Abstract

To improve the thermal stability of a resonator fiber optic gyro (R-FOG), a transmission-type polarizing resonator by inserting two in-line polarizers in a polarization-maintaining fiber resonator with twin 90° polarization-axis rotated splices is proposed and experimentally demonstrated. The in-line polarizers attenuate the unwanted resonance by introducing high loss for the unwanted eigenstates of polarization in the resonator. The desired resonance in the resonator can keep excellent stability in a wide temperature range, thus the temperature-related polarization error in the R-FOG is dramatically suppressed. Both our numerical simulation and experimental verification are carried out, which for the first time to our best knowledge demonstrate that the open-loop output of the R-FOG is insensitive to environmental temperature variations. A bias stability below 2°/h in the temperature range of 36.2°C to 33°C is successfully demonstrated.

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References

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  1. M. N. Armenise, C. Ciminelli, F. Dell'Olio, and V. Passaro, Advances in Gyroscope Technologies (Springer Verlag, 2010).
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    [CrossRef] [PubMed]
  3. G. A. Sanders, N. Demma, G. F. Rouse, and R. B. Smith, “Evaluation of polarization maintaining fiber resonator for rotation sensing applications,” in OFS(Opt. Soc. America, New Orleans, 1988), 409–412.
  4. K. Iwatsuki, K. Hotate, and M. Higashiguchi, “Eigenstate of polarization in a fiber ring resonator and its effect in an optical passive ring-resonator gyro,” Appl. Opt.25(15), 2606–2612 (1986).
    [CrossRef] [PubMed]
  5. G. A. Sanders, R. B. Smith, and G. F. Rouse, “Novel polarization-rotating fiber resonator for rotation sensing applications,” in Fiber Optic and Laser Sensors(SPIE, 1989), 373–381.
  6. L. K. Strandjord and G. A. Sanders, “Resonator fiber optic gyro employing a polarization-rotating resonator,” in Fiber Optic Gyros: 15th Anniversary Conference(SPIE, 1991), 163–172.
  7. L. K. Strandjord and G. A. Sanders, “Performance improvements of a polarization-rotating resonator fiber optic gyroscope,” in Fiber Optic and Laser Sensors X (SPIE, Boston, MA, USA, 1992), 94–104.
  8. X. Wang, Z. He, and K. Hotate, “Reduction of polarization-fluctuation induced drift in resonator fiber optic gyro by a resonator with twin 90 degrees polarization-axis rotated splices,” Opt. Express18(2), 1677–1683 (2010).
    [CrossRef] [PubMed]
  9. Z. Jin, X. Yu, and H. Ma, “Resonator fiber optic gyro employing a semiconductor laser,” Appl. Opt.51(15), 2856–2864 (2012).
    [CrossRef] [PubMed]
  10. R. P. Dahlgren and R. E. Sutherland, “Single-polarization fiber optic resonator for gyro applications,” in Fiber Optic Gyros: 15th Anniversary Conf (SPIE, 1991), 128–135.
  11. K. Takiguchi and K. Hotate, “Reduction of a polarization-fluctuation-induced error in an optical passive ring-resonator gyro by using a single-polarization optical fiber,” J. Lightwave Technol.11(10), 1687–1693 (1993).
    [CrossRef]
  12. H. Ma, X. Yu, and Z. Jin, “Reduction of polarization-fluctuation induced drift in resonator fiber optic gyro by a resonator integrating in-line polarizers,” Opt. Lett.37(16), 3342–3344 (2012).
    [CrossRef]
  13. F. Zarinetchi, Studies in Optical Resonator Gyroscope (Massachusetts Institute of Technology, 1992).
  14. 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(1), 85–90 (2011).
    [CrossRef]
  15. 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(5), 645–649 (2012).
    [CrossRef]

2012

2011

2010

1993

K. Takiguchi and K. Hotate, “Reduction of a polarization-fluctuation-induced error in an optical passive ring-resonator gyro by using a single-polarization optical fiber,” J. Lightwave Technol.11(10), 1687–1693 (1993).
[CrossRef]

1986

1983

Ezekiel, S.

He, Z.

Higashiguchi, M.

Hotate, K.

Iwatsuki, K.

Jin, Z.

Ma, H.

Mao, H.

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(5), 645–649 (2012).
[CrossRef]

Meyer, R. E.

Stowe, D. W.

Takiguchi, K.

K. Takiguchi and K. Hotate, “Reduction of a polarization-fluctuation-induced error in an optical passive ring-resonator gyro by using a single-polarization optical fiber,” J. Lightwave Technol.11(10), 1687–1693 (1993).
[CrossRef]

Tekippe, V. J.

Wang, X.

Yu, X.

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(5), 645–649 (2012).
[CrossRef]

Appl. Opt.

J. Lightwave Technol.

K. Takiguchi and K. Hotate, “Reduction of a polarization-fluctuation-induced error in an optical passive ring-resonator gyro by using a single-polarization optical fiber,” J. Lightwave Technol.11(10), 1687–1693 (1993).
[CrossRef]

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(1), 85–90 (2011).
[CrossRef]

Opt. Commun.

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(5), 645–649 (2012).
[CrossRef]

Opt. Express

Opt. Lett.

Other

F. Zarinetchi, Studies in Optical Resonator Gyroscope (Massachusetts Institute of Technology, 1992).

R. P. Dahlgren and R. E. Sutherland, “Single-polarization fiber optic resonator for gyro applications,” in Fiber Optic Gyros: 15th Anniversary Conf (SPIE, 1991), 128–135.

G. A. Sanders, N. Demma, G. F. Rouse, and R. B. Smith, “Evaluation of polarization maintaining fiber resonator for rotation sensing applications,” in OFS(Opt. Soc. America, New Orleans, 1988), 409–412.

M. N. Armenise, C. Ciminelli, F. Dell'Olio, and V. Passaro, Advances in Gyroscope Technologies (Springer Verlag, 2010).

G. A. Sanders, R. B. Smith, and G. F. Rouse, “Novel polarization-rotating fiber resonator for rotation sensing applications,” in Fiber Optic and Laser Sensors(SPIE, 1989), 373–381.

L. K. Strandjord and G. A. Sanders, “Resonator fiber optic gyro employing a polarization-rotating resonator,” in Fiber Optic Gyros: 15th Anniversary Conference(SPIE, 1991), 163–172.

L. K. Strandjord and G. A. Sanders, “Performance improvements of a polarization-rotating resonator fiber optic gyroscope,” in Fiber Optic and Laser Sensors X (SPIE, Boston, MA, USA, 1992), 94–104.

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Figures (9)

Fig. 1
Fig. 1

Configuration of the transmission PMF resonator by inserting two in-line polarizers.

Fig. 2
Fig. 2

Calculated shapes of the two ESOPs as a function of one roundtrip phase separation between the two ESOPs in the resonator. Resonator without in-line polarizer for (a), (c), (e), (g) and (i); resonator with in-line polarizers for (b), (d), (f), (h) and (j). The simulation parameters: k = 0.03, θt1 = θt2 = 6°, l1 = 3.8m, l2 = 3.2m, l3 = 3.9m, l4 = 3.35m, εf2 = εs2 = 27dB.

Fig. 3
Fig. 3

Simulated resonant curves as a function of one roundtrip phase separation between the two ESOPs in the resonator. (a) to (d) correspond to the case of 0, 0.5π, π, 1.5π, respectively. The simulation parameters: k = 0.03, θt1 = θt2 = 6°, θk1 = θk2 = 8°, l1 = 3.8 m, l2 = 3.2m, l3 = 3.9 m, l4 = 3.35 m, εf2 = εs2 = 27dB.

Fig. 4
Fig. 4

Resonant curves of the resonator with in-line polarizers when the one roundtrip phase separation between the two ESOPs is 0.

Fig. 5
Fig. 5

Calculated polarization-fluctuation induced error. The simulation parameter: k = 0.03, θt1 = θt2 = 6°, θk1 = θk2 = 8°, l1 = 3.8m, l2 = 3.2m, l3 = 3.9m, l4 = 3.35m. εs2 and εf2 are the PERs of the polarizer PX and PY, respectively.

Fig. 6
Fig. 6

Measured resonances for the resonator integrating in-line polarizers from temperature 27°C to 40°C.

Fig. 7
Fig. 7

Basic configuration of the R-FOG based on the PMF resonator integrating two in-line polarizers

Fig. 8
Fig. 8

Open-loop output thermal stability. (a) Open-loop output vs. temperature. (b) Allan deviation of open-loop output.

Fig. 9
Fig. 9

Open-loop output under room temperature, (a) measured for an hour. (b) The Allan deviation of open-loop output.

Equations (26)

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F 12 = e jβ( l 1 + l 2 ) ( 0 ε f e jΔβ( l 2 l 1 )/2 e jΔβ( l 1 l 2 )/2 0 ),
{ β x =β+1/2Δβ β y =β1/2Δβ ,
C ti,cw =( 1 k x cos θ ti 1 k x sin θ ti 1 k y sin θ ti 1 k y cos θ ti ),
C k i,cw =( j k x cos θ ki j k x sin θ ki j k y sin θ ki j k y cos θ ki ),
F 34 = e jβ( l 3 + l 4 ) ( 0 e jΔβ( l 4 l 3 )/2 ε s e jΔβ( l 3 l 4 )/2 0 ),
S cw = α t C t1,cw F 34 C t2,cw F 12 = α t (1-k) e jβl ( p 11,cw p 12,cw p 21,cw p 22,cw ),
p 11,cw = ε s sin θ t1 sin θ t2 e jΔβΔ l 2 /2 cos θ t1 cos θ t2 e jΔβΔ l 1 /2 ;
p 12,cw = ε s ε f sin θ t1 cos θ t2 e jΔβΔ l 1 /2 + ε f cos θ t1 sin θ t2 e jΔβΔ l 2 /2 ;
p 21,cw = ε s cos θ t1 sin θ t2 e jΔβΔ l 2 /2 sin θ t1 cos θ t2 e jΔβΔ l 1 /2 ;
p 22,cw = ε s ε f cos q t1 cos θ t2 e jΔβΔ l 1 /2 + ε f sin θ t1 sin θ t2 e jΔβΔ l 2 /2 ;
l= l 1 + l 2 + l 3 + l 4 ;
Δ l 1 =( l 1 + l 4 )( l 2 + l 3 );
Δ l 2 =( l 1 + l 3 )( l 2 + l 4 ).
S cw v m,cw = λ m,cw v m,cw (m=1,2),
E 11 =( 1 0 ),
E 14 = C k1,cw E 11 =a v 1,cw +b v 2,cw =V( a b ),
{ E 14,ESOP1 =a v 1,cw n λ 1,cw n =a v 1,cw 1 1 λ 1,cw E 14,ESOP2 =b v 2,cw n λ 2,cw n =b v 2,cw 1 1 λ 2,cw ,
{ E 23,ESOP1 = C k2,cw α C2 α PY F 12 E 14,ESOP1 E 23,ESOP2 = C k2,cw α C2 α PY F 12 E 14,ESOP2 ,
{ E ESOP1 = a 1 v 1,cw ' j Γ 1 /2 f+j Γ 1 /2 E ESOP2 = b 1 v 2,cw ' j Γ 2 /2 (f f d )+j Γ 2 /2 ,
{ Γ 1 = c πnl acos( 2| λ 1,cw | 1+ | λ 1,cw | 2 ) Γ 2 = c πnl acos( 2| λ 2,cw | 1+ | λ 2,cw | 2 ) ,
{ v 1,cw ' = C k2,cw v 1,cw v 2,cw ' = C k2,cw v 2,cw ,
I=[ E ESOP1 H + E ESOP2 H ][ E ESOP1 + E ESOP2 ] = | E ESOP1 | 2 + | E ESOP2 | 2 +2real[ E ESOP1 H E ESOP2 ], = I 1 + I 2 +2real[ I 3 ]
I f | f=Δ f pol,cw =[ I 1 f + I 2 f +2real( I 3 f )]| f=Δ f pol.cw =0,
Δ f pol,cw Γ 1 2 8 a 1 2 | v 1,cw ' | 2 [ I 2 f +2real( I 3 f )],
Δ f pol Γ 1 2 4 a 1 2 | v 1,cw ' | 2 [ I 2 f +2real( I 3 f )],
Δ f pol b 1 2 | v ' 2,cw | 2 a 1 2 | v ' 1,cw | 2 ( Γ 1 Γ 2 ) 2 8 f d 3 -real( b 1 v ' 1,cw H v 2,cw ' a 1 | v ' 1,cw | 2 Γ 1 Γ 2 2 f d ),

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