Abstract

A resonator fiber-optic gyro (R-FOG) is a high-accuracy inertial rotation sensor based on the Sagnac effect. A fiber ring resonator is the core sensing element in the R-FOG. When the frequency of the fiber ring resonator input laser is swept linearly with time, ringing of the output resonance curve is observed. The output field of the fiber ring resonator is derived from the superposition of the light transmitted through the directional coupler directly and the multiple light components circulated in the fiber ring resonator when the frequency of the laser is swept. The amplitude and phase of the output field are analyzed, and it is found that the difference in time for different light components in the fiber ring resonator to reach a point of destructive interference causes the ringing phenomenon. Finally the ringing phenomenon is observed in experiments, and the experimental results agree with the theoretical analysis well.

© 2007 Optical Society of America

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References

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  1. W. W. Chow, J. Gea-Banaciloche, and L. M. Pedrotti, "The ring laser gyro," Rev. Mod. Phys. 57, 61-103 (1985).
    [CrossRef]
  2. L. F. Stokes, M. Chodorow, and H. J. Shaw, "All single-mode fiber resonator," Opt. Lett. 7, 288-290 (1982).
    [CrossRef] [PubMed]
  3. R. A. Bergh, H. C. Lefevre, and H. J. Shaw, "All-single-mode fiber-optic gyroscope with long-term stability," Opt. Lett. 6, 502-504 (1981).
    [CrossRef] [PubMed]
  4. 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] [PubMed]
  5. Z. K. Ioannidis, P. M. Radmore, and I. P. Giles, "Dynamic response of an all-fiber ring resonator," Opt. Lett. 13, 422-424 (1988).
    [CrossRef] [PubMed]
  6. K. Kalli and D. A. Jackson, "Analysis of dynamic response of a ring resonator to a time-varying input signal," Opt. Lett. 18, 465-467 (1993).
    [CrossRef] [PubMed]
  7. 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).
  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. Strandjord and G. A. Sanders, "Effects of imperfect serrodyne phase modulation in resonator fiber optic gyroscopes," Proc. SPIE 2292, 272-282 (1994).
    [CrossRef]
  10. N. L. Swanson and J. D. Kalata, "Measurement of temporal coherence loss in laser light scattered from simulated coastal waters," in Proceedings of the IEEE Southeastcon '93 (IEEE, 1993) pp. 684-690.
  11. J. P. Goedgebuer, H. Porte, and A. Hamel, "Electrooptic modulation of multilongitudinal mode laser diodes: demonstration at 850 nm with simultaneous data transmission by coherence multiplexing," IEEE J. Quantum Electron. 23, 1135-1144 (1987).
    [CrossRef]

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).

1997

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

1994

L. K. Strandjord and G. A. Sanders, "Effects of imperfect serrodyne phase modulation in resonator fiber optic gyroscopes," Proc. SPIE 2292, 272-282 (1994).
[CrossRef]

1993

N. L. Swanson and J. D. Kalata, "Measurement of temporal coherence loss in laser light scattered from simulated coastal waters," in Proceedings of the IEEE Southeastcon '93 (IEEE, 1993) pp. 684-690.

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

1988

1987

J. P. Goedgebuer, H. Porte, and A. Hamel, "Electrooptic modulation of multilongitudinal mode laser diodes: demonstration at 850 nm with simultaneous data transmission by coherence multiplexing," IEEE J. Quantum Electron. 23, 1135-1144 (1987).
[CrossRef]

1985

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

1983

1982

1981

Bergh, R. A.

Chodorow, M.

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]

Ding, C.

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.

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]

Giles, I. P.

Goedgebuer, J. P.

J. P. Goedgebuer, H. Porte, and A. Hamel, "Electrooptic modulation of multilongitudinal mode laser diodes: demonstration at 850 nm with simultaneous data transmission by coherence multiplexing," IEEE J. Quantum Electron. 23, 1135-1144 (1987).
[CrossRef]

Hamel, A.

J. P. Goedgebuer, H. Porte, and A. Hamel, "Electrooptic modulation of multilongitudinal mode laser diodes: demonstration at 850 nm with simultaneous data transmission by coherence multiplexing," IEEE J. Quantum Electron. 23, 1135-1144 (1987).
[CrossRef]

Harumoto, M.

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

Hotate, K.

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

Ioannidis, Z. K.

Jackson, D. A.

Jin, Z.

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).

Kalata, J. D.

N. L. Swanson and J. D. Kalata, "Measurement of temporal coherence loss in laser light scattered from simulated coastal waters," in Proceedings of the IEEE Southeastcon '93 (IEEE, 1993) pp. 684-690.

Kalli, K.

Lefevre, H. C.

Ma, H.

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).

Meyer, R. E.

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]

Porte, H.

J. P. Goedgebuer, H. Porte, and A. Hamel, "Electrooptic modulation of multilongitudinal mode laser diodes: demonstration at 850 nm with simultaneous data transmission by coherence multiplexing," IEEE J. Quantum Electron. 23, 1135-1144 (1987).
[CrossRef]

Radmore, P. M.

Sanders, G. A.

L. K. Strandjord and G. A. Sanders, "Effects of imperfect serrodyne phase modulation in resonator fiber optic gyroscopes," Proc. SPIE 2292, 272-282 (1994).
[CrossRef]

Shaw, H. J.

Stokes, L. F.

Stowe, D. W.

Strandjord, L. K.

L. K. Strandjord and G. A. Sanders, "Effects of imperfect serrodyne phase modulation in resonator fiber optic gyroscopes," Proc. SPIE 2292, 272-282 (1994).
[CrossRef]

Swanson, N. L.

N. L. Swanson and J. D. Kalata, "Measurement of temporal coherence loss in laser light scattered from simulated coastal waters," in Proceedings of the IEEE Southeastcon '93 (IEEE, 1993) pp. 684-690.

Tekippe, V. J.

Wang, Y.

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).

Chin. J. Lasers

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).

IEEE J. Quantum Electron.

J. P. Goedgebuer, H. Porte, and A. Hamel, "Electrooptic modulation of multilongitudinal mode laser diodes: demonstration at 850 nm with simultaneous data transmission by coherence multiplexing," IEEE J. Quantum Electron. 23, 1135-1144 (1987).
[CrossRef]

J. Lightwave Technol.

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

Opt. Lett.

Proc. SPIE

L. K. Strandjord and G. A. Sanders, "Effects of imperfect serrodyne phase modulation in resonator fiber optic gyroscopes," Proc. SPIE 2292, 272-282 (1994).
[CrossRef]

Rev. Mod. Phys.

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

Other

N. L. Swanson and J. D. Kalata, "Measurement of temporal coherence loss in laser light scattered from simulated coastal waters," in Proceedings of the IEEE Southeastcon '93 (IEEE, 1993) pp. 684-690.

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Figures (4)

Fig. 1
Fig. 1

Experimental setup used to observe the time response of the fiber ring resonator when the frequency of the laser is swept.

Fig. 2
Fig. 2

(a) Time response of the normalized amplitude of the light component E c r o s s ( t ) , (b) phase difference between the light components E t h r o u g h ( t ) and E c r o s s ( t ) , and (c) output intensity normalized by the input intensity T with k = 8 × 10 7 Hz / s .

Fig. 3
Fig. 3

(a) Time response of the normalized amplitude of the light component E c r o s s ( t ) , (b) phase difference between the light components E t h r o u g h ( t ) and E c r o s s ( t ) , and (c) output intensity normalized by the input intensity T with k = 5 × 10 11 Hz / s .

Fig. 4
Fig. 4

Resonance curve by experiments at different frequency sweep rates with (a) k = 8 × 10 7 Hz / s and (b) k = 5 × 10 11 Hz / s .

Equations (161)

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3 .5   ps / ( nm   km )
1550   nm
60   kHz
1550   nm
250 MHz / V
2.22   ns
k v
E l a s e r ( t ) = E 0   exp [ i ( 2 π f 0 t + 0 t 2 π k t d t + φ 0 ) ] ,
E 0
f 0
φ 0
k = p k v ,
p = 250 MHz / V
k v
E t h r o u g h ( t )
E t h r o u g h ( t ) = E 0   exp [ i 2 π ( f 0 + k t / 2 ) t ] × exp ( i φ 0 ) ( 1 k C ) 1 / 2 ( 1 α C ) 1 / 2 ,
k C
α C
E c r o s s n ( t ) = k C ( 1 α C ) ( 1 α L ) 1 / 2 [ ( 1 k C ) 1 / 2 ( 1 α C ) 1 / 2 × ( 1 α L ) 1 / 2 ] n 1  exp ( i π ) E l a s e r ( t n τ ) = E 0 k C ( 1 α C ) ( 1 α L ) 1 / 2  exp [ i 2 π ( f 0 + k t / 2 ) t ] × exp ( i φ 0 ) exp ( i π ) [ ( 1 k C ) 1 / 2 ( 1 α C ) 1 / 2 × ( 1 α L ) 1 / 2 ] n 1  exp [ i 2 π ( f 0 n τ + k n τ t k n 2 τ 2 / 2 ) ] ,
α L
τ = n r L / c
n r
Δ φ n
E t h r o u g h ( t )
E c r o s s n ( t )
Δ φ n = π + 2 π n ( f 0 τ + k τ t ) π k n 2 τ 2 .
E t h r o u g h ( t )
E c r o s s 1 ( t )
E t h r o u g h ( t )
E c r o s s 1 ( t )
n = 1
t 1 D I
E t h r o u g h ( t )
E c r o s s 1 ( t )
t 1 D I = q + k τ 2 / 2 f 0 τ k τ ,
E t h r o u g h ( t )
E c r o s s n ( t )
t = t 1 D I
Δ φ n | t = t 1 D I = π ( 2 q n 1 ) + π k τ 2 ( n n 2 ) .
π ( 2 q n 1 )
π k τ 2 ( n n 2 )
E t h r o u g h ( t )
E c r o s s n ( t )
( n > 1 )
t 1 D I
t 1 D I
E c r o s s n ( t )
π k τ 2 n 2
( 2 π   rad )
E t h r o u g h ( t )
E c r o s s n ( t )
t = t 1 D I
Δ φ n | t = t 1 D I ( 2 q n 1 ) π .
E t h r o u g h ( t )
E c r o s s n ( t )
t 1 D I
E t h r o u g h ( t )
E c r o s s n ( t ) ( n > 1 )
t 1 D I
E c r o s s n ( t )
E c r o s s ( t ) = n = 1 N E c r o s s n ( t ) = E 0 k C ( 1 α C ) ( 1 α L ) 1 / 2  exp [ i 2 π ( f 0 + k t / 2 ) t ] × exp ( i φ 0 ) exp ( i π ) × n = 1 N [ ( 1 k C ) 1 / 2 ( 1 α C ) 1 / 2 ( 1 α L ) 1 / 2 ] n 1 × exp [ i 2 π ( f 0 n τ + k n τ t k n 2 τ 2 / 2 ) ] ,
E o u t ( t ) = E t h r o u g h ( t ) + E c r o s s ( t ) = E 0  exp [ i 2 π ( f 0 + k t / 2 ) t ] exp ( i φ 0 ) { ( 1 k C ) 1 / 2 × ( 1 α C ) 1 / 2 k C ( 1 α C ) ( 1 α L ) 1 / 2 × n = 1 N [ ( 1 k C ) 1 / 2 ( 1 α C ) 1 / 2 ( 1 α L ) 1 / 2 ] n 1 × exp [ i 2 π ( f 0 n τ + k n τ t k n 2 τ 2 / 2 ) ] } .
T = | E o u t ( t ) E 0 | 2 = | ( 1 k C ) 1 / 2 ( 1 α C ) 1 / 2 k C ( 1 α C ) ( 1 α L ) 1 / 2 × n = 1 N [ ( 1 k C ) 1 / 2 ( 1 α C ) 1 / 2 ( 1 α L ) 1 / 2 ] n 1 × exp [ i 2 π ( f 0 n τ + k n τ t k n 2 τ 2 / 2 ) ] | 2 ,
| E t h r o u g h ( t ) |
| E c r o s s ( t ) |
E t h r o u g h ( t )
E c r o s s ( t )
| E t h r o u g h ( t ) | = E 0 ( 1 k C ) 1 / 2 ( 1 α C ) 1 / 2
| E c r o s s ( t ) |
Δ φ
Δ φ
E t h r o u g h ( t )
E c r o s s ( t )
| E c r o s s ( t ) |
Δ φ
E t h r o u g h ( t )
E c r o s s ( t )
| E c r o s s ( t ) |
| E c r o s s ( t ) |
E c r o s s ( t )
| E c r o s s ( t ) / E 0 |
E t h r o u g h ( t )
E c r o s s ( t )
k = 8 × 10 7 Hz / s
12   m
n r
k C
α C
α L
1.7 × 10 7   Hz
t = 0
N th   ( N > N )
| E c r o s s N ( t ) |
| E c r o s s 1 ( t ) |
( N > N )
| E c r o s s N ( t ) |
N = 105
N > 105
3448.3   m
60   kHz
π k n 2 τ 2
k = 8 × 10 7 Hz / s
N = 105
π k N 2 τ 2 = 0.0093   rad
2 π   rad
π k n 2 τ 2
E c r o s s n ( t )
| E c r o s s ( t ) |
Δ φ
π
E c r o s s ( t )
| E c r o s s ( t ) / E 0 |
E t h r o u g h ( t )
E c r o s s ( t )
k = 5 × 10 11 Hz / s
0.0189   ms
0.0189   ms
k = 5 × 10 11 Hz / s
N = 105
π k N 2 τ 2 = 58.26   rad
π k n 2 τ 2
E c r o s s n ( t )
Δ φ
t 1
| E c r o s s ( t ) / E 0 |
t 1
t 2
t 1
Δ φ
0   rad
t 3
| E c r o s s ( t ) / E 0 |
t 2
t 3
t 3
| E c r o s s ( t ) / E 0 |
t 3
t 3
Δ φ
t 4
| E c r o s s ( t ) / E 0 |
t 4
t 5
t 4
Δ φ
E c r o s s ( t )
Δ φ
| E c r o s s ( t ) / E 0 |
k = 8 × 10 7 Hz / s
k = 5 × 10 11 Hz / s
E c r o s s ( t )
E t h r o u g h ( t )
E c r o s s ( t )
k = 8 × 10 7 Hz / s
E c r o s s ( t )
E t h r o u g h ( t )
E c r o s s ( t )
k = 5 × 10 11 Hz / s
k = 8 × 10 7 Hz / s
k = 5 × 10 11 Hz / s

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