Abstract

An optical fiber ring resonator (OFRR) is the key rotation-sensing element in the resonator fiber optic gyro (R-FOG). In comparing between different OFRR types, a simulation model that can apply to all cases is set up. Both the polarization crosstalk and polarization-dependent loss in the coupler are fully investigated for the first time to our knowledge. Three different splicing schemes, including a single 0°, a single 90°, and twin 90° polarization axis rotated spices, are compared. Two general configurations of the OFRR are considered. One is a reflector OFRR, the other is a transmitter OFRR. This leads to six different OFRR types. The output stability of the R-FOG with six OFRR types is fully investigated theoretically and experimentally. Additional Kerr noise due to the polarization fluctuation is discovered. The OFRR with twin 90° polarization axis rotated splices is of lower additional Kerr noise and hence has better temperature stability. As the coupler is polarization dependent, we notice that in a reflector OFRR, the straight-through component of the output lightwave, which can be isolated by a transmitter configuration, would produce large polarization fluctuation–induced noise. The experimental results show that the bias stability of the transmitter OFRR is 8 times improved over that of the reflector OFRR, which is in accord with the theoretical analysis. By the analysis and experiments above, it is reasonable to make a conclusion that an R-FOG based on a transmitter OFRR with twin 90° polarization axis rotated splices is of better temperature stability and smaller additional Kerr effect noise.

© 2012 Optical Society of America

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References

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  1. R. E. Meyer and S. Ezekiel, “Passive fiber optic ring resonator for rotation sensing,” Opt. Lett. 8, 644–646 (1983).
    [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. S. Ezekiel, “Optical gyroscope options: principles and challenges,” in 18th International Optical Fiber Sensors Conference Technical Digest (Optical Society of America, 2006), paper MC1.
  5. T. J. Kaiser, D. Cardarelli, and J. Walsh, “Experimental development in the RFOG,” Proc. SPIE 1367, 121–126 (1990).
    [CrossRef]
  6. 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]
  7. L. K. Strandjord and G. A. Sanders, “Resonator fiber-optic gyro employing a polarization-rotationg resonator,” Proc. SPIE 1585, 163–172 (1991).
  8. K. Takiguchi and K. Hotate, “Evaluation of the output error in an optical passive ring resonator gyro with a 90° polarization axis rotation in the polarization maintaining fiber resonator,” IEEE Photon. Technol. Lett. 3, 88–90 (1991).
    [CrossRef]
  9. L. K. Strandjord and G. A. Sanders, “Performance improvements of a polarization rotating resonator fiber optic gyroscope,” Proc. SPIE 1795, 94–104 (1992).
  10. X. Wang, Z. He, and K. Hotate, “Reduction of polarization fluctuation induced drift in resonator fiber optic gyro by a resonator with twin 90° polarization-axis rotated splices,” Opt. Express 18, 1677–1683 (2010).
    [CrossRef]
  11. K. Iwatsuki, K. Hotate, and M. Higashinguchi, “Eigenstate of polarization in a fiber ring resonator and its effect in an optical passive ring resonator gyro,” Appl. Opt. 25, 2606–2612(1986).
    [CrossRef]
  12. K. Takiguchi and K. Hotate, “Bias of an optical passive ring resonator gyro caused by the misalignment of the polarization axis in the polarization maintaining fiber resonator,” J. Lightwave Technol. 10, 514–522 (1992).
    [CrossRef]
  13. K. Iwatsuki, K. Hotate, and M. Higashiguchi, “Kerr effect in an optical passive ring resonator gyro,” J. Lightwave Technol. 4, 645–651 (1986).
    [CrossRef]
  14. K. Takiguchi and K. Hotate, “Method to reduce the optical Kerr effect induced bias in an optical passive ring resonator gyro,” IEEE Photon. Technol. Lett. 4, 203–206 (1992).
    [CrossRef]
  15. G. A. Sanders, “Critical review of resonator fiber optic gyroscope technology,” Proc. SPIE CR44, 133–159 (1992).

2011

2010

1992

K. Takiguchi and K. Hotate, “Bias of an optical passive ring resonator gyro caused by the misalignment of the polarization axis in the polarization maintaining fiber resonator,” J. Lightwave Technol. 10, 514–522 (1992).
[CrossRef]

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

G. A. Sanders, “Critical review of resonator fiber optic gyroscope technology,” Proc. SPIE CR44, 133–159 (1992).

L. K. Strandjord and G. A. Sanders, “Performance improvements of a polarization rotating resonator fiber optic gyroscope,” Proc. SPIE 1795, 94–104 (1992).

1991

L. K. Strandjord and G. A. Sanders, “Resonator fiber-optic gyro employing a polarization-rotationg resonator,” Proc. SPIE 1585, 163–172 (1991).

K. Takiguchi and K. Hotate, “Evaluation of the output error in an optical passive ring resonator gyro with a 90° polarization axis rotation in the polarization maintaining fiber resonator,” IEEE Photon. Technol. Lett. 3, 88–90 (1991).
[CrossRef]

1990

T. J. Kaiser, D. Cardarelli, and J. Walsh, “Experimental development in the RFOG,” Proc. SPIE 1367, 121–126 (1990).
[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. Higashinguchi, “Eigenstate of polarization in a fiber ring resonator and its effect in an optical passive ring resonator gyro,” Appl. Opt. 25, 2606–2612(1986).
[CrossRef]

1983

Cardarelli, D.

T. J. Kaiser, D. Cardarelli, and J. Walsh, “Experimental development in the RFOG,” Proc. SPIE 1367, 121–126 (1990).
[CrossRef]

Ezekiel, S.

R. E. Meyer and S. Ezekiel, “Passive fiber optic ring resonator for rotation sensing,” Opt. Lett. 8, 644–646 (1983).
[CrossRef]

S. Ezekiel, “Optical gyroscope options: principles and challenges,” in 18th International Optical Fiber Sensors Conference Technical Digest (Optical Society of America, 2006), paper MC1.

He, Z.

Higashiguchi, M.

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

Higashinguchi, M.

Hotate, K.

X. Wang, Z. He, and K. Hotate, “Reduction of polarization fluctuation induced drift in resonator fiber optic gyro by a resonator with twin 90° polarization-axis rotated splices,” Opt. Express 18, 1677–1683 (2010).
[CrossRef]

K. Takiguchi and K. Hotate, “Bias of an optical passive ring resonator gyro caused by the misalignment of the polarization axis in the polarization maintaining fiber resonator,” J. Lightwave Technol. 10, 514–522 (1992).
[CrossRef]

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

K. Takiguchi and K. Hotate, “Evaluation of the output error in an optical passive ring resonator gyro with a 90° polarization axis rotation in the polarization maintaining fiber resonator,” IEEE Photon. Technol. Lett. 3, 88–90 (1991).
[CrossRef]

K. Iwatsuki, K. Hotate, and M. Higashinguchi, “Eigenstate of polarization in a fiber ring resonator and its effect in an optical passive ring resonator gyro,” Appl. Opt. 25, 2606–2612(1986).
[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]

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.

Iwatsuki, K.

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. Higashinguchi, “Eigenstate of polarization in a fiber ring resonator and its effect in an optical passive ring resonator gyro,” Appl. Opt. 25, 2606–2612(1986).
[CrossRef]

Jin, Z.

Kaiser, T. J.

T. J. Kaiser, D. Cardarelli, and J. Walsh, “Experimental development in the RFOG,” Proc. SPIE 1367, 121–126 (1990).
[CrossRef]

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.

Ma, H.

Mao, H.

Meyer, R. E.

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.

Sanders, G. A.

L. K. Strandjord and G. A. Sanders, “Performance improvements of a polarization rotating resonator fiber optic gyroscope,” Proc. SPIE 1795, 94–104 (1992).

G. A. Sanders, “Critical review of resonator fiber optic gyroscope technology,” Proc. SPIE CR44, 133–159 (1992).

L. K. Strandjord and G. A. Sanders, “Resonator fiber-optic gyro employing a polarization-rotationg resonator,” Proc. SPIE 1585, 163–172 (1991).

Strandjord, L. K.

L. K. Strandjord and G. A. Sanders, “Performance improvements of a polarization rotating resonator fiber optic gyroscope,” Proc. SPIE 1795, 94–104 (1992).

L. K. Strandjord and G. A. Sanders, “Resonator fiber-optic gyro employing a polarization-rotationg resonator,” Proc. SPIE 1585, 163–172 (1991).

Takiguchi, K.

K. Takiguchi and K. Hotate, “Bias of an optical passive ring resonator gyro caused by the misalignment of the polarization axis in the polarization maintaining fiber resonator,” J. Lightwave Technol. 10, 514–522 (1992).
[CrossRef]

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

K. Takiguchi and K. Hotate, “Evaluation of the output error in an optical passive ring resonator gyro with a 90° polarization axis rotation in the polarization maintaining fiber resonator,” IEEE Photon. Technol. Lett. 3, 88–90 (1991).
[CrossRef]

Walsh, J.

T. J. Kaiser, D. Cardarelli, and J. Walsh, “Experimental development in the RFOG,” Proc. SPIE 1367, 121–126 (1990).
[CrossRef]

Wang, X.

Appl. Opt.

IEEE Photon. Technol. Lett.

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

K. Takiguchi and K. Hotate, “Evaluation of the output error in an optical passive ring resonator gyro with a 90° polarization axis rotation in the polarization maintaining fiber resonator,” IEEE Photon. Technol. Lett. 3, 88–90 (1991).
[CrossRef]

J. Lightwave Technol.

K. Takiguchi and K. Hotate, “Bias of an optical passive ring resonator gyro caused by the misalignment of the polarization axis in the polarization maintaining fiber resonator,” J. Lightwave Technol. 10, 514–522 (1992).
[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]

Opt. Express

Opt. Lett.

Proc. SPIE

L. K. Strandjord and G. A. Sanders, “Resonator fiber-optic gyro employing a polarization-rotationg resonator,” Proc. SPIE 1585, 163–172 (1991).

L. K. Strandjord and G. A. Sanders, “Performance improvements of a polarization rotating resonator fiber optic gyroscope,” Proc. SPIE 1795, 94–104 (1992).

T. J. Kaiser, D. Cardarelli, and J. Walsh, “Experimental development in the RFOG,” Proc. SPIE 1367, 121–126 (1990).
[CrossRef]

G. A. Sanders, “Critical review of resonator fiber optic gyroscope technology,” Proc. SPIE CR44, 133–159 (1992).

Other

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.

S. Ezekiel, “Optical gyroscope options: principles and challenges,” in 18th International Optical Fiber Sensors Conference Technical Digest (Optical Society of America, 2006), paper MC1.

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Figures (8)

Fig. 1.
Fig. 1.

Two general configurations of the OFRR. (a) reflector OFRR: L=LR+LL and ΔL=LRLL; (b) transmitter OFRR: L=L1+L2+L3+L4 and ΔL=L1+L4L2L3.

Fig. 2.
Fig. 2.

Gyro bias error caused by the polarization fluctuations. (a) resonance point separation and PER between the two ESOPs. (b) output error of the R-FOG.

Fig. 3.
Fig. 3.

OFRR with a single 90° polarization axis rotated splice. (a) resonance point separation and PER between the two ESOPs. (b) output error of the R-FOG.

Fig. 4.
Fig. 4.

Results of the power variation with change of the phase difference θ. (a) simulation results. (b) experimental results.

Fig. 5.
Fig. 5.

Influence of the PDL on the polarization-induced error in an R-FOG with a transmitter OFRR.

Fig. 6.
Fig. 6.

Polarization-induced error as a function of the phase difference of the input lightwave with different ESOPs distances.

Fig. 7.
Fig. 7.

Schematic for simultaneously measuring the bias stabilities of the R-FOG with reflector and transmitter OFRRs.

Fig. 8.
Fig. 8.

Bias outputs of the R-FOG based on a reflector and a transmitter OFRR, respectively.

Equations (56)

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(E3jE4j)=(CtCrCrCt)(Cl00Cl)(E1jE2j).
Cl=(1αcx001αcy),Ct=(jkcx00jkcy),Cr=(1kcx001kcy),
(E3cwE4cw)=(CtClTtcwCrClTrccwCrClTrcwCtClTtccw)(E1cwE2cw),(E3ccwE4ccw)=(CtClTtcwCrClTrcwCrClTrccwCtClTtccw)(E1ccwE2ccw),
Trcw=(cosθcrsinθcrsinθcrcosθcr),
Ttcw=(cosθctsinθctsinθctcosθct),
Trccw=(cosθcrsinθcrsinθcrcosθcr),
Ttccw=(cosθctsinθctsinθctcosθct).
|ClE1j|2+|ClE2j|2=|E3j|2+|E4j|2.
I4j=|E4j|2=|ClE1j|2+|ClE2j|2|E3j|2=E1jH{ClHClTtjHClHCtHSjH[IFjHClHClFj]SjCtClTtj}E1j,
Scw=n=0(S¯cw)n=n=0(CrClTrccwFcw)n,
Sccw=n=0(S¯ccw)n=n=0(CrClTrcwFccw)n.
Fcw=BcwRcwAcw,Fccw=AccwRccwBccw.
{Acw=F(θu)|z=LRBcw=F(θu)|z=LL,{Accw=F(θu)|z=LRBccw=F(θu)|z=LL,
Rcw=1αs·(cosθssinθssinθscosθs),Rccw=1αs·(cosθssinθssinθscosθs),
F(θu)=exp(jβz)·(exp(αfxz/2)00exp(αfyz/2))C(θu),
C(φ)=(C11C12C21C22),
C11=C22*=cos(ηrz)j·[Δβ/(2ηr)]sin(ηrz),
C12=C21=(θu/ηr)sin(ηrz),
ηr=(Δβ/2)2+θu2,
θu=θs/z,
β=βx+βy2=πλ0(nx+ny),
Δβ=βxβy=2πλ0(nxny)=2πλ0Δn,
S¯cw=CrClTrccwFcw=tfexp(jβL)(S11cwS12cwS21cwS22cw),
S¯ccw=(S¯cw)t=CrClTrcwFccw=tfexp(jβL)(S11ccwS12ccwS21ccwS22ccw),
S11cw=S11ccw=cosθcrexp(jΔβL2),
S22cw=S22ccw=S11cw*=S11ccw*=cosθcrexp(jΔβL2),
S12cw=S21cw*=S12ccw=S21ccw*=sinθcrexp(jΔβL2),
S21cw=S12cw*=S12ccw*=S21ccw=sinθcrexp(jΔβL2).
I4j=|aj|2|U1j|2+|bj|2|U2j|2,
|U1j|2=eαc{1ρjΓj(βLξ)},
|U2j|2=eαc{1ρjΓj(βL+ξ)},
ρj=gfCcross2(1tf|S11j|2+|S12j|2)2,
gf=1exp(αfL)(1αsm)(1αc),
Γj(x)=(1tf|S11j|2+|S12j|2)2(1tf|S11j|2+|S12j|2)2+4tf|S11j|2+|S12j|2sin2(x/2).
[ajbj]=xjV1j+yjV2j,
ϕerror_p=arcsin{2|bcw|2sin(2ξ)|acw|2/[1+4tf(1tf)2sin2(ξ)]2}arcsin{2|bccw|2sin(2ξ)|accw|2/[1+4tf(1tf)2sin2(ξ)]2}.
Ωerror_p=cλ02πLDϕerror_p.
S11cw=S22cw*=S22ccw=S11ccw*=sinθcrexp(jΔβΔL2),
S22cw=S11cw*=S11ccw=S22ccw*=sinθcrexp(jΔβΔL2),
S12cw=S21cw*=S21ccw=S12ccw*=cosθcrexp(jΔβΔL2),
S21cw=S12cw*=S12ccw=S21ccw*=cosθcrexp(jΔβΔL2),
E0j=aj·x^+bjexp(jθ)·y^=xjV1j·cos(θ/2)+yjV2j·sin(θ/2),
I4j=|aj|2|U1j|2k2(eΔαc+eΔαc|Y1j|2)+|bj|2|U2j|2k2(eΔαc|X2j|2+eΔαc)+2k2(eΔαceΔαc)Re[aj*bjU1j*U2jX2j],
αc=(αcx+αcy)/2,
Δαc=αcxαcy,
|U1j|2=eαc{1ρjΓj(βLξ)},
|U2j|2=eαc{1ρjΓj(βL+ξ)},
U1j=eαc/2(Cbar+Ccross2Cbarλ1j1λ1j),
U2j=eαc/2(Cbar+Ccross2Cbarλ2j1λ2j).
E4cw=CtE3cw=CtScwCtClTtcwE1cw,
E4ccw=CtE3ccw=CtSccwCtClTtcwE1ccw.
Ioj=|aj|2|U1j|2k2(eΔαc+eΔαc|Y1j|2)+|bj|2|U2j|2k2(eΔαc|X2j|2+eΔαc)+2k2(eΔαceΔαc)Re[aj*bjU1j*U2jX2j],
|U1j|2=Ccross4eαc(1tf|S11j|2+|S12j|2)2Γj(βLξ),
|U2j|2=Ccross4eαc(1tf|S11j|2+|S12j|2)2Γj(βL+ξ),
U1j=Ccross2eαc/2/(1λ1j),
U2j=Ccross2eαc/2/(1λ2j).

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