Abstract

We present an in-depth analysis of the resonance asymmetry in a silica waveguide ring resonator (WRR) and its influence on the waveguide-type optical passive resonator gyro (OPRG). A big bias error appears at the output of the OPRG. This big error is caused not only by the resonance asymmetry in the WRR, but also by the modulation parameters in the phase modulation spectroscopy technique (PMST). It has been proved that the bias error is proportional to the modulation frequency difference between the clockwise (CW) and counterclockwise (CCW) lightwaves. Three types of resonance asymmetries are thoroughly introduced and discussed. Methods to overcome the big bias error are demonstrated. A high reciprocal resonator is crucial to reduce the bias error. For a certain resonator, a proper temperature needs to be set to minimize the resonance asymmetry. A proper modulation frequency difference between the CW and CCW lightwaves is also helpful to reduce the bias error.

© 2012 Optical Society of America

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  1. S. Ezekiel and S. R. Balsmo, “Passive ring resonator laser gyroscope,” Appl. Phys. Lett. 30, 478–480 (1977).
    [CrossRef]
  2. G. A. Pavlath, “Fiber optic gyros: the vision realized,” in 18th International Optical Fiber Sensors Conference Technical Digest (Optical Society of America, 2006), paper MA3.
  3. A. Ohno, A. Kurokawa, T. Kumagai, S. Nakamura, and K. Hotate, “Applications and technical progress of fiber optic gyros in Japan,” in 18th International Optical Fiber Sensors Conference Technical Digest (Optical Society of America, 2006), paper MA4.
  4. A. W. Lawrence and W. Mass, “Thin film laser gyro,” U.S. Patent 4,326,803 (27April1982).
  5. H. Ma, X. Zhang, Z. Jin, and C. Ding, “Waveguide-type optical passive ring resonator gyro using phase modulation spectroscopy technique,” Opt. Eng. 45, 080506 (2006).
    [CrossRef]
  6. H. Ma, Z. He, and K. Hotate. “Reduction of backscattering induced noise by carrier suppression in waveguide-type optical ring resonator gyro,” J. Lightwave Technol. 29, 85–90 (2011).
    [CrossRef]
  7. H. Mao, H. Ma, and Z. Jin, “Polarization maintaining silica waveguide resonator optic gyro using double phase modulation technique,” Opt. Express 19, 4632–4643 (2011).
    [CrossRef]
  8. Z. Jin, G. Zhang, H. Mao, and H. Ma, “Resonator micro optic gyro with double phase modulation technique using an FPGA-based digital processor,” Opt. Commun.285, 645–649 (2012).
    [CrossRef]
  9. R. C. Youngquist, L. F. Stokes, and H. J. Shaw, “Effects of normal mode loss in dielectric waveguide directional couplers and interferometers,” IEEE J. Quantum Electron. QE-19, 1888–1896 (1983).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  13. K. Kalli and D. A. Jackson, “Analysis of the dynamic response of a ring resonator to a time-varying input signal,” Opt. Lett. 18, 465–467 (1993).
    [CrossRef]
  14. M. Takahashi, S. Tai, and K. Kyuma, “Nondestructive measuring technique for misaligned angle in polarisation-maintaining fibre coupler,” Electron. Lett. 25, 600–602 (1989).
    [CrossRef]
  15. B. Lamouroux, B. Prade, and J. Y. Vinet, “Kerr effect in all-fiber cavities of optical gyros,” Appl. Opt. 29, 750–753 (1990).
    [CrossRef]
  16. X. Chang, H. Ma, and Z. Jin, “Resonance asymmetry phenomenon in waveguide-type optical ring resonator gyro,” Opt. Commun.286, 1134–1139 (2012).
    [CrossRef]
  17. H. Ma, H. Bao, S. Wang, and Z. Jin, “Temperature characteristic of ring resonator in polarization maintaining silica optical waveguide,” J. Optoelectron. Laser 20, 1029–1032 (2009).
    [CrossRef]
  18. G. A. Sanders, “Critical review of resonator fiber optic gyroscope technology,” Proc. SPIE CR44, 133–159 (1993).
    [CrossRef]
  19. M. Wang, Y. Cui, and T. Zhang, “Investigation on the determination of the optimized modulating frequency for the R-IOG,” Chinese J. Electron. Devices 30, 2291–2293 (2007).
    [CrossRef]

2011

2009

H. Ma, H. Bao, S. Wang, and Z. Jin, “Temperature characteristic of ring resonator in polarization maintaining silica optical waveguide,” J. Optoelectron. Laser 20, 1029–1032 (2009).
[CrossRef]

2007

M. Wang, Y. Cui, and T. Zhang, “Investigation on the determination of the optimized modulating frequency for the R-IOG,” Chinese J. Electron. Devices 30, 2291–2293 (2007).
[CrossRef]

2006

H. Ma, X. Zhang, Z. Jin, and C. Ding, “Waveguide-type optical passive ring resonator gyro using phase modulation spectroscopy technique,” Opt. Eng. 45, 080506 (2006).
[CrossRef]

1993

R. Carroll and R. Dahlgren, “Theoretical comparison of low and high splitting ratio resonators,” Proc. SPIE 2070, 293–292 (1993).
[CrossRef]

G. A. Sanders, “Critical review of resonator fiber optic gyroscope technology,” Proc. SPIE CR44, 133–159 (1993).
[CrossRef]

K. Kalli and D. A. Jackson, “Analysis of the dynamic response of a ring resonator to a time-varying input signal,” Opt. Lett. 18, 465–467 (1993).
[CrossRef]

1990

1989

M. Takahashi, S. Tai, and K. Kyuma, “Nondestructive measuring technique for misaligned angle in polarisation-maintaining fibre coupler,” Electron. Lett. 25, 600–602 (1989).
[CrossRef]

1988

1983

R. C. Youngquist, L. F. Stokes, and H. J. Shaw, “Effects of normal mode loss in dielectric waveguide directional couplers and interferometers,” IEEE J. Quantum Electron. QE-19, 1888–1896 (1983).
[CrossRef]

1977

S. Ezekiel and S. R. Balsmo, “Passive ring resonator laser gyroscope,” Appl. Phys. Lett. 30, 478–480 (1977).
[CrossRef]

Balsmo, S. R.

S. Ezekiel and S. R. Balsmo, “Passive ring resonator laser gyroscope,” Appl. Phys. Lett. 30, 478–480 (1977).
[CrossRef]

Bao, H.

H. Ma, H. Bao, S. Wang, and Z. Jin, “Temperature characteristic of ring resonator in polarization maintaining silica optical waveguide,” J. Optoelectron. Laser 20, 1029–1032 (2009).
[CrossRef]

Carroll, R.

R. Carroll and R. Dahlgren, “Theoretical comparison of low and high splitting ratio resonators,” Proc. SPIE 2070, 293–292 (1993).
[CrossRef]

Chang, X.

X. Chang, H. Ma, and Z. Jin, “Resonance asymmetry phenomenon in waveguide-type optical ring resonator gyro,” Opt. Commun.286, 1134–1139 (2012).
[CrossRef]

Cui, Y.

M. Wang, Y. Cui, and T. Zhang, “Investigation on the determination of the optimized modulating frequency for the R-IOG,” Chinese J. Electron. Devices 30, 2291–2293 (2007).
[CrossRef]

Dahlgren, R.

R. Carroll and R. Dahlgren, “Theoretical comparison of low and high splitting ratio resonators,” Proc. SPIE 2070, 293–292 (1993).
[CrossRef]

Ding, C.

H. Ma, X. Zhang, Z. Jin, and C. Ding, “Waveguide-type optical passive ring resonator gyro using phase modulation spectroscopy technique,” Opt. Eng. 45, 080506 (2006).
[CrossRef]

Ezekiel, S.

S. Ezekiel and S. R. Balsmo, “Passive ring resonator laser gyroscope,” Appl. Phys. Lett. 30, 478–480 (1977).
[CrossRef]

He, Z.

Hotate, K.

H. Ma, Z. He, and K. Hotate. “Reduction of backscattering induced noise by carrier suppression in waveguide-type optical ring resonator gyro,” J. Lightwave Technol. 29, 85–90 (2011).
[CrossRef]

A. Ohno, A. Kurokawa, T. Kumagai, S. Nakamura, and K. Hotate, “Applications and technical progress of fiber optic gyros in Japan,” in 18th International Optical Fiber Sensors Conference Technical Digest (Optical Society of America, 2006), paper MA4.

Jackson, D. A.

Jin, Z.

H. Mao, H. Ma, and Z. Jin, “Polarization maintaining silica waveguide resonator optic gyro using double phase modulation technique,” Opt. Express 19, 4632–4643 (2011).
[CrossRef]

H. Ma, H. Bao, S. Wang, and Z. Jin, “Temperature characteristic of ring resonator in polarization maintaining silica optical waveguide,” J. Optoelectron. Laser 20, 1029–1032 (2009).
[CrossRef]

H. Ma, X. Zhang, Z. Jin, and C. Ding, “Waveguide-type optical passive ring resonator gyro using phase modulation spectroscopy technique,” Opt. Eng. 45, 080506 (2006).
[CrossRef]

X. Chang, H. Ma, and Z. Jin, “Resonance asymmetry phenomenon in waveguide-type optical ring resonator gyro,” Opt. Commun.286, 1134–1139 (2012).
[CrossRef]

Z. Jin, G. Zhang, H. Mao, and H. Ma, “Resonator micro optic gyro with double phase modulation technique using an FPGA-based digital processor,” Opt. Commun.285, 645–649 (2012).
[CrossRef]

Kalli, K.

Kumagai, T.

A. Ohno, A. Kurokawa, T. Kumagai, S. Nakamura, and K. Hotate, “Applications and technical progress of fiber optic gyros in Japan,” in 18th International Optical Fiber Sensors Conference Technical Digest (Optical Society of America, 2006), paper MA4.

Kurokawa, A.

A. Ohno, A. Kurokawa, T. Kumagai, S. Nakamura, and K. Hotate, “Applications and technical progress of fiber optic gyros in Japan,” in 18th International Optical Fiber Sensors Conference Technical Digest (Optical Society of America, 2006), paper MA4.

Kyuma, K.

M. Takahashi, S. Tai, and K. Kyuma, “Nondestructive measuring technique for misaligned angle in polarisation-maintaining fibre coupler,” Electron. Lett. 25, 600–602 (1989).
[CrossRef]

Lamouroux, B.

Lawrence, A. W.

A. W. Lawrence and W. Mass, “Thin film laser gyro,” U.S. Patent 4,326,803 (27April1982).

Lit, J. W. Y.

Ma, H.

H. Ma, Z. He, and K. Hotate. “Reduction of backscattering induced noise by carrier suppression in waveguide-type optical ring resonator gyro,” J. Lightwave Technol. 29, 85–90 (2011).
[CrossRef]

H. Mao, H. Ma, and Z. Jin, “Polarization maintaining silica waveguide resonator optic gyro using double phase modulation technique,” Opt. Express 19, 4632–4643 (2011).
[CrossRef]

H. Ma, H. Bao, S. Wang, and Z. Jin, “Temperature characteristic of ring resonator in polarization maintaining silica optical waveguide,” J. Optoelectron. Laser 20, 1029–1032 (2009).
[CrossRef]

H. Ma, X. Zhang, Z. Jin, and C. Ding, “Waveguide-type optical passive ring resonator gyro using phase modulation spectroscopy technique,” Opt. Eng. 45, 080506 (2006).
[CrossRef]

X. Chang, H. Ma, and Z. Jin, “Resonance asymmetry phenomenon in waveguide-type optical ring resonator gyro,” Opt. Commun.286, 1134–1139 (2012).
[CrossRef]

Z. Jin, G. Zhang, H. Mao, and H. Ma, “Resonator micro optic gyro with double phase modulation technique using an FPGA-based digital processor,” Opt. Commun.285, 645–649 (2012).
[CrossRef]

Mao, H.

H. Mao, H. Ma, and Z. Jin, “Polarization maintaining silica waveguide resonator optic gyro using double phase modulation technique,” Opt. Express 19, 4632–4643 (2011).
[CrossRef]

Z. Jin, G. Zhang, H. Mao, and H. Ma, “Resonator micro optic gyro with double phase modulation technique using an FPGA-based digital processor,” Opt. Commun.285, 645–649 (2012).
[CrossRef]

Mass, W.

A. W. Lawrence and W. Mass, “Thin film laser gyro,” U.S. Patent 4,326,803 (27April1982).

Nakamura, S.

A. Ohno, A. Kurokawa, T. Kumagai, S. Nakamura, and K. Hotate, “Applications and technical progress of fiber optic gyros in Japan,” in 18th International Optical Fiber Sensors Conference Technical Digest (Optical Society of America, 2006), paper MA4.

Ohno, A.

A. Ohno, A. Kurokawa, T. Kumagai, S. Nakamura, and K. Hotate, “Applications and technical progress of fiber optic gyros in Japan,” in 18th International Optical Fiber Sensors Conference Technical Digest (Optical Society of America, 2006), paper MA4.

Pavlath, G. A.

G. A. Pavlath, “Fiber optic gyros: the vision realized,” in 18th International Optical Fiber Sensors Conference Technical Digest (Optical Society of America, 2006), paper MA3.

Prade, B.

Sanders, G. A.

G. A. Sanders, “Critical review of resonator fiber optic gyroscope technology,” Proc. SPIE CR44, 133–159 (1993).
[CrossRef]

Shaw, H. J.

R. C. Youngquist, L. F. Stokes, and H. J. Shaw, “Effects of normal mode loss in dielectric waveguide directional couplers and interferometers,” IEEE J. Quantum Electron. QE-19, 1888–1896 (1983).
[CrossRef]

Stokes, L. F.

R. C. Youngquist, L. F. Stokes, and H. J. Shaw, “Effects of normal mode loss in dielectric waveguide directional couplers and interferometers,” IEEE J. Quantum Electron. QE-19, 1888–1896 (1983).
[CrossRef]

L. F. Stokes, “Single-mode optical fiber resonator and applications to sensing (fiber sensor, fiber laser, fiber gyroscope),” Ph.D. dissertation (Stanford University, 1984).

Tai, S.

M. Takahashi, S. Tai, and K. Kyuma, “Nondestructive measuring technique for misaligned angle in polarisation-maintaining fibre coupler,” Electron. Lett. 25, 600–602 (1989).
[CrossRef]

Takahashi, M.

M. Takahashi, S. Tai, and K. Kyuma, “Nondestructive measuring technique for misaligned angle in polarisation-maintaining fibre coupler,” Electron. Lett. 25, 600–602 (1989).
[CrossRef]

Vinet, J. Y.

Wang, M.

M. Wang, Y. Cui, and T. Zhang, “Investigation on the determination of the optimized modulating frequency for the R-IOG,” Chinese J. Electron. Devices 30, 2291–2293 (2007).
[CrossRef]

Wang, S.

H. Ma, H. Bao, S. Wang, and Z. Jin, “Temperature characteristic of ring resonator in polarization maintaining silica optical waveguide,” J. Optoelectron. Laser 20, 1029–1032 (2009).
[CrossRef]

Youngquist, R. C.

R. C. Youngquist, L. F. Stokes, and H. J. Shaw, “Effects of normal mode loss in dielectric waveguide directional couplers and interferometers,” IEEE J. Quantum Electron. QE-19, 1888–1896 (1983).
[CrossRef]

Zhang, F.

Zhang, G.

Z. Jin, G. Zhang, H. Mao, and H. Ma, “Resonator micro optic gyro with double phase modulation technique using an FPGA-based digital processor,” Opt. Commun.285, 645–649 (2012).
[CrossRef]

Zhang, T.

M. Wang, Y. Cui, and T. Zhang, “Investigation on the determination of the optimized modulating frequency for the R-IOG,” Chinese J. Electron. Devices 30, 2291–2293 (2007).
[CrossRef]

Zhang, X.

H. Ma, X. Zhang, Z. Jin, and C. Ding, “Waveguide-type optical passive ring resonator gyro using phase modulation spectroscopy technique,” Opt. Eng. 45, 080506 (2006).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

S. Ezekiel and S. R. Balsmo, “Passive ring resonator laser gyroscope,” Appl. Phys. Lett. 30, 478–480 (1977).
[CrossRef]

Chinese J. Electron. Devices

M. Wang, Y. Cui, and T. Zhang, “Investigation on the determination of the optimized modulating frequency for the R-IOG,” Chinese J. Electron. Devices 30, 2291–2293 (2007).
[CrossRef]

Electron. Lett.

M. Takahashi, S. Tai, and K. Kyuma, “Nondestructive measuring technique for misaligned angle in polarisation-maintaining fibre coupler,” Electron. Lett. 25, 600–602 (1989).
[CrossRef]

IEEE J. Quantum Electron.

R. C. Youngquist, L. F. Stokes, and H. J. Shaw, “Effects of normal mode loss in dielectric waveguide directional couplers and interferometers,” IEEE J. Quantum Electron. QE-19, 1888–1896 (1983).
[CrossRef]

J. Lightwave Technol.

J. Opt. Soc. Am. A

J. Optoelectron. Laser

H. Ma, H. Bao, S. Wang, and Z. Jin, “Temperature characteristic of ring resonator in polarization maintaining silica optical waveguide,” J. Optoelectron. Laser 20, 1029–1032 (2009).
[CrossRef]

Opt. Eng.

H. Ma, X. Zhang, Z. Jin, and C. Ding, “Waveguide-type optical passive ring resonator gyro using phase modulation spectroscopy technique,” Opt. Eng. 45, 080506 (2006).
[CrossRef]

Opt. Express

Opt. Lett.

Proc. SPIE

G. A. Sanders, “Critical review of resonator fiber optic gyroscope technology,” Proc. SPIE CR44, 133–159 (1993).
[CrossRef]

R. Carroll and R. Dahlgren, “Theoretical comparison of low and high splitting ratio resonators,” Proc. SPIE 2070, 293–292 (1993).
[CrossRef]

Other

X. Chang, H. Ma, and Z. Jin, “Resonance asymmetry phenomenon in waveguide-type optical ring resonator gyro,” Opt. Commun.286, 1134–1139 (2012).
[CrossRef]

Z. Jin, G. Zhang, H. Mao, and H. Ma, “Resonator micro optic gyro with double phase modulation technique using an FPGA-based digital processor,” Opt. Commun.285, 645–649 (2012).
[CrossRef]

L. F. Stokes, “Single-mode optical fiber resonator and applications to sensing (fiber sensor, fiber laser, fiber gyroscope),” Ph.D. dissertation (Stanford University, 1984).

G. A. Pavlath, “Fiber optic gyros: the vision realized,” in 18th International Optical Fiber Sensors Conference Technical Digest (Optical Society of America, 2006), paper MA3.

A. Ohno, A. Kurokawa, T. Kumagai, S. Nakamura, and K. Hotate, “Applications and technical progress of fiber optic gyros in Japan,” in 18th International Optical Fiber Sensors Conference Technical Digest (Optical Society of America, 2006), paper MA4.

A. W. Lawrence and W. Mass, “Thin film laser gyro,” U.S. Patent 4,326,803 (27April1982).

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Figures (6)

Fig. 1.
Fig. 1.

Schematic configuration of the OPRG with a silica WRR based on the sinusoidal phase modulation spectroscopy technique. ISO: isolator; C1, C2, C3, C4: couplers; Syn: synchronized signal.

Fig. 2.
Fig. 2.

Resonance curves of the CCW and the CW lightwaves detected by PD1 and PD2, respectively. (a) An obvious sunken part on the left side of the resonance curve at a temperature of 15 °C. (b) A slight bend near the FWHM of the resonance curve at a temperature of 23 °C. (c) A sunken dip being weakened to a light bend near the resonance dip at a temperature of 25 °C. (d) A slight bend on the right side of the resonance curve at a temperature of 35 °C. The dashed circle shows the deformation part of the resonance curve.

Fig. 3.
Fig. 3.

(a) Measured bias errors of the OPRG when the modulation frequency f2 applied with the CW lightwave increases from 3 to 20 MHz. The modulation frequency f1 applied with the CCW lightwave is kept at 12.1 MHz. The temperature of the WRR takes five different values of 15 °C, 23 °C, 25 °C, 27 °C, and 35 °C. (b) Measured peak-to-peak bias stabilities of the OPRG.

Fig. 4.
Fig. 4.

Modulation and demodulation process considering three types of resonance asymmetries in the WRR: (a) perfect symmetry, (b) same asymmetry, (c) different asymmetry. The top row is the modulation process in the CW lightwave, and the bottom row is the modulation process in the CCW lightwave. Symbol I is the demodulation output of the OPRG.

Fig. 5.
Fig. 5.

Simulation results when the resonance curves of the CW and CCW lightwaves have the same asymmetric feature. (a) Relationship between the modulation frequency f2 and the bias error at different RARs. The modulation frequency f1 applied with the CCW lightwave is kept at 12.1 MHz. The RAR of the resonance curves takes six different values of 1.3%, 2.67%, 5.57%, 1.39%, 2.75%, and 5.54%. (b) Relationship between the RAR and the corresponding fitted slope; squares show the simulation results and stars show the experimental results.

Fig. 6.
Fig. 6.

Simulation results when the resonance curves of the CW and CCW lightwaves have different asymmetric features. (a) Relationship between the modulation frequency f2 and the bias error at different RARs in the CW lightwave. The RAR in the CCW lightwave is kept at 1.3%. The RAR in the CW lightwave takes five different values of 0.26%, 0.81%, 1.30%, 2.19%, and 2.74%. (b) Relationship between the RAR difference and the optimum modulation frequency; squares show the simulation results and stars show the experimental results.

Tables (1)

Tables Icon

Table 1. Measured RARs of the CW and CCW Lightwaves at Five Different Temperatures

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