Abstract

We report several findings on the optical-axis perturbation of monolithic triaxial ring resonator. A criterion, C, which represents the mismatching error of the monolithic triaxial ring resonator, has been found out and it cannot be decreased by modifying the angles of the terminal surfaces or the terminal mirrors of the resonator. When C0, an optimization method to share the mismatching error C in some specific directions equally and simultaneously has been proposed. The interesting findings are important to cavity design, cavity improvement, and alignment of the monolithic triaxial ring resonator.

© 2008 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. W. W. Chow, J. Gea-Banacloche, L. M. Pedrotti, V. E. Sanders, W. Schleich, and M. O. Scully, “The ring laser gyro,” Rev. Mod. Phys. 57, 61-86 (1985).
    [CrossRef]
  2. M. Faucheux, D. Fayoux, and J. J. Roland, “The ring laser gyro,” J. Opt. (Paris) 19, 101-115 (1988).
  3. A. E. Siegman, “Laser beams and resonators: beyond the 1960s,” IEEE J. Sel. Top. Quantum Electron. 6, 1389-1399 (2000).
    [CrossRef]
  4. M. L. Stitch and M. Bass, Laser Handbook (North-Holland, 1985), Vol. 4, Chap. 3, pp. 229-332.
  5. A. H. Paxton and W. P. Latham, “Unstable resonators with 90° beam rotation,” Appl. Opt. 25, 2939-2946 (1986).
    [CrossRef] [PubMed]
  6. J. A. Arnaud, “Degenerate optical cavities. II. Effects of misalignments,” Appl. Opt. 8, 1909-1917 (1969).
    [CrossRef] [PubMed]
  7. G. B. Altshuler, E. D. Isyanova, V. B. Karasev, A. L. Levit, V. M. Ovchinnikov, and S. F. Sharlai, “Analysis of misalignment sensitivity of ring laser resonators,” Sov. J. Quantum Electron. 7, 857-859 (1977).
    [CrossRef]
  8. I. W. Smith, “Optical resonator axis stability and instability from first principles,” in Fiber Optic and Laser Sensors, Proc. SPIE 412, 203-206 (1983).
  9. A. L. Levit and V. M. Ovchinnikov, “Stability of a ring resonator with a nonplane axial contour,” J. Appl. Spectrosc. 40, 657-660 (1984).
    [CrossRef]
  10. S.-C. Sheng, “Optical-axis perturbation singularity in an out-of-palne ring resonator,” Opt. Lett. 19, 683-685 (1994).
    [CrossRef] [PubMed]
  11. J. Yuan, X. Long, B. Zhang, F. Wang, and H. Zhao, “Optical axis perturbation in folded planar ring resonators,” Appl. Opt. 46, 6314-6322 (2007).
    [CrossRef] [PubMed]
  12. A. H. Paxton and W. P. Latham, Jr., “Ray matrix method for the analysis of optical resonators with image rotation,” Proc. Soc. Photo-Opt. Instrum. Eng. 554, 159-163 (1985).
  13. R. Rodloff, “A laser gyro with optimized resonator geometry,” IEEE J. Quantum Electron. QE-23, 438-445 (1987).
    [CrossRef]
  14. J. Yuan and X. W. Long, “Optical-axis perturbation in nonplanar ring resonators,” Opt. Commun. 281, 1204-1210 (2008).
    [CrossRef]
  15. J. C. Stiles and B. H. G. Ljung, “Monolithic three axis ring laser gyroscope,” U.S. patent 4,477,188 (16 October 1984).
  16. A. E. Siegman, Lasers (University Science, 1986), Chap. 15.
  17. A. Gerrard and J. M. Burch, Introduction of Matrix Methods in Optics (Gersham, 1975).

2008 (1)

J. Yuan and X. W. Long, “Optical-axis perturbation in nonplanar ring resonators,” Opt. Commun. 281, 1204-1210 (2008).
[CrossRef]

2007 (1)

2000 (1)

A. E. Siegman, “Laser beams and resonators: beyond the 1960s,” IEEE J. Sel. Top. Quantum Electron. 6, 1389-1399 (2000).
[CrossRef]

1994 (1)

1988 (1)

M. Faucheux, D. Fayoux, and J. J. Roland, “The ring laser gyro,” J. Opt. (Paris) 19, 101-115 (1988).

1987 (1)

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

1986 (1)

1985 (2)

W. W. Chow, J. Gea-Banacloche, L. M. Pedrotti, V. E. Sanders, W. Schleich, and M. O. Scully, “The ring laser gyro,” Rev. Mod. Phys. 57, 61-86 (1985).
[CrossRef]

A. H. Paxton and W. P. Latham, Jr., “Ray matrix method for the analysis of optical resonators with image rotation,” Proc. Soc. Photo-Opt. Instrum. Eng. 554, 159-163 (1985).

1984 (1)

A. L. Levit and V. M. Ovchinnikov, “Stability of a ring resonator with a nonplane axial contour,” J. Appl. Spectrosc. 40, 657-660 (1984).
[CrossRef]

1977 (1)

G. B. Altshuler, E. D. Isyanova, V. B. Karasev, A. L. Levit, V. M. Ovchinnikov, and S. F. Sharlai, “Analysis of misalignment sensitivity of ring laser resonators,” Sov. J. Quantum Electron. 7, 857-859 (1977).
[CrossRef]

1969 (1)

Altshuler, G. B.

G. B. Altshuler, E. D. Isyanova, V. B. Karasev, A. L. Levit, V. M. Ovchinnikov, and S. F. Sharlai, “Analysis of misalignment sensitivity of ring laser resonators,” Sov. J. Quantum Electron. 7, 857-859 (1977).
[CrossRef]

Arnaud, J. A.

Bass, M.

M. L. Stitch and M. Bass, Laser Handbook (North-Holland, 1985), Vol. 4, Chap. 3, pp. 229-332.

Burch, J. M.

A. Gerrard and J. M. Burch, Introduction of Matrix Methods in Optics (Gersham, 1975).

Chow, W. W.

W. W. Chow, J. Gea-Banacloche, L. M. Pedrotti, V. E. Sanders, W. Schleich, and M. O. Scully, “The ring laser gyro,” Rev. Mod. Phys. 57, 61-86 (1985).
[CrossRef]

Faucheux, M.

M. Faucheux, D. Fayoux, and J. J. Roland, “The ring laser gyro,” J. Opt. (Paris) 19, 101-115 (1988).

Fayoux, D.

M. Faucheux, D. Fayoux, and J. J. Roland, “The ring laser gyro,” J. Opt. (Paris) 19, 101-115 (1988).

Gea-Banacloche, J.

W. W. Chow, J. Gea-Banacloche, L. M. Pedrotti, V. E. Sanders, W. Schleich, and M. O. Scully, “The ring laser gyro,” Rev. Mod. Phys. 57, 61-86 (1985).
[CrossRef]

Gerrard, A.

A. Gerrard and J. M. Burch, Introduction of Matrix Methods in Optics (Gersham, 1975).

Isyanova, E. D.

G. B. Altshuler, E. D. Isyanova, V. B. Karasev, A. L. Levit, V. M. Ovchinnikov, and S. F. Sharlai, “Analysis of misalignment sensitivity of ring laser resonators,” Sov. J. Quantum Electron. 7, 857-859 (1977).
[CrossRef]

Karasev, V. B.

G. B. Altshuler, E. D. Isyanova, V. B. Karasev, A. L. Levit, V. M. Ovchinnikov, and S. F. Sharlai, “Analysis of misalignment sensitivity of ring laser resonators,” Sov. J. Quantum Electron. 7, 857-859 (1977).
[CrossRef]

Latham, W. P.

A. H. Paxton and W. P. Latham, “Unstable resonators with 90° beam rotation,” Appl. Opt. 25, 2939-2946 (1986).
[CrossRef] [PubMed]

A. H. Paxton and W. P. Latham, Jr., “Ray matrix method for the analysis of optical resonators with image rotation,” Proc. Soc. Photo-Opt. Instrum. Eng. 554, 159-163 (1985).

Levit, A. L.

A. L. Levit and V. M. Ovchinnikov, “Stability of a ring resonator with a nonplane axial contour,” J. Appl. Spectrosc. 40, 657-660 (1984).
[CrossRef]

G. B. Altshuler, E. D. Isyanova, V. B. Karasev, A. L. Levit, V. M. Ovchinnikov, and S. F. Sharlai, “Analysis of misalignment sensitivity of ring laser resonators,” Sov. J. Quantum Electron. 7, 857-859 (1977).
[CrossRef]

Ljung, B. H. G.

J. C. Stiles and B. H. G. Ljung, “Monolithic three axis ring laser gyroscope,” U.S. patent 4,477,188 (16 October 1984).

Long, X.

Long, X. W.

J. Yuan and X. W. Long, “Optical-axis perturbation in nonplanar ring resonators,” Opt. Commun. 281, 1204-1210 (2008).
[CrossRef]

Ovchinnikov, V. M.

A. L. Levit and V. M. Ovchinnikov, “Stability of a ring resonator with a nonplane axial contour,” J. Appl. Spectrosc. 40, 657-660 (1984).
[CrossRef]

G. B. Altshuler, E. D. Isyanova, V. B. Karasev, A. L. Levit, V. M. Ovchinnikov, and S. F. Sharlai, “Analysis of misalignment sensitivity of ring laser resonators,” Sov. J. Quantum Electron. 7, 857-859 (1977).
[CrossRef]

Paxton, A. H.

A. H. Paxton and W. P. Latham, “Unstable resonators with 90° beam rotation,” Appl. Opt. 25, 2939-2946 (1986).
[CrossRef] [PubMed]

A. H. Paxton and W. P. Latham, Jr., “Ray matrix method for the analysis of optical resonators with image rotation,” Proc. Soc. Photo-Opt. Instrum. Eng. 554, 159-163 (1985).

Pedrotti, L. M.

W. W. Chow, J. Gea-Banacloche, L. M. Pedrotti, V. E. Sanders, W. Schleich, and M. O. Scully, “The ring laser gyro,” Rev. Mod. Phys. 57, 61-86 (1985).
[CrossRef]

Rodloff, R.

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

Roland, J. J.

M. Faucheux, D. Fayoux, and J. J. Roland, “The ring laser gyro,” J. Opt. (Paris) 19, 101-115 (1988).

Sanders, V. E.

W. W. Chow, J. Gea-Banacloche, L. M. Pedrotti, V. E. Sanders, W. Schleich, and M. O. Scully, “The ring laser gyro,” Rev. Mod. Phys. 57, 61-86 (1985).
[CrossRef]

Schleich, W.

W. W. Chow, J. Gea-Banacloche, L. M. Pedrotti, V. E. Sanders, W. Schleich, and M. O. Scully, “The ring laser gyro,” Rev. Mod. Phys. 57, 61-86 (1985).
[CrossRef]

Scully, M. O.

W. W. Chow, J. Gea-Banacloche, L. M. Pedrotti, V. E. Sanders, W. Schleich, and M. O. Scully, “The ring laser gyro,” Rev. Mod. Phys. 57, 61-86 (1985).
[CrossRef]

Sharlai, S. F.

G. B. Altshuler, E. D. Isyanova, V. B. Karasev, A. L. Levit, V. M. Ovchinnikov, and S. F. Sharlai, “Analysis of misalignment sensitivity of ring laser resonators,” Sov. J. Quantum Electron. 7, 857-859 (1977).
[CrossRef]

Sheng, S.-C.

Siegman, A. E.

A. E. Siegman, “Laser beams and resonators: beyond the 1960s,” IEEE J. Sel. Top. Quantum Electron. 6, 1389-1399 (2000).
[CrossRef]

A. E. Siegman, Lasers (University Science, 1986), Chap. 15.

Smith, I. W.

I. W. Smith, “Optical resonator axis stability and instability from first principles,” in Fiber Optic and Laser Sensors, Proc. SPIE 412, 203-206 (1983).

Stiles, J. C.

J. C. Stiles and B. H. G. Ljung, “Monolithic three axis ring laser gyroscope,” U.S. patent 4,477,188 (16 October 1984).

Stitch, M. L.

M. L. Stitch and M. Bass, Laser Handbook (North-Holland, 1985), Vol. 4, Chap. 3, pp. 229-332.

Wang, F.

Yuan, J.

J. Yuan and X. W. Long, “Optical-axis perturbation in nonplanar ring resonators,” Opt. Commun. 281, 1204-1210 (2008).
[CrossRef]

J. Yuan, X. Long, B. Zhang, F. Wang, and H. Zhao, “Optical axis perturbation in folded planar ring resonators,” Appl. Opt. 46, 6314-6322 (2007).
[CrossRef] [PubMed]

Zhang, B.

Zhao, H.

Appl. Opt. (3)

IEEE J. Quantum Electron. (1)

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

IEEE J. Sel. Top. Quantum Electron. (1)

A. E. Siegman, “Laser beams and resonators: beyond the 1960s,” IEEE J. Sel. Top. Quantum Electron. 6, 1389-1399 (2000).
[CrossRef]

J. Appl. Spectrosc. (1)

A. L. Levit and V. M. Ovchinnikov, “Stability of a ring resonator with a nonplane axial contour,” J. Appl. Spectrosc. 40, 657-660 (1984).
[CrossRef]

J. Opt. (Paris) (1)

M. Faucheux, D. Fayoux, and J. J. Roland, “The ring laser gyro,” J. Opt. (Paris) 19, 101-115 (1988).

Opt. Commun. (1)

J. Yuan and X. W. Long, “Optical-axis perturbation in nonplanar ring resonators,” Opt. Commun. 281, 1204-1210 (2008).
[CrossRef]

Opt. Lett. (1)

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

A. H. Paxton and W. P. Latham, Jr., “Ray matrix method for the analysis of optical resonators with image rotation,” Proc. Soc. Photo-Opt. Instrum. Eng. 554, 159-163 (1985).

Rev. Mod. Phys. (1)

W. W. Chow, J. Gea-Banacloche, L. M. Pedrotti, V. E. Sanders, W. Schleich, and M. O. Scully, “The ring laser gyro,” Rev. Mod. Phys. 57, 61-86 (1985).
[CrossRef]

Sov. J. Quantum Electron. (1)

G. B. Altshuler, E. D. Isyanova, V. B. Karasev, A. L. Levit, V. M. Ovchinnikov, and S. F. Sharlai, “Analysis of misalignment sensitivity of ring laser resonators,” Sov. J. Quantum Electron. 7, 857-859 (1977).
[CrossRef]

Other (5)

I. W. Smith, “Optical resonator axis stability and instability from first principles,” in Fiber Optic and Laser Sensors, Proc. SPIE 412, 203-206 (1983).

M. L. Stitch and M. Bass, Laser Handbook (North-Holland, 1985), Vol. 4, Chap. 3, pp. 229-332.

J. C. Stiles and B. H. G. Ljung, “Monolithic three axis ring laser gyroscope,” U.S. patent 4,477,188 (16 October 1984).

A. E. Siegman, Lasers (University Science, 1986), Chap. 15.

A. Gerrard and J. M. Burch, Introduction of Matrix Methods in Optics (Gersham, 1975).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

Fig. 1
Fig. 1

Schematic of monolithic triaxial ring resonator.

Fig. 2
Fig. 2

Schematic of a square ring resonator.

Fig. 3
Fig. 3

Definition of the mirror's misalignments angle θ a x .

Equations (35)

Equations on this page are rendered with MathJax. Learn more.

Δ x e = 2 4 R ( θ a x + θ b x + θ c x + θ d x ) ,
Δ y e = 2 2 R ( θ a y + θ b y + θ c y + θ d y ) .
Δ x A = 2 4 R ( θ 2 y θ 3 x θ 4 x + θ 6 y ) ,
Δ y A = 2 2 R ( θ 2 x θ 3 y + θ 4 y θ 6 x ) ,
Δ x B = 2 4 R ( θ 3 y θ 1 x θ 6 x + θ 5 y ) ,
Δ y B = 2 2 R ( θ 3 x θ 1 y + θ 6 y θ 5 x ) ,
Δ x C = 2 4 R ( θ 1 y θ 2 x θ 5 x + θ 4 y ) ,
Δ y C = 2 2 R ( θ 1 x θ 2 y + θ 5 y θ 4 x ) .
x A = x A , y A = y A / 2 , x B = x B , y B = y B / 2 ,
x C = x C , y C = y C / 2 .
Δ x A = Δ x A , Δ y A = Δ y A / 2 , Δ x B = Δ x B ,
Δ y B = Δ y B / 2 , Δ x C = Δ x C , Δ y C = Δ y C / 2 ,
Δ x A + Δ y A + Δ x B + Δ y B + Δ x C + Δ y C = 0 .
Δ x A ( 0 t ) = x A ( t ) x A ( 0 ) ,
Δ y A ( 0 t ) = y A ( t ) y A ( 0 ) ,
Δ x B ( 0 t ) = x B ( t ) x B ( 0 ) ,
Δ y B ( 0 t ) = y B ( t ) y B ( 0 ) ,
Δ x C ( 0 t ) = x C ( t ) x C ( 0 ) ,
Δ y C ( 0 t ) = y C ( t ) y C ( 0 ) .
Δ x A ( 0 t ) + Δ y A ( 0 t ) + Δ x B ( 0 t ) + Δ y B ( 0 t ) + Δ x C ( 0 t ) + Δ y C ( 0 t ) = 0 .
x A ( t ) + y A ( t ) + x B ( t ) + y B ( t ) + x C ( t ) + y C ( t ) = x A ( 0 )
+ y A ( 0 ) + x B ( 0 ) + y B ( 0 ) + x C ( 0 ) + y C ( 0 ) .
x A ( t ) + y A ( t ) + x B ( t ) + y B ( t ) + x C ( t ) + y C ( t ) = C .
D A = x A 2 + y A 2 = x A 2 + 4 y A 2 ,
D B = x B 2 + y B 2 = x B 2 + 4 y B 2 ,
D C = x C 2 + y C 2 = x C 2 + 4 y C 2 .
x A ( t ) = x B ( t ) = x C ( t ) = C / 3 ,
y A ( t ) = y B ( t ) = y C ( t ) = 0 ,
D A = D B = D C = | C | 3 .
y A ( t ) = y B ( t ) = y C ( t ) = C / 3 ,
x A ( t ) = x B ( t ) = x C ( t ) = 0 ,
D A = D B = D C = 2 3 | C | .
x A ( t ) = C / 3 , x B ( t ) = C , x C ( t ) = C / 3 ,
y A ( t ) = y B ( t ) = y C ( t ) = 0 ,
D A = 1 3 | C | , D B = | C | , D C = 1 3 | C | .

Metrics