Abstract

We present an in-depth analysis of the Kerr effect in resonator fiber optic gyros (R-FOGs) based on triangular wave phase modulation. Formulations that relate gyro output to the rotation rate, the Kerr nonlinearity, and other fiber and gyro parameters are derived and used to study the effect of Kerr nonlinearity on the gyro performance. Numerical investigation shows that the Kerr effect results in a nonzero gyro output even when the gyro is at stationary, which is interpreted as an error in the measurement of rotation rate. This error was found to increase as the frequencies of the two triangular phase modulations deviate from each other, and is not zero even if the intensities of the two counterpropagating beams are exactly the same. For fixed frequencies of the triangular phase modulations, there exists an optimal intensity splitting ratio for the two counterpropagating beams, which leads to zero gyro error. Calculation shows that the measurement error due to the Kerr effect for an R-FOG with a hollow-core photonic bandgap fiber as the fiber loop can be one to two orders of magnitude smaller than an R-FOG with a conventional single mode fiber loop.

© 2010 Optical Society of America

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    [CrossRef]
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    [CrossRef]
  3. K. Iwatsuki, K. Hotate, and M. Higashiguchi, “Resonance characteristics of backscattering in optical passive-ring resonator gyro: experiment,” Appl. Opt. 25, 4448-4451 (1986).
    [CrossRef]
  4. K. Iwatsuki, K. Hotate, and M. Higashiguchi, “Effect of Rayleigh backscattering in an optical passive ring-resonator gyro,” Appl. Opt. 23, 3916-3924 (1984).
    [CrossRef]
  5. K. Iwatsuki, K. Hotate, and M. Higashiguchi, “Kerr effect in an optical passive ring-resonator gyro,” J. Lightwave Technol. 4, 645-651 (1986).
    [CrossRef]
  6. K. Takiguchi and K. Hotate, “Method to reduce the optical Kerr-effect-induced bias in an optical passive ring-resonator gyro,” IEEE Photonics Technol. Lett. 4, 203-206 (1992).
    [CrossRef]
  7. K. Hotate and K. Tabe, “Drift of an optical fiber gyroscope caused by the Faraday effect: experiment,” J. Lightwave Technol. 5, 997-1001 (1987).
    [CrossRef]
  8. T. Ito and K. Hotate, “Closed-loop operation in the resonator fiber optic gyro using Faraday effect with a twisted single-mode-fiber resonator,” Proc. SPIE 2837, 260-271 (1996).
  9. K. Hotate and Y. Kikuchi, “Analysis of thermo-optically induced bias drift in resonator fiber optic gyro,” Proc. SPIE 4204, 81-88 (2001).
  10. R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allan, “Single-mode photonic band gap guidance of light in air,” Science 285, 1537-1539(1999).
    [CrossRef]
  11. G. A. Sanders, L. K. Strandjord, and T. C. Qiu, “Hollow core fiber optic ring resonator for rotation sensing,” in Optical Fiber Sensors (Optical Society of America, 2006), paper ME6.
  12. C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Muller, J. A. West, N. F. Borrelli, D. C. Allan, and K. W. Koch, “Low-loss hollow-core silica/air photonic bandgap fibre,” Nature 424, 657-659 (2003).
  13. H. K. Kim, M. J. F. Digonnet, and G. S. Kino, “Air-core photonic-bandgap fiber-optic gyroscope,” J. Lightwave Technol. 24, 3169-3174 (2006).
    [CrossRef]
  14. Q. Yao, Y. Hu, Z. Song, and Y. Xie, “Study on Kerr-effect-induced bias reduction method for resonator fiber optic gyroscope,” Acta Photonica Sin. 34, 1320-1323 (2005).
  15. X. Yu, Y. Liao, M. Zhang, Y. Yu, and D. Li, “Kerr effect in an optical passive ring-resonator gyro using a hollow-core photonic band-gap fiber,” Chin. J. Lasers 35, 430-435 (2008).
    [CrossRef]
  16. D. Ying, H. Ma, and Z. Jin, “Resonator fiber optic gyro using the triangle wave phase modulation technique,” Opt. Commun. 281, 580-586 (2008).
    [CrossRef]
  17. Z. Jin, Z. Yang, H. Ma, and D. Ying, “Open-loop experiments in a resonator fiber-optic gyro using digital triangle wave phase modulation,” IEEE Photonics Technol. Lett. 19, 1685-1687(2007).
    [CrossRef]
  18. D. Ying, H. Ma, and Z. Jin, “Dynamic characteristics of R-FOG based on the triangle wave phase modulation technique,” Opt. Commun. 281, 5340-5343 (2008).
    [CrossRef]
  19. K. Hotate and M. Harumoto, “Resonator fiber optic gyro using digital serrodyne modulation,” J. Lightwave Technol. 15, 466-473 (1997).
    [CrossRef]
  20. K. Hotate and G. Hayashi, “Resonator fiber optic gyro using digital serrodyne modulation-method to reduce the noise induced by the backscattering and closed-loop operation using digital signal processing,” Proc. SPIE 3746, 104-107 (1999).
  21. H. Ma, Z. Jin, C. Ding, and Y. Wang, “Influence of spectral linewidth of laser on resonance characteristics in fiber ring resonator,” Chin. J. Lasers 30, 731-734 (2003).
  22. Y. Ohtsuka, “Optical coherence effects on a fiber-sensing Fabry-Perot interferometer,” Appl. Opt. 21, 4316-4320 (1982).
    [CrossRef]
  23. X. Zhang, H. Ma, C. Ding, and Z. Jin, “Optical Kerr effect in phase modulation spectroscopy resonator fiber optic gyro,” Chin. J. Lasers 33, 814-818 (2006).
  24. H. Ma, Z. Jin, C. Ding, and Y. Wang, “Research on signal detection method of resonator fiber optical gyro,” Chin. J. Lasers 31, 1001-1005 (2004).
  25. R. E. Meyer, S. Ezekiel, D. W. Stowe, and V. J. Tekippe, “Passive fiber-optic ring resonator for rotation sensing,” Opt. Lett. 8, 644-646 (1983).
    [CrossRef]
  26. H. C. Lefevre, The Fiber-Optic Gyroscope (Artech, 1993).

2008

X. Yu, Y. Liao, M. Zhang, Y. Yu, and D. Li, “Kerr effect in an optical passive ring-resonator gyro using a hollow-core photonic band-gap fiber,” Chin. J. Lasers 35, 430-435 (2008).
[CrossRef]

D. Ying, H. Ma, and Z. Jin, “Resonator fiber optic gyro using the triangle wave phase modulation technique,” Opt. Commun. 281, 580-586 (2008).
[CrossRef]

D. Ying, H. Ma, and Z. Jin, “Dynamic characteristics of R-FOG based on the triangle wave phase modulation technique,” Opt. Commun. 281, 5340-5343 (2008).
[CrossRef]

2007

Z. Jin, Z. Yang, H. Ma, and D. Ying, “Open-loop experiments in a resonator fiber-optic gyro using digital triangle wave phase modulation,” IEEE Photonics Technol. Lett. 19, 1685-1687(2007).
[CrossRef]

2006

X. Zhang, H. Ma, C. Ding, and Z. Jin, “Optical Kerr effect in phase modulation spectroscopy resonator fiber optic gyro,” Chin. J. Lasers 33, 814-818 (2006).

H. K. Kim, M. J. F. Digonnet, and G. S. Kino, “Air-core photonic-bandgap fiber-optic gyroscope,” J. Lightwave Technol. 24, 3169-3174 (2006).
[CrossRef]

2005

Q. Yao, Y. Hu, Z. Song, and Y. Xie, “Study on Kerr-effect-induced bias reduction method for resonator fiber optic gyroscope,” Acta Photonica Sin. 34, 1320-1323 (2005).

2004

H. Ma, Z. Jin, C. Ding, and Y. Wang, “Research on signal detection method of resonator fiber optical gyro,” Chin. J. Lasers 31, 1001-1005 (2004).

2003

C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Muller, J. A. West, N. F. Borrelli, D. C. Allan, and K. W. Koch, “Low-loss hollow-core silica/air photonic bandgap fibre,” Nature 424, 657-659 (2003).

H. Ma, Z. Jin, C. Ding, and Y. Wang, “Influence of spectral linewidth of laser on resonance characteristics in fiber ring resonator,” Chin. J. Lasers 30, 731-734 (2003).

2001

K. Hotate and Y. Kikuchi, “Analysis of thermo-optically induced bias drift in resonator fiber optic gyro,” Proc. SPIE 4204, 81-88 (2001).

1999

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allan, “Single-mode photonic band gap guidance of light in air,” Science 285, 1537-1539(1999).
[CrossRef]

K. Hotate and G. Hayashi, “Resonator fiber optic gyro using digital serrodyne modulation-method to reduce the noise induced by the backscattering and closed-loop operation using digital signal processing,” Proc. SPIE 3746, 104-107 (1999).

1997

K. Hotate and M. Harumoto, “Resonator fiber optic gyro using digital serrodyne modulation,” J. Lightwave Technol. 15, 466-473 (1997).
[CrossRef]

1996

T. Ito and K. Hotate, “Closed-loop operation in the resonator fiber optic gyro using Faraday effect with a twisted single-mode-fiber resonator,” Proc. SPIE 2837, 260-271 (1996).

1992

K. Takiguchi and K. Hotate, “Method to reduce the optical Kerr-effect-induced bias in an optical passive ring-resonator gyro,” IEEE Photonics Technol. Lett. 4, 203-206 (1992).
[CrossRef]

1987

K. Hotate and K. Tabe, “Drift of an optical fiber gyroscope caused by the Faraday effect: experiment,” J. Lightwave Technol. 5, 997-1001 (1987).
[CrossRef]

1986

K. Iwatsuki, K. Hotate, and M. Higashiguchi, “Kerr effect in an optical passive ring-resonator gyro,” J. Lightwave Technol. 4, 645-651 (1986).
[CrossRef]

K. Iwatsuki, K. Hotate, and M. Higashiguchi, “Resonance characteristics of backscattering in optical passive-ring resonator gyro: experiment,” Appl. Opt. 25, 4448-4451 (1986).
[CrossRef]

1985

W. W. Chow, J. Gea-Banaciloche, and L. M. Pedrotti, “The ring laser gyro,” Rev. Mod. Phys. 57, 61-103 (1985).
[CrossRef]

1984

1983

1982

1981

Allan, D. C.

C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Muller, J. A. West, N. F. Borrelli, D. C. Allan, and K. W. Koch, “Low-loss hollow-core silica/air photonic bandgap fibre,” Nature 424, 657-659 (2003).

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allan, “Single-mode photonic band gap guidance of light in air,” Science 285, 1537-1539(1999).
[CrossRef]

Birks, T. A.

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allan, “Single-mode photonic band gap guidance of light in air,” Science 285, 1537-1539(1999).
[CrossRef]

Borrelli, N. F.

C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Muller, J. A. West, N. F. Borrelli, D. C. Allan, and K. W. Koch, “Low-loss hollow-core silica/air photonic bandgap fibre,” Nature 424, 657-659 (2003).

Chow, W. W.

W. W. Chow, J. Gea-Banaciloche, and L. M. Pedrotti, “The ring laser gyro,” Rev. Mod. Phys. 57, 61-103 (1985).
[CrossRef]

Cregan, R. F.

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allan, “Single-mode photonic band gap guidance of light in air,” Science 285, 1537-1539(1999).
[CrossRef]

Digonnet, M. J. F.

Ding, C.

X. Zhang, H. Ma, C. Ding, and Z. Jin, “Optical Kerr effect in phase modulation spectroscopy resonator fiber optic gyro,” Chin. J. Lasers 33, 814-818 (2006).

H. Ma, Z. Jin, C. Ding, and Y. Wang, “Research on signal detection method of resonator fiber optical gyro,” Chin. J. Lasers 31, 1001-1005 (2004).

H. Ma, Z. Jin, C. Ding, and Y. Wang, “Influence of spectral linewidth of laser on resonance characteristics in fiber ring resonator,” Chin. J. Lasers 30, 731-734 (2003).

Ezekiel, S.

Gallagher, M. T.

C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Muller, J. A. West, N. F. Borrelli, D. C. Allan, and K. W. Koch, “Low-loss hollow-core silica/air photonic bandgap fibre,” Nature 424, 657-659 (2003).

Gea-Banaciloche, J.

W. W. Chow, J. Gea-Banaciloche, and L. M. Pedrotti, “The ring laser gyro,” Rev. Mod. Phys. 57, 61-103 (1985).
[CrossRef]

Harumoto, M.

K. Hotate and M. Harumoto, “Resonator fiber optic gyro using digital serrodyne modulation,” J. Lightwave Technol. 15, 466-473 (1997).
[CrossRef]

Hayashi, G.

K. Hotate and G. Hayashi, “Resonator fiber optic gyro using digital serrodyne modulation-method to reduce the noise induced by the backscattering and closed-loop operation using digital signal processing,” Proc. SPIE 3746, 104-107 (1999).

Higashiguchi, M.

Hotate, K.

K. Hotate and Y. Kikuchi, “Analysis of thermo-optically induced bias drift in resonator fiber optic gyro,” Proc. SPIE 4204, 81-88 (2001).

K. Hotate and G. Hayashi, “Resonator fiber optic gyro using digital serrodyne modulation-method to reduce the noise induced by the backscattering and closed-loop operation using digital signal processing,” Proc. SPIE 3746, 104-107 (1999).

K. Hotate and M. Harumoto, “Resonator fiber optic gyro using digital serrodyne modulation,” J. Lightwave Technol. 15, 466-473 (1997).
[CrossRef]

T. Ito and K. Hotate, “Closed-loop operation in the resonator fiber optic gyro using Faraday effect with a twisted single-mode-fiber resonator,” Proc. SPIE 2837, 260-271 (1996).

K. Takiguchi and K. Hotate, “Method to reduce the optical Kerr-effect-induced bias in an optical passive ring-resonator gyro,” IEEE Photonics Technol. Lett. 4, 203-206 (1992).
[CrossRef]

K. Hotate and K. Tabe, “Drift of an optical fiber gyroscope caused by the Faraday effect: experiment,” J. Lightwave Technol. 5, 997-1001 (1987).
[CrossRef]

K. Iwatsuki, K. Hotate, and M. Higashiguchi, “Kerr effect in an optical passive ring-resonator gyro,” J. Lightwave Technol. 4, 645-651 (1986).
[CrossRef]

K. Iwatsuki, K. Hotate, and M. Higashiguchi, “Resonance characteristics of backscattering in optical passive-ring resonator gyro: experiment,” Appl. Opt. 25, 4448-4451 (1986).
[CrossRef]

K. Iwatsuki, K. Hotate, and M. Higashiguchi, “Effect of Rayleigh backscattering in an optical passive ring-resonator gyro,” Appl. Opt. 23, 3916-3924 (1984).
[CrossRef]

Hu, Y.

Q. Yao, Y. Hu, Z. Song, and Y. Xie, “Study on Kerr-effect-induced bias reduction method for resonator fiber optic gyroscope,” Acta Photonica Sin. 34, 1320-1323 (2005).

Ito, T.

T. Ito and K. Hotate, “Closed-loop operation in the resonator fiber optic gyro using Faraday effect with a twisted single-mode-fiber resonator,” Proc. SPIE 2837, 260-271 (1996).

Iwatsuki, K.

Jin, Z.

D. Ying, H. Ma, and Z. Jin, “Dynamic characteristics of R-FOG based on the triangle wave phase modulation technique,” Opt. Commun. 281, 5340-5343 (2008).
[CrossRef]

D. Ying, H. Ma, and Z. Jin, “Resonator fiber optic gyro using the triangle wave phase modulation technique,” Opt. Commun. 281, 580-586 (2008).
[CrossRef]

Z. Jin, Z. Yang, H. Ma, and D. Ying, “Open-loop experiments in a resonator fiber-optic gyro using digital triangle wave phase modulation,” IEEE Photonics Technol. Lett. 19, 1685-1687(2007).
[CrossRef]

X. Zhang, H. Ma, C. Ding, and Z. Jin, “Optical Kerr effect in phase modulation spectroscopy resonator fiber optic gyro,” Chin. J. Lasers 33, 814-818 (2006).

H. Ma, Z. Jin, C. Ding, and Y. Wang, “Research on signal detection method of resonator fiber optical gyro,” Chin. J. Lasers 31, 1001-1005 (2004).

H. Ma, Z. Jin, C. Ding, and Y. Wang, “Influence of spectral linewidth of laser on resonance characteristics in fiber ring resonator,” Chin. J. Lasers 30, 731-734 (2003).

Kikuchi, Y.

K. Hotate and Y. Kikuchi, “Analysis of thermo-optically induced bias drift in resonator fiber optic gyro,” Proc. SPIE 4204, 81-88 (2001).

Kim, H. K.

Kino, G. S.

Knight, J. C.

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allan, “Single-mode photonic band gap guidance of light in air,” Science 285, 1537-1539(1999).
[CrossRef]

Koch, K. W.

C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Muller, J. A. West, N. F. Borrelli, D. C. Allan, and K. W. Koch, “Low-loss hollow-core silica/air photonic bandgap fibre,” Nature 424, 657-659 (2003).

Lefevre, H. C.

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

Li, D.

X. Yu, Y. Liao, M. Zhang, Y. Yu, and D. Li, “Kerr effect in an optical passive ring-resonator gyro using a hollow-core photonic band-gap fiber,” Chin. J. Lasers 35, 430-435 (2008).
[CrossRef]

Liao, Y.

X. Yu, Y. Liao, M. Zhang, Y. Yu, and D. Li, “Kerr effect in an optical passive ring-resonator gyro using a hollow-core photonic band-gap fiber,” Chin. J. Lasers 35, 430-435 (2008).
[CrossRef]

Ma, H.

D. Ying, H. Ma, and Z. Jin, “Resonator fiber optic gyro using the triangle wave phase modulation technique,” Opt. Commun. 281, 580-586 (2008).
[CrossRef]

D. Ying, H. Ma, and Z. Jin, “Dynamic characteristics of R-FOG based on the triangle wave phase modulation technique,” Opt. Commun. 281, 5340-5343 (2008).
[CrossRef]

Z. Jin, Z. Yang, H. Ma, and D. Ying, “Open-loop experiments in a resonator fiber-optic gyro using digital triangle wave phase modulation,” IEEE Photonics Technol. Lett. 19, 1685-1687(2007).
[CrossRef]

X. Zhang, H. Ma, C. Ding, and Z. Jin, “Optical Kerr effect in phase modulation spectroscopy resonator fiber optic gyro,” Chin. J. Lasers 33, 814-818 (2006).

H. Ma, Z. Jin, C. Ding, and Y. Wang, “Research on signal detection method of resonator fiber optical gyro,” Chin. J. Lasers 31, 1001-1005 (2004).

H. Ma, Z. Jin, C. Ding, and Y. Wang, “Influence of spectral linewidth of laser on resonance characteristics in fiber ring resonator,” Chin. J. Lasers 30, 731-734 (2003).

Mangan, B. J.

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allan, “Single-mode photonic band gap guidance of light in air,” Science 285, 1537-1539(1999).
[CrossRef]

Meyer, R. E.

Muller, D.

C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Muller, J. A. West, N. F. Borrelli, D. C. Allan, and K. W. Koch, “Low-loss hollow-core silica/air photonic bandgap fibre,” Nature 424, 657-659 (2003).

Ohtsuka, Y.

Pedrotti, L. M.

W. W. Chow, J. Gea-Banaciloche, and L. M. Pedrotti, “The ring laser gyro,” Rev. Mod. Phys. 57, 61-103 (1985).
[CrossRef]

Qiu, T. C.

G. A. Sanders, L. K. Strandjord, and T. C. Qiu, “Hollow core fiber optic ring resonator for rotation sensing,” in Optical Fiber Sensors (Optical Society of America, 2006), paper ME6.

Roberts, P. J.

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allan, “Single-mode photonic band gap guidance of light in air,” Science 285, 1537-1539(1999).
[CrossRef]

Russell, P. St. J.

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allan, “Single-mode photonic band gap guidance of light in air,” Science 285, 1537-1539(1999).
[CrossRef]

Sanders, G. A.

G. A. Sanders, L. K. Strandjord, and T. C. Qiu, “Hollow core fiber optic ring resonator for rotation sensing,” in Optical Fiber Sensors (Optical Society of America, 2006), paper ME6.

Shupe, D. M.

Smith, C. M.

C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Muller, J. A. West, N. F. Borrelli, D. C. Allan, and K. W. Koch, “Low-loss hollow-core silica/air photonic bandgap fibre,” Nature 424, 657-659 (2003).

Song, Z.

Q. Yao, Y. Hu, Z. Song, and Y. Xie, “Study on Kerr-effect-induced bias reduction method for resonator fiber optic gyroscope,” Acta Photonica Sin. 34, 1320-1323 (2005).

Stowe, D. W.

Strandjord, L. K.

G. A. Sanders, L. K. Strandjord, and T. C. Qiu, “Hollow core fiber optic ring resonator for rotation sensing,” in Optical Fiber Sensors (Optical Society of America, 2006), paper ME6.

Tabe, K.

K. Hotate and K. Tabe, “Drift of an optical fiber gyroscope caused by the Faraday effect: experiment,” J. Lightwave Technol. 5, 997-1001 (1987).
[CrossRef]

Takiguchi, K.

K. Takiguchi and K. Hotate, “Method to reduce the optical Kerr-effect-induced bias in an optical passive ring-resonator gyro,” IEEE Photonics Technol. Lett. 4, 203-206 (1992).
[CrossRef]

Tekippe, V. J.

Venkataraman, N.

C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Muller, J. A. West, N. F. Borrelli, D. C. Allan, and K. W. Koch, “Low-loss hollow-core silica/air photonic bandgap fibre,” Nature 424, 657-659 (2003).

Wang, Y.

H. Ma, Z. Jin, C. Ding, and Y. Wang, “Research on signal detection method of resonator fiber optical gyro,” Chin. J. Lasers 31, 1001-1005 (2004).

H. Ma, Z. Jin, C. Ding, and Y. Wang, “Influence of spectral linewidth of laser on resonance characteristics in fiber ring resonator,” Chin. J. Lasers 30, 731-734 (2003).

West, J. A.

C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Muller, J. A. West, N. F. Borrelli, D. C. Allan, and K. W. Koch, “Low-loss hollow-core silica/air photonic bandgap fibre,” Nature 424, 657-659 (2003).

Xie, Y.

Q. Yao, Y. Hu, Z. Song, and Y. Xie, “Study on Kerr-effect-induced bias reduction method for resonator fiber optic gyroscope,” Acta Photonica Sin. 34, 1320-1323 (2005).

Yang, Z.

Z. Jin, Z. Yang, H. Ma, and D. Ying, “Open-loop experiments in a resonator fiber-optic gyro using digital triangle wave phase modulation,” IEEE Photonics Technol. Lett. 19, 1685-1687(2007).
[CrossRef]

Yao, Q.

Q. Yao, Y. Hu, Z. Song, and Y. Xie, “Study on Kerr-effect-induced bias reduction method for resonator fiber optic gyroscope,” Acta Photonica Sin. 34, 1320-1323 (2005).

Ying, D.

D. Ying, H. Ma, and Z. Jin, “Resonator fiber optic gyro using the triangle wave phase modulation technique,” Opt. Commun. 281, 580-586 (2008).
[CrossRef]

D. Ying, H. Ma, and Z. Jin, “Dynamic characteristics of R-FOG based on the triangle wave phase modulation technique,” Opt. Commun. 281, 5340-5343 (2008).
[CrossRef]

Z. Jin, Z. Yang, H. Ma, and D. Ying, “Open-loop experiments in a resonator fiber-optic gyro using digital triangle wave phase modulation,” IEEE Photonics Technol. Lett. 19, 1685-1687(2007).
[CrossRef]

Yu, X.

X. Yu, Y. Liao, M. Zhang, Y. Yu, and D. Li, “Kerr effect in an optical passive ring-resonator gyro using a hollow-core photonic band-gap fiber,” Chin. J. Lasers 35, 430-435 (2008).
[CrossRef]

Yu, Y.

X. Yu, Y. Liao, M. Zhang, Y. Yu, and D. Li, “Kerr effect in an optical passive ring-resonator gyro using a hollow-core photonic band-gap fiber,” Chin. J. Lasers 35, 430-435 (2008).
[CrossRef]

Zhang, M.

X. Yu, Y. Liao, M. Zhang, Y. Yu, and D. Li, “Kerr effect in an optical passive ring-resonator gyro using a hollow-core photonic band-gap fiber,” Chin. J. Lasers 35, 430-435 (2008).
[CrossRef]

Zhang, X.

X. Zhang, H. Ma, C. Ding, and Z. Jin, “Optical Kerr effect in phase modulation spectroscopy resonator fiber optic gyro,” Chin. J. Lasers 33, 814-818 (2006).

Acta Photonica Sin.

Q. Yao, Y. Hu, Z. Song, and Y. Xie, “Study on Kerr-effect-induced bias reduction method for resonator fiber optic gyroscope,” Acta Photonica Sin. 34, 1320-1323 (2005).

Appl. Opt.

Chin. J. Lasers

X. Yu, Y. Liao, M. Zhang, Y. Yu, and D. Li, “Kerr effect in an optical passive ring-resonator gyro using a hollow-core photonic band-gap fiber,” Chin. J. Lasers 35, 430-435 (2008).
[CrossRef]

H. Ma, Z. Jin, C. Ding, and Y. Wang, “Influence of spectral linewidth of laser on resonance characteristics in fiber ring resonator,” Chin. J. Lasers 30, 731-734 (2003).

X. Zhang, H. Ma, C. Ding, and Z. Jin, “Optical Kerr effect in phase modulation spectroscopy resonator fiber optic gyro,” Chin. J. Lasers 33, 814-818 (2006).

H. Ma, Z. Jin, C. Ding, and Y. Wang, “Research on signal detection method of resonator fiber optical gyro,” Chin. J. Lasers 31, 1001-1005 (2004).

IEEE Photonics Technol. Lett.

Z. Jin, Z. Yang, H. Ma, and D. Ying, “Open-loop experiments in a resonator fiber-optic gyro using digital triangle wave phase modulation,” IEEE Photonics Technol. Lett. 19, 1685-1687(2007).
[CrossRef]

K. Takiguchi and K. Hotate, “Method to reduce the optical Kerr-effect-induced bias in an optical passive ring-resonator gyro,” IEEE Photonics Technol. Lett. 4, 203-206 (1992).
[CrossRef]

J. Lightwave Technol.

K. Hotate and K. Tabe, “Drift of an optical fiber gyroscope caused by the Faraday effect: experiment,” J. Lightwave Technol. 5, 997-1001 (1987).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

System configuration of the R-FOG based on the triangular wave phase modulation: FL, fiber laser; CW, clockwise; CCW, counterclockwise; C1–C4, couplers; PD1, PD2, photodetectors; DMC1, DMC2, demodulation circuits; PM1, PM2, phase modulators; FBC, feedback circuit.

Fig. 2
Fig. 2

Waveform of the triangular wave phase modulation signal for CW beam.

Fig. 3
Fig. 3

PBF R-FOG’s demodulation curve with different modulation frequencies for CCW beam.

Fig. 4
Fig. 4

Relationship between the Kerr-induced error Ω e and modulation frequency F M \_ CCW when the intensity coefficients of the two counterpropagating beams u CW and u CCW are the same: (a) result of the PBF R-FOG with practical parameters, (b) result of the PBF R-FOG with “ideal” parameters, and (c) result of the conventional fiber R-FOG.

Fig. 5
Fig. 5

Relationship between the zero point error Ω e and difference of the intensity coefficients Δ u with different modulation frequencies for CCW beam: (a) result of the PBF R-FOG with “ideal” parameters and (b) result of the conventional fiber R-FOG.

Equations (26)

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f s _ CW ( t ) = { 2 F M \_ CW for     [ p F M \_ CW < t ( p + 1 2 ) 1 F M \_ CW ] 2 F M \_ CW for     [ ( p + 1 2 ) 1 F M \_ CW < t ( p + 1 ) 1 F M \_ CW ] ,
E Laser ( t ) = E 0 exp { i [ 2 π f 0 t + φ ( t ) ] } ,
I FRR _ CW ( t , z ) = u CW exp ( α L z ) B ( f CW + f Kerr CW ) ,
B ( X ) = I 0 k C ( 1 α C ) ( 1 α s ) 1 1 ( 1 k C ) ( 1 α C ) ( 1 α s ) 2 exp ( α L L ) × 1 ( 1 k C ) ( 1 α C ) ( 1 α s ) 2 exp ( α L L ) exp ( 2 π δ f τ 0 ) 1 + ( 1 k C ) ( 1 α C ) ( 1 α s ) 2 exp ( α L L ) exp ( 2 π δ f τ 0 ) 2 [ ( 1 k C ) ( 1 α C ) ( 1 α s ) 2 exp ( α L L ) ] 1 / 2 exp ( π δ f τ 0 ) cos ( 2 π X τ 0 ) ,
f CW = f 0 f RES CW + f s _ CW ( t ) ,
I FRR _ CCW ( t , z ) = u CCW exp [ α L ( L z ) ] B ( f CCW + f Kerr CCW ) ,
f CCW = f 0 f RES CCW + f s _ CCW ( t ) = f 0 f RES CW Δ f RES + f s _ CCW ( t ) ,
Δ f RES = f RES CCW f RES CW .
f 0 + f Kerr CW = f RES CW .
I FRR _ CW 0 ( t , z ) = u CW exp ( α L z ) B ( f s _ CW ) .
I FRR _ CCW 0 ( t , z ) = u CCW exp [ α L ( L z ) ] B ( f Kerr CCW f Kerr CW Δ f RES + f s _ CCW ) .
f Kerr CW = 1 2 π τ 0 0 L Δ β K _ CW 0 d z = 1 2 π τ 0 2 ω Z n 2 c A 1 exp ( α L L ) α L [ u CW B ( f s _ CW ) + 2 u CCW B ( f Kerr CCW f Kerr CW Δ f RES + f s _ CCW ) ] ,
f Kerr CCW = 1 2 π τ 0 0 L Δ β K _ CCW 0 d z = 1 2 π τ 0 2 ω Z n 2 c A 1 exp ( α L L ) α L [ u CCW B ( f Kerr CCW f Kerr CW Δ f RES + f s _ CCW ) + 2 u CW B ( f s _ CW ) ] ,
Δ f Kerr = 1 2 π τ 0 2 ω Z n 2 c A 1 exp ( α L L ) α L [ u CW B ( f s _ CW ) u CCW B ( Δ f Kerr Δ f RES + f s _ CCW ) ] ,
Δ f Kerr = f Kerr CCW f Kerr CW .
I D _ CCW ( Δ f RES ) = 1 2 N ( 1 a C 3 ) ( 1 a C ) [ 1 ρ ( 1 Q ) 2 ( 1 Q ) 2 + 4 Q sin 2 ( π · F CCW τ 0 ) ] u CCW I 0 ,
F CCW = f 0 f RES CW Δ f RES + f s _ CCW ( t ) + f Kerr CCW = Δ f Kerr ( t ) Δ f RES + f s _ CCW ( t ) ,
ρ = 1 1 1 α C · [ T 2 2 TR 1 Q + ( R ) 2 1 ( Q ) 2 · 1 + Q 1 Q ] ,
T = 1 k C · 1 α C ,
R = k C · ( 1 α C ) · exp ( α L L / 2 ) · ( 1 α s ) , R = R exp ( π δ f τ 0 ) ,
Q = exp ( α L L / 2 ) · ( 1 α s ) · 1 k C · 1 α C , Q = Q exp ( π δ f τ 0 ) .
S CCW ( t ) = { 1 for     [ q F M \_ CCW < t ( q + 1 2 ) 1 F M \_ CCW ] 1 for     [ ( q + 1 2 ) 1 F M \_ CCW < t ( q + 1 ) 1 F M \_ CCW ] ,
V d = GF M \_ CCW 0 1 / F M \_ CCW I D _ CCW ( Δ f RES ) S CCW ( t ) d t ,
n 2 = η n 2 , silica + ( 1 η ) n 2 , air ,
V d ( Δ f RES ) | Δ f RES = Δ f e = 0.
Ω e = Δ f e · n r · λ D ,

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