Abstract

A detection system in the resonator fiber-optic gyro is set up by the phase modulation (PM) spectroscopy technique. The slope of the demodulated curve near the resonant point is found to affect the ultimate sensitivity of the gyro. To maximize the demodulated signal slope, the modulation frequency and index are optimized by the expansion of the Bessel function and optical field overlapping method. Using different PM frequencies for the light waves, the open-loop gyro output signal is observed. The modulation frequency in this PM technique is limited only by the cutoff frequency of the LiNbO3 phase modulators, which can reach several gigahertz. This detection technique and system can be applied to the resonator micro-optic gyro with a less than 10 cm long integrated optical ring.

© 2006 Optical Society of America

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References

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  1. E. J. Post, "Sagnac effect," Rev. Mod. Phys. 39, 475-493 (1967).
    [CrossRef]
  2. K. Hotate, "Fiber sensor technology today," Opt. Fiber Technol. 3, 356-402 (1997).
    [CrossRef]
  3. R. Carroll, C. D. Coccoli, D. Cardarelli, and G. T. Coate, "The passive resonator fiber optic gyro and comparison to the interferometer fiber gyro," in Fiber Optic Gyros: Tenth Anniversary Conference, E. Udd, ed., Proc. SPIE 719, 169-177 (1986).
  4. N. Barbour and G. Schmidt, "Inertial sensor technique trends," IEEE Sens. J 1, 332-339 (2001).
    [CrossRef]
  5. T. Imai, K.-I. Nishide, H. Ochi, and M. Ohtsu, "The passive ring resonator fiber optic gyro using modulatable highly coherent laser diode module," in Fiber Optic Gyros: 15th Anniversary Conference, S.Ezekiel and E.Udd, eds., Proc. SPIE 1585, 153-162 (1991).
  6. Y. Yi, K. Shi, W. Lu, and S. Jian, "Phase modulation spectroscopy for resonator fiber gyroscope by using all-fiber PZT phase modulator," Appl. Opt. 34, 7383-7386 (1995).
    [CrossRef] [PubMed]
  7. K. Suzuki, K. Takiguchi, and K. Hotate, "Monolithically integrated resonator micro-optic gyro on Silica planar lightwave circuit," J. Lightwave Technol. 18, 66-72 (2000).
    [CrossRef]
  8. K. Hotate and M. Harumoto, "Resonator fiber optic gyro using digital serrodyne modulation," J. Lightwave Technol. 15, 466-473 (1997).
    [CrossRef]
  9. L. K. Strandiord and G. A. Sanders, "Resonator optic gyro employing a polarization-rotating resonator," in Fiber Optic Gyros: 15th Anniversary Conference, S.Ezekiel and E.Udd, eds., Proc. SPIE 1585, 163-172 (1991).
  10. 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] [PubMed]
  11. K. Hotate and K. Takiguchi, "Drift reduction in an optical passive ring-resonator gyro," in Fiber Optic Gyros: 15th Anniversary Conference, S.Ezekiel and E.Udd, ed., Proc. SPIE 1585, 116-127 (1991).

2001

N. Barbour and G. Schmidt, "Inertial sensor technique trends," IEEE Sens. J 1, 332-339 (2001).
[CrossRef]

2000

1997

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

K. Hotate, "Fiber sensor technology today," Opt. Fiber Technol. 3, 356-402 (1997).
[CrossRef]

1995

1984

1967

E. J. Post, "Sagnac effect," Rev. Mod. Phys. 39, 475-493 (1967).
[CrossRef]

Barbour, N.

N. Barbour and G. Schmidt, "Inertial sensor technique trends," IEEE Sens. J 1, 332-339 (2001).
[CrossRef]

Cardarelli, D.

R. Carroll, C. D. Coccoli, D. Cardarelli, and G. T. Coate, "The passive resonator fiber optic gyro and comparison to the interferometer fiber gyro," in Fiber Optic Gyros: Tenth Anniversary Conference, E. Udd, ed., Proc. SPIE 719, 169-177 (1986).

Carroll, R.

R. Carroll, C. D. Coccoli, D. Cardarelli, and G. T. Coate, "The passive resonator fiber optic gyro and comparison to the interferometer fiber gyro," in Fiber Optic Gyros: Tenth Anniversary Conference, E. Udd, ed., Proc. SPIE 719, 169-177 (1986).

Coate, G. T.

R. Carroll, C. D. Coccoli, D. Cardarelli, and G. T. Coate, "The passive resonator fiber optic gyro and comparison to the interferometer fiber gyro," in Fiber Optic Gyros: Tenth Anniversary Conference, E. Udd, ed., Proc. SPIE 719, 169-177 (1986).

Coccoli, C. D.

R. Carroll, C. D. Coccoli, D. Cardarelli, and G. T. Coate, "The passive resonator fiber optic gyro and comparison to the interferometer fiber gyro," in Fiber Optic Gyros: Tenth Anniversary Conference, E. Udd, ed., Proc. SPIE 719, 169-177 (1986).

Harumoto, M.

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

Higashiguchi, M.

Hotate, K.

K. Suzuki, K. Takiguchi, and K. Hotate, "Monolithically integrated resonator micro-optic gyro on Silica planar lightwave circuit," J. Lightwave Technol. 18, 66-72 (2000).
[CrossRef]

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

K. Hotate, "Fiber sensor technology today," Opt. Fiber Technol. 3, 356-402 (1997).
[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] [PubMed]

K. Hotate and K. Takiguchi, "Drift reduction in an optical passive ring-resonator gyro," in Fiber Optic Gyros: 15th Anniversary Conference, S.Ezekiel and E.Udd, ed., Proc. SPIE 1585, 116-127 (1991).

Imai, T.

T. Imai, K.-I. Nishide, H. Ochi, and M. Ohtsu, "The passive ring resonator fiber optic gyro using modulatable highly coherent laser diode module," in Fiber Optic Gyros: 15th Anniversary Conference, S.Ezekiel and E.Udd, eds., Proc. SPIE 1585, 153-162 (1991).

Iwatsuki, K.

Jian, S.

Lu, W.

Nishide, K.-I.

T. Imai, K.-I. Nishide, H. Ochi, and M. Ohtsu, "The passive ring resonator fiber optic gyro using modulatable highly coherent laser diode module," in Fiber Optic Gyros: 15th Anniversary Conference, S.Ezekiel and E.Udd, eds., Proc. SPIE 1585, 153-162 (1991).

Ochi, H.

T. Imai, K.-I. Nishide, H. Ochi, and M. Ohtsu, "The passive ring resonator fiber optic gyro using modulatable highly coherent laser diode module," in Fiber Optic Gyros: 15th Anniversary Conference, S.Ezekiel and E.Udd, eds., Proc. SPIE 1585, 153-162 (1991).

Ohtsu, M.

T. Imai, K.-I. Nishide, H. Ochi, and M. Ohtsu, "The passive ring resonator fiber optic gyro using modulatable highly coherent laser diode module," in Fiber Optic Gyros: 15th Anniversary Conference, S.Ezekiel and E.Udd, eds., Proc. SPIE 1585, 153-162 (1991).

Post, E. J.

E. J. Post, "Sagnac effect," Rev. Mod. Phys. 39, 475-493 (1967).
[CrossRef]

Sanders, G. A.

L. K. Strandiord and G. A. Sanders, "Resonator optic gyro employing a polarization-rotating resonator," in Fiber Optic Gyros: 15th Anniversary Conference, S.Ezekiel and E.Udd, eds., Proc. SPIE 1585, 163-172 (1991).

Schmidt, G.

N. Barbour and G. Schmidt, "Inertial sensor technique trends," IEEE Sens. J 1, 332-339 (2001).
[CrossRef]

Shi, K.

Strandiord, L. K.

L. K. Strandiord and G. A. Sanders, "Resonator optic gyro employing a polarization-rotating resonator," in Fiber Optic Gyros: 15th Anniversary Conference, S.Ezekiel and E.Udd, eds., Proc. SPIE 1585, 163-172 (1991).

Suzuki, K.

Takiguchi, K.

K. Suzuki, K. Takiguchi, and K. Hotate, "Monolithically integrated resonator micro-optic gyro on Silica planar lightwave circuit," J. Lightwave Technol. 18, 66-72 (2000).
[CrossRef]

K. Hotate and K. Takiguchi, "Drift reduction in an optical passive ring-resonator gyro," in Fiber Optic Gyros: 15th Anniversary Conference, S.Ezekiel and E.Udd, ed., Proc. SPIE 1585, 116-127 (1991).

Yi, Y.

Appl. Opt.

IEEE Sens. J

N. Barbour and G. Schmidt, "Inertial sensor technique trends," IEEE Sens. J 1, 332-339 (2001).
[CrossRef]

J. Lightwave Technol.

K. Suzuki, K. Takiguchi, and K. Hotate, "Monolithically integrated resonator micro-optic gyro on Silica planar lightwave circuit," J. Lightwave Technol. 18, 66-72 (2000).
[CrossRef]

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

Opt. Fiber Technol.

K. Hotate, "Fiber sensor technology today," Opt. Fiber Technol. 3, 356-402 (1997).
[CrossRef]

Rev. Mod. Phys.

E. J. Post, "Sagnac effect," Rev. Mod. Phys. 39, 475-493 (1967).
[CrossRef]

Other

R. Carroll, C. D. Coccoli, D. Cardarelli, and G. T. Coate, "The passive resonator fiber optic gyro and comparison to the interferometer fiber gyro," in Fiber Optic Gyros: Tenth Anniversary Conference, E. Udd, ed., Proc. SPIE 719, 169-177 (1986).

T. Imai, K.-I. Nishide, H. Ochi, and M. Ohtsu, "The passive ring resonator fiber optic gyro using modulatable highly coherent laser diode module," in Fiber Optic Gyros: 15th Anniversary Conference, S.Ezekiel and E.Udd, eds., Proc. SPIE 1585, 153-162 (1991).

L. K. Strandiord and G. A. Sanders, "Resonator optic gyro employing a polarization-rotating resonator," in Fiber Optic Gyros: 15th Anniversary Conference, S.Ezekiel and E.Udd, eds., Proc. SPIE 1585, 163-172 (1991).

K. Hotate and K. Takiguchi, "Drift reduction in an optical passive ring-resonator gyro," in Fiber Optic Gyros: 15th Anniversary Conference, S.Ezekiel and E.Udd, ed., Proc. SPIE 1585, 116-127 (1991).

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Figures (7)

Fig. 1
Fig. 1

R-FOG diagram by the PM spectroscopy technique.

Fig. 2
Fig. 2

Slopes of demodulated signal V out at resonant point f CW versus modulation index M with modulation frequencies f 2 of 10, 1, 0.3, and 0.1   MHz .

Fig. 3
Fig. 3

Slopes of the demodulated signal V out at resonant point f CW versus modulation frequency f 2 with modulation indices M of 0.8, 1.0, and 1.4.

Fig. 4
Fig. 4

Demodulated signal with modulation frequency f 2 of 1   MHz and modulation index M of 1.0.

Fig. 5
Fig. 5

Slopes of demodulated signal V out at resonant point f CW versus modulation frequency f 2 with modulation indices M of 0.8, 1.0, and 1.4.

Fig. 6
Fig. 6

Demodulated signal with modulation frequency f 2 of 30   MHz and modulation index M of 1.0.

Fig. 7
Fig. 7

Gyro output signal from LIA2.

Equations (105)

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LiNbO 3
10   m
LiNbO 3
0.5   ns
LiNbO 3
LiNbO 3
50 %
LiNbO 3
f 1
f 2
( f FL )
( f CCW )
E R in ( t ) = ( 1 α c 1 ) ( 1 α c 2 ) 2 E 0 n = J n ( M ) × exp   i2 π ( f FL + n f 2 ) t ,
E 0
α c 1
α c2
M = V 2 π / V π
V π
V 2
f 2
E R out = ( 1 α c 1 ) ( 1 α c 2 ) 2 E 0 n = J n ( M ) e i2 π f n t h n e i ϕ n ,
h n = ( 1 α c ) 1 ρ ( 1 Q ) 2 ( 1 Q ) 2 + 4 Q sin 2 ( π Δ f + n f 2 FSR ) ,
ρ = 1 1 ( 1 α c ) [ T ( T Q + R ) ( 1 Q ) ] 2 ,
ϕ n = arctan [ R   sin ( 2 π Δ f + n f 2 FSR ) T + ( T Q + R ) Q ( 2 T Q + R ) cos ( 2 π Δ f + n f 2 FSR ) ] ,
T = 1 k C 1 α c ,
R = k C ( 1 α c ) 1 α L ,
Q = 1 α L 1 k C 1 α c .
h n
ϕ n
c 0 / n 0 L ; n 0
c 0
f n = f FL + n f 2
Δ f = f FL f CW
f CW
α L
k C
α c
V PD out = 1 2 A n = n = J n ( M ) J n ( M ) × e i [ 2 π ( n n ) f 2 t ] h n h n e i ( φ n φ n ) ,
A = 1 4 ( 1 α c 3 ) ( 1 α c 2 ) ( 1 α c 1 ) N E 0 2 .
α c 3
sin 2 π f 2
V out = A G n J n J n + 1 h n h n + 1   sin ( ϕ n +1 ϕ n ) ,
J 2 n + 1 ( M ) = J ( 2 n + 1 ) ( M )
J 2 n ( M ) = J 2 n ( M )
V out = A G n J n ( M ) J n + 1 ( M ) { h n h n + 1   sin ( ϕ n +1 ϕ n ) h n h ( n + 1 )   sin [ ϕ - n ϕ ( n 1 ) ] } .
h ( · )
ϕ ( · )
V out
f CW
K = | d V out d Δ f | Δ f = 0 = | A G n J n J n + 1 { [ h n h n + 1   sin ( ϕ n + 1 ϕ n ) + h n h n + 1 × sin ( ϕ n + 1 ϕ n ) + h n h n + 1 ( ϕ n + 1 ϕ n ) × cos ( ϕ n + 1 ϕ n ) ] [ h n h ( n + 1 )   sin ( ϕ n ϕ n 1 ) + h n h ( n + 1 )   sin ( ϕ n ϕ n 1 ) + h n h ( n + 1 ) ( ϕ n 1 ϕ n ) × cos ( ϕ n ϕ n 1 ) ] } | Δ f = 0 ,
ϕ
h
f 2
f 2
f 2
f 2
f m 0
f m 1
f 2
f m 0
f 2
f 2
f m 1
f m 0 < f 2 < f m 1
f 2
f 2
f m 0
5   m
10 %
1550   nm
4.45 × 10 4 Hz / ( rad / s )
0.5   dB
0.05   dB
9 V / mW
7   mW
7 × 10 7 rad / s
f FL
f 2
1   MHz
f 2
f m 0
f 2
30   MHz
f FL
f CCW
0.1 rad / s
0.1 rad / s
21.9   mV
2   mV
0.01 rad / s
7 × 10 7 rad / s
LiNbO 3
V out
f CW
f 2
0.1   MHz
V out
f CW
f 2
1   MHz
V out
f CW
f 2
f 2
30   MHz

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