equations (20)

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[ a a d d b d r o p ] = 1 κ * [ t * 1 1 t ] [ 0 exp ( i ϕ R ) exp ( i ϕ R ) 0 ] ( 1 κ ) [ t 1 1 t * ] [ a i n b o u t ] ,
ϕ R = ϕ r i n g + ϕ S R i π R α 2 = π R n r i n g ω c + π R 2 Ω ω c 2 i π R α 2 ,
ϕ S a g n a c = 2 ω ( A Ω ) / c 2 ,
b o u t = t t * exp ( i 2 ϕ R ) 1 ( t * ) 2 exp ( i 2 ϕ R )     and    b d r o p = | κ | 2 exp ( i ϕ R ) 1 ( t * ) 2 exp ( i 2 ϕ R ) .
S = 1 P 0 d P d Ω ,
S m a x , R F O G = 4 R ω / ( 3 3 α c 2 ) ,
S m a x , 2 I O , S R = 1.1 R ω / ( α c 2 ) 1.4 S m a x , R F O G .
[ b i n b 1 ] = P [ a i n a 1 ] ,    [ b d r o p b 1 ] = P [ a d r o p a 1 ] , [ b o u t b 2 ] = P [ a o u t a 2 ] ,   and   [ b a d d b 2 ] = P [ a a d d a 2 ] ,
where  P = [ t κ κ * t * ] .
a d r o p = b a d d exp ( i ϕ W )  and   a o u t = b i n exp ( i ϕ W ) ,
where  ϕ W = ϕ w g + ϕ S W i L w g α 2 = n w g L w g ω c + R L w g Ω ω c 2 i L w g α 2 .
a 1 = b 1 exp ( i ϕ R ) ,   a 2 = b 2 exp ( i ϕ R ) ,
a 1 = t * a 1 exp ( i ϕ R ) κ * a d r o p exp [ i ( ϕ R + ϕ S W ) ] ,
and   a 2 = t * a 2 exp ( i ϕ R ) κ * a o u t exp [ i ( ϕ R + ϕ S W ) ] ,
b o u t = { B C exp ( i ϕ W ) D exp ( i ϕ R ) [ | t | 2 ( t * ) 2 exp ( i 2 ϕ R ) ] } / ( B 2 D 2 )
and  b d r o p = { C D exp ( i ϕ W ) + [ D 2 B | κ | 2 ] exp ( i ϕ R ) } / ( B 2 D 2 ) ,
where  B = 1 ( t * ) 2 exp ( i 2 ϕ R ) ,   C = t 2 | t | 2 exp ( i 2 ϕ R ) ,
and  D = | κ | 2 exp [ i ( ϕ R + ϕ W + ϕ S W ) ] .
S m a x , 2 I O , T R = 1.1 ( R 2 + L w g π ) ω α c 2 .
S m a x , 2 I O , T R  per area S m a x , 2 I O , S R  per area = [ 1.1 ( R 2 + L w g π ) ω α c 2 ] / ( π R 2 + 2 R L w g ) ( 1.1 R ω α c 2 ) / ( π R 2 ) = 1 2 .

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