Abstract

In this letter, the relationship between the change of the closed-loop optical path and the movement of two adjacent spherical mirrors in ring laser gyros is investigated by matrix optical approach. When one spherical mirror is pushed forward and the other is pulled backward to maintain the total length of the closed-loop optical path constant, an equivalent rotation of the closed-loop optical path is found for the first time. Both numerical simulations and experimental results show the equivalent rotation rate is proportional to the velocities of the mirrors’ movement.

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References

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  1. W. Chow, J. Gea-Banacloche, L. Pedrotti, V. Sanders, W. Schleich, and M. Scully, “The ring laser gyro,” Rev. Mod. Phys.57(1), 61–104 (1985).
    [CrossRef]
  2. M. Faucheux, D. Fayoux, and J. J. Roland, “The ring laser gyro,” J. Opt.19(3), 101–115 (1988).
    [CrossRef]
  3. F. Aronowitz, “Mode coupling due to backscattering in a He-Ne traveling-wave ring laser,” Appl. Phys. Lett.9(1), 55–58 (1966).
    [CrossRef]
  4. F. Aronowitz, “Fundamentals of the ring laser gyro,” Gyroscopes Optiques Et Leurs Applications15, 339 (1999).
  5. D. Loukianov, R. Rodloff, H. Sorg, and B. Stieler, “Optical gyros and their application,” RTO-AGA-339(1999).
  6. R. Rodloff, “A laser gyro with optimized resonator geometry,” IEEE J. Quantum Electron.23(4), 438–445 (1987).
    [CrossRef]
  7. J. E. Killpatrick, “Random bias for laser angular rate sensor,” U.S.A Patent No.3467472 (1969).
  8. J. E. Killpatrick, Dither control system for a ring laser gyro,” U.S.A Patent No.6476918B1 (2002).
  9. C. Guo and J. L. Wang, and H. G. Lv, “Test System of frequency stabilization and lock stabilization control parameter for ring laser gyroscope,” Opt. Technol.32, 448–451 (2006).
  10. W. H. Egli, and Minneapolis, “Ring laser angular rate sensor with modulated scattered waves,” U.S.A Patent No.4592656 (1986).
  11. W. L. Lim and F. H. Zeman, “Laser gyro system,” U.S.A Patent No.4824252 (1989).
  12. J. H. Simpson and J. G. Koper, “Ring laser gyroscope utilizing phase detector for minimizing beam lock-in,” U.S.A Patent No.4473297 (1984).
  13. X. G. Kong, T. S. Feng, and G. F. Jin, “Lock-in variation in the frequency-stabilized ring laser gyroscope,” Chin. J. Lasers19, 744–748 (1992).
  14. A. E. Siegman, Lasers, (University Science Books, Mill Valley, CA, 1986) Chap. 15.
  15. O. Svelto, Principles of Lasers, (Springer , 1998).
  16. J. Yuan, X. Long, B. Zhang, F. Wang, and H. Zhao, “Optical axis perturbation in folded planar ring resonators,” Appl. Opt.46(25), 6314–6322 (2007).
    [CrossRef] [PubMed]

2007

2006

C. Guo and J. L. Wang, and H. G. Lv, “Test System of frequency stabilization and lock stabilization control parameter for ring laser gyroscope,” Opt. Technol.32, 448–451 (2006).

1999

F. Aronowitz, “Fundamentals of the ring laser gyro,” Gyroscopes Optiques Et Leurs Applications15, 339 (1999).

1992

X. G. Kong, T. S. Feng, and G. F. Jin, “Lock-in variation in the frequency-stabilized ring laser gyroscope,” Chin. J. Lasers19, 744–748 (1992).

1988

M. Faucheux, D. Fayoux, and J. J. Roland, “The ring laser gyro,” J. Opt.19(3), 101–115 (1988).
[CrossRef]

1987

R. Rodloff, “A laser gyro with optimized resonator geometry,” IEEE J. Quantum Electron.23(4), 438–445 (1987).
[CrossRef]

1985

W. Chow, J. Gea-Banacloche, L. Pedrotti, V. Sanders, W. Schleich, and M. Scully, “The ring laser gyro,” Rev. Mod. Phys.57(1), 61–104 (1985).
[CrossRef]

1966

F. Aronowitz, “Mode coupling due to backscattering in a He-Ne traveling-wave ring laser,” Appl. Phys. Lett.9(1), 55–58 (1966).
[CrossRef]

Aronowitz, F.

F. Aronowitz, “Fundamentals of the ring laser gyro,” Gyroscopes Optiques Et Leurs Applications15, 339 (1999).

F. Aronowitz, “Mode coupling due to backscattering in a He-Ne traveling-wave ring laser,” Appl. Phys. Lett.9(1), 55–58 (1966).
[CrossRef]

Chow, W.

W. Chow, J. Gea-Banacloche, L. Pedrotti, V. Sanders, W. Schleich, and M. Scully, “The ring laser gyro,” Rev. Mod. Phys.57(1), 61–104 (1985).
[CrossRef]

Faucheux, M.

M. Faucheux, D. Fayoux, and J. J. Roland, “The ring laser gyro,” J. Opt.19(3), 101–115 (1988).
[CrossRef]

Fayoux, D.

M. Faucheux, D. Fayoux, and J. J. Roland, “The ring laser gyro,” J. Opt.19(3), 101–115 (1988).
[CrossRef]

Feng, T. S.

X. G. Kong, T. S. Feng, and G. F. Jin, “Lock-in variation in the frequency-stabilized ring laser gyroscope,” Chin. J. Lasers19, 744–748 (1992).

Gea-Banacloche, J.

W. Chow, J. Gea-Banacloche, L. Pedrotti, V. Sanders, W. Schleich, and M. Scully, “The ring laser gyro,” Rev. Mod. Phys.57(1), 61–104 (1985).
[CrossRef]

Guo, C.

C. Guo and J. L. Wang, and H. G. Lv, “Test System of frequency stabilization and lock stabilization control parameter for ring laser gyroscope,” Opt. Technol.32, 448–451 (2006).

Jin, G. F.

X. G. Kong, T. S. Feng, and G. F. Jin, “Lock-in variation in the frequency-stabilized ring laser gyroscope,” Chin. J. Lasers19, 744–748 (1992).

Kong, X. G.

X. G. Kong, T. S. Feng, and G. F. Jin, “Lock-in variation in the frequency-stabilized ring laser gyroscope,” Chin. J. Lasers19, 744–748 (1992).

Long, X.

Pedrotti, L.

W. Chow, J. Gea-Banacloche, L. Pedrotti, V. Sanders, W. Schleich, and M. Scully, “The ring laser gyro,” Rev. Mod. Phys.57(1), 61–104 (1985).
[CrossRef]

Rodloff, R.

R. Rodloff, “A laser gyro with optimized resonator geometry,” IEEE J. Quantum Electron.23(4), 438–445 (1987).
[CrossRef]

Roland, J. J.

M. Faucheux, D. Fayoux, and J. J. Roland, “The ring laser gyro,” J. Opt.19(3), 101–115 (1988).
[CrossRef]

Sanders, V.

W. Chow, J. Gea-Banacloche, L. Pedrotti, V. Sanders, W. Schleich, and M. Scully, “The ring laser gyro,” Rev. Mod. Phys.57(1), 61–104 (1985).
[CrossRef]

Schleich, W.

W. Chow, J. Gea-Banacloche, L. Pedrotti, V. Sanders, W. Schleich, and M. Scully, “The ring laser gyro,” Rev. Mod. Phys.57(1), 61–104 (1985).
[CrossRef]

Scully, M.

W. Chow, J. Gea-Banacloche, L. Pedrotti, V. Sanders, W. Schleich, and M. Scully, “The ring laser gyro,” Rev. Mod. Phys.57(1), 61–104 (1985).
[CrossRef]

Wang, F.

Wang, J. L.

C. Guo and J. L. Wang, and H. G. Lv, “Test System of frequency stabilization and lock stabilization control parameter for ring laser gyroscope,” Opt. Technol.32, 448–451 (2006).

Yuan, J.

Zhang, B.

Zhao, H.

Appl. Opt.

Appl. Phys. Lett.

F. Aronowitz, “Mode coupling due to backscattering in a He-Ne traveling-wave ring laser,” Appl. Phys. Lett.9(1), 55–58 (1966).
[CrossRef]

Chin. J. Lasers

X. G. Kong, T. S. Feng, and G. F. Jin, “Lock-in variation in the frequency-stabilized ring laser gyroscope,” Chin. J. Lasers19, 744–748 (1992).

Gyroscopes Optiques Et Leurs Applications

F. Aronowitz, “Fundamentals of the ring laser gyro,” Gyroscopes Optiques Et Leurs Applications15, 339 (1999).

IEEE J. Quantum Electron.

R. Rodloff, “A laser gyro with optimized resonator geometry,” IEEE J. Quantum Electron.23(4), 438–445 (1987).
[CrossRef]

J. Opt.

M. Faucheux, D. Fayoux, and J. J. Roland, “The ring laser gyro,” J. Opt.19(3), 101–115 (1988).
[CrossRef]

Opt. Technol.

C. Guo and J. L. Wang, and H. G. Lv, “Test System of frequency stabilization and lock stabilization control parameter for ring laser gyroscope,” Opt. Technol.32, 448–451 (2006).

Rev. Mod. Phys.

W. Chow, J. Gea-Banacloche, L. Pedrotti, V. Sanders, W. Schleich, and M. Scully, “The ring laser gyro,” Rev. Mod. Phys.57(1), 61–104 (1985).
[CrossRef]

Other

D. Loukianov, R. Rodloff, H. Sorg, and B. Stieler, “Optical gyros and their application,” RTO-AGA-339(1999).

W. H. Egli, and Minneapolis, “Ring laser angular rate sensor with modulated scattered waves,” U.S.A Patent No.4592656 (1986).

W. L. Lim and F. H. Zeman, “Laser gyro system,” U.S.A Patent No.4824252 (1989).

J. H. Simpson and J. G. Koper, “Ring laser gyroscope utilizing phase detector for minimizing beam lock-in,” U.S.A Patent No.4473297 (1984).

J. E. Killpatrick, “Random bias for laser angular rate sensor,” U.S.A Patent No.3467472 (1969).

J. E. Killpatrick, Dither control system for a ring laser gyro,” U.S.A Patent No.6476918B1 (2002).

A. E. Siegman, Lasers, (University Science Books, Mill Valley, CA, 1986) Chap. 15.

O. Svelto, Principles of Lasers, (Springer , 1998).

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Figures (7)

Fig. 1
Fig. 1

Light path in the square ring resonator before and after the positions of P1 and P2 are changed.

Fig. 2
Fig. 2

Schematic diagram of the light path before and after changing the position of P1.

Fig. 3
Fig. 3

The cavity structures of the two types of RLG.

Fig. 4
Fig. 4

Sensitivity of equivalent rotation with incident angles of 15°, 30° and 45° versus l, with R = 8m and different values for m: (a) m = 2, (b) m = 3, (c) m = 4.

Fig. 5
Fig. 5

Schematic diagram of the experimental system

Fig. 6
Fig. 6

Real time output of the gyro when spherical mirrors P1 and P2 are vibrated in opposite directions.

Fig. 7
Fig. 7

Equivalent rotation rate vs. velocity of mirrors’ movement

Equations (20)

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{ A C = r i cos A i C B =2| ε 1 |tg A i | r 0 |=( A C + C B )cos A i
{ β+ A i =| θ o |+ A i | θ i |+ A i =β+ A i β= A C +| ε 1 |tg A i R
| r o |=| r i |+2| ε 1 |sin A i ,
| θ o |=| θ i |+ | r i | f + | ε 1 |sin A i f .
r o = r i +2 ε 1 sin A i ,
θ o = θ i r i f ε 1 sin A i f .
[ r o θ o 1 ]=M( P 1 )[ r i θ i 1 ].
M( P 1 )=[ 1 0 2 ε 1 sin A i 1 f 1 ε 1 sin A i f 0 0 1 ]
M( P 2 )=M( P 1 )=[ 1 0 2εsin A i 1 f 1 εsin A i f 0 0 1 ].
M( l i )=[ 1 l i 0 0 1 0 0 0 1 ],( i=1,2,3,4 ).
M=[ A B β C D δ 0 0 1 ]=M( l 4 )M( l 3 )M( l 2 )M( P 2 )M( l 1 )M( P 1 ),
[ r 1 θ 1 1 ]=M[ r 1 θ 1 1 ].
r 1 = m( l R 2cos A i ) ( m+1 )cos A i m l R εsin A i ,
θ 1 = 2 l R 4cos A i ( ( m+1 )cos A i m l R )l εsin A i .
θ 2 = θ 1 + 2(m1) l R i ( ( m+1 )cos A i m l R )l εsin A i ,
θ 3 = θ 1 ,
θ 4 = θ 1 .
Ω= 2l R 4cos A i l[ ( m+1 )cos A i ml R ] sin A i dε dt .
l R < cos A i m .
Ω= 4 l( m+1 ) sin A i dε dt .

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