Abstract

By utilizing the generalized ray matrix for spherical mirror reflection, two new sensitivity factors are introduced considering the perturbation of the optical-axis caused by the radial and axial displacements of a spherical mirror in a nonplanar ring resonator. Based on this, a novel way for finding the location of the singular points of the sensitivity factors is presented. It is found that some nonplanar ring resonators with the effective modes may have the singular points of the sensitivity factors. The unsuitable regions for nonplanar ring resonators are also obtained from the perspective of the sensitivity factors.

© 2011 OSA

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References

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  1. H. Statz, T. A. Dorschner, M. Holtz, and I. W. Smith, “The multioscillator ring laser gyroscope,” in Laser Handbook, M. I. Stitch, and M. Bass, eds. (North Holland, 1985), pp. 229–327.
  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(1), 61–104 (1985).
    [CrossRef]
  3. A. E. Siegman, “Laser beams and resonators: beyond the 1960s,” IEEE J. Sel. Top. Quantum Electron. 6(6), 1389–1399 (2000).
    [CrossRef]
  4. F. Zomer, Y. Fedala, N. Pavloff, V. Soskov, and A. Variola, “Polarization induced instabilities in external four-mirror Fabry-Perot cavities,” Appl. Opt. 48(35), 6651–6661 (2009).
    [CrossRef] [PubMed]
  5. Y. Honda, H. Shimizu, M. Fukuda, T. Omori, J. Urakawa, K. Sakaue, H. Sakai, and N. Sasao, “Stabilization of a non-planar optical cavity using its polarization property,” Opt. Commun. 282(15), 3108–3112 (2009).
    [CrossRef]
  6. R. Rodloff, “A laser gyro with optimized resonator geometry,” IEEE J. Quantum Electron. 23(4), 438–445 (1987).
    [CrossRef]
  7. J. Yuan and X. W. Long, “Optical-axis perturbation in nonplanar ring resonators,” Opt. Commun. 281(5), 1204–1210 (2008).
    [CrossRef]
  8. G. B. Al’tshuler, 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(7), 857–859 (1977).
    [CrossRef]
  9. I. W. Smith, “Optical resonator axis stability and instability from first principles,” Proc. SPIE 412, 203–206 (1983).
  10. A. L. Levkit and V. M. Ovchinnikov, “Stability of a ring resonator with a nonplane axial contour,” J. Appl. Spectros. (USSR) 40(6), 657–660 (1984).
    [CrossRef]
  11. S.-C. Sheng, “Optical-axis perturbation singularity in an out-of-plane ring resonator,” Opt. Lett. 19(10), 683–685 (1994).
    [CrossRef] [PubMed]
  12. A. H. Paxton and W. P. Latham., “Unstable resonators with 90 ° beam rotation,” Appl. Opt. 25(17), 2939–2946 (1986).
    [CrossRef] [PubMed]
  13. A. H. Paxton and W. P. Latham., “Ray matrix method for the analysis of optical resonators with image rotation,” Proc. SPIE 554, 159–163 (1985).
  14. A. E. Siegman, Lasers (University Science, 1986).
  15. J. Yuan, X. W. Long, and M. X. Chen, “Generalized ray matrix for spherical mirror reflection and its application in square ring resonators and monolithic triaxial ring resonators,” Opt. Express 19(7), 6762–6776 (2011).
    [CrossRef] [PubMed]
  16. X. W. Long and J. Yuan, “Method for eliminating mismatching error in monolithic triaxial ring resonators,” Chin. Opt. Lett. 8(12), 1135–1138 (2010).
    [CrossRef]
  17. J. Yuan, X. W. Long, L. M. Liang, B. Zhang, F. Wang, and H. C. Zhao, “Nonplanar ring resonator modes: generalized Gaussian beams,” Appl. Opt. 46(15), 2980–2989 (2007).
    [CrossRef] [PubMed]

2011

2010

2009

F. Zomer, Y. Fedala, N. Pavloff, V. Soskov, and A. Variola, “Polarization induced instabilities in external four-mirror Fabry-Perot cavities,” Appl. Opt. 48(35), 6651–6661 (2009).
[CrossRef] [PubMed]

Y. Honda, H. Shimizu, M. Fukuda, T. Omori, J. Urakawa, K. Sakaue, H. Sakai, and N. Sasao, “Stabilization of a non-planar optical cavity using its polarization property,” Opt. Commun. 282(15), 3108–3112 (2009).
[CrossRef]

2008

J. Yuan and X. W. Long, “Optical-axis perturbation in nonplanar ring resonators,” Opt. Commun. 281(5), 1204–1210 (2008).
[CrossRef]

2007

2000

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

1994

1987

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

1986

1985

A. H. Paxton and W. P. Latham., “Ray matrix method for the analysis of optical resonators with image rotation,” Proc. SPIE 554, 159–163 (1985).

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(1), 61–104 (1985).
[CrossRef]

1984

A. L. Levkit and V. M. Ovchinnikov, “Stability of a ring resonator with a nonplane axial contour,” J. Appl. Spectros. (USSR) 40(6), 657–660 (1984).
[CrossRef]

1983

I. W. Smith, “Optical resonator axis stability and instability from first principles,” Proc. SPIE 412, 203–206 (1983).

1977

G. B. Al’tshuler, 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(7), 857–859 (1977).
[CrossRef]

Al’tshuler, G. B.

G. B. Al’tshuler, 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(7), 857–859 (1977).
[CrossRef]

Chen, M. X.

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(1), 61–104 (1985).
[CrossRef]

Fedala, Y.

Fukuda, M.

Y. Honda, H. Shimizu, M. Fukuda, T. Omori, J. Urakawa, K. Sakaue, H. Sakai, and N. Sasao, “Stabilization of a non-planar optical cavity using its polarization property,” Opt. Commun. 282(15), 3108–3112 (2009).
[CrossRef]

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(1), 61–104 (1985).
[CrossRef]

Honda, Y.

Y. Honda, H. Shimizu, M. Fukuda, T. Omori, J. Urakawa, K. Sakaue, H. Sakai, and N. Sasao, “Stabilization of a non-planar optical cavity using its polarization property,” Opt. Commun. 282(15), 3108–3112 (2009).
[CrossRef]

Isyanova, E. D.

G. B. Al’tshuler, 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(7), 857–859 (1977).
[CrossRef]

Karasev, V. B.

G. B. Al’tshuler, 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(7), 857–859 (1977).
[CrossRef]

Latham, W. P.

A. H. Paxton and W. P. Latham., “Unstable resonators with 90 ° beam rotation,” Appl. Opt. 25(17), 2939–2946 (1986).
[CrossRef] [PubMed]

A. H. Paxton and W. P. Latham., “Ray matrix method for the analysis of optical resonators with image rotation,” Proc. SPIE 554, 159–163 (1985).

Levit, A. L.

G. B. Al’tshuler, 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(7), 857–859 (1977).
[CrossRef]

Levkit, A. L.

A. L. Levkit and V. M. Ovchinnikov, “Stability of a ring resonator with a nonplane axial contour,” J. Appl. Spectros. (USSR) 40(6), 657–660 (1984).
[CrossRef]

Liang, L. M.

Long, X. W.

Omori, T.

Y. Honda, H. Shimizu, M. Fukuda, T. Omori, J. Urakawa, K. Sakaue, H. Sakai, and N. Sasao, “Stabilization of a non-planar optical cavity using its polarization property,” Opt. Commun. 282(15), 3108–3112 (2009).
[CrossRef]

Ovchinnikov, V. M.

A. L. Levkit and V. M. Ovchinnikov, “Stability of a ring resonator with a nonplane axial contour,” J. Appl. Spectros. (USSR) 40(6), 657–660 (1984).
[CrossRef]

G. B. Al’tshuler, 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(7), 857–859 (1977).
[CrossRef]

Pavloff, N.

Paxton, A. H.

A. H. Paxton and W. P. Latham., “Unstable resonators with 90 ° beam rotation,” Appl. Opt. 25(17), 2939–2946 (1986).
[CrossRef] [PubMed]

A. H. Paxton and W. P. Latham., “Ray matrix method for the analysis of optical resonators with image rotation,” Proc. SPIE 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(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]

Sakai, H.

Y. Honda, H. Shimizu, M. Fukuda, T. Omori, J. Urakawa, K. Sakaue, H. Sakai, and N. Sasao, “Stabilization of a non-planar optical cavity using its polarization property,” Opt. Commun. 282(15), 3108–3112 (2009).
[CrossRef]

Sakaue, K.

Y. Honda, H. Shimizu, M. Fukuda, T. Omori, J. Urakawa, K. Sakaue, H. Sakai, and N. Sasao, “Stabilization of a non-planar optical cavity using its polarization property,” Opt. Commun. 282(15), 3108–3112 (2009).
[CrossRef]

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(1), 61–104 (1985).
[CrossRef]

Sasao, N.

Y. Honda, H. Shimizu, M. Fukuda, T. Omori, J. Urakawa, K. Sakaue, H. Sakai, and N. Sasao, “Stabilization of a non-planar optical cavity using its polarization property,” Opt. Commun. 282(15), 3108–3112 (2009).
[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(1), 61–104 (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(1), 61–104 (1985).
[CrossRef]

Sharlai, S. F.

G. B. Al’tshuler, 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(7), 857–859 (1977).
[CrossRef]

Sheng, S.-C.

Shimizu, H.

Y. Honda, H. Shimizu, M. Fukuda, T. Omori, J. Urakawa, K. Sakaue, H. Sakai, and N. Sasao, “Stabilization of a non-planar optical cavity using its polarization property,” Opt. Commun. 282(15), 3108–3112 (2009).
[CrossRef]

Siegman, A. E.

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

Smith, I. W.

I. W. Smith, “Optical resonator axis stability and instability from first principles,” Proc. SPIE 412, 203–206 (1983).

Soskov, V.

Urakawa, J.

Y. Honda, H. Shimizu, M. Fukuda, T. Omori, J. Urakawa, K. Sakaue, H. Sakai, and N. Sasao, “Stabilization of a non-planar optical cavity using its polarization property,” Opt. Commun. 282(15), 3108–3112 (2009).
[CrossRef]

Variola, A.

Wang, F.

Yuan, J.

Zhang, B.

Zhao, H. C.

Zomer, F.

Appl. Opt.

Chin. Opt. Lett.

IEEE J. Quantum Electron.

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

IEEE J. Sel. Top. Quantum Electron.

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

J. Appl. Spectros. (USSR)

A. L. Levkit and V. M. Ovchinnikov, “Stability of a ring resonator with a nonplane axial contour,” J. Appl. Spectros. (USSR) 40(6), 657–660 (1984).
[CrossRef]

Opt. Commun.

J. Yuan and X. W. Long, “Optical-axis perturbation in nonplanar ring resonators,” Opt. Commun. 281(5), 1204–1210 (2008).
[CrossRef]

Y. Honda, H. Shimizu, M. Fukuda, T. Omori, J. Urakawa, K. Sakaue, H. Sakai, and N. Sasao, “Stabilization of a non-planar optical cavity using its polarization property,” Opt. Commun. 282(15), 3108–3112 (2009).
[CrossRef]

Opt. Express

Opt. Lett.

Proc. SPIE

A. H. Paxton and W. P. Latham., “Ray matrix method for the analysis of optical resonators with image rotation,” Proc. SPIE 554, 159–163 (1985).

I. W. Smith, “Optical resonator axis stability and instability from first principles,” Proc. SPIE 412, 203–206 (1983).

Rev. Mod. Phys.

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(1), 61–104 (1985).
[CrossRef]

Sov. J. Quantum Electron.

G. B. Al’tshuler, 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(7), 857–859 (1977).
[CrossRef]

Other

H. Statz, T. A. Dorschner, M. Holtz, and I. W. Smith, “The multioscillator ring laser gyroscope,” in Laser Handbook, M. I. Stitch, and M. Bass, eds. (North Holland, 1985), pp. 229–327.

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

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Figures (5)

Fig. 1
Fig. 1

Geometrical construction of a nonplanar ring resonator

Fig. 2
Fig. 2

Sensitivity factors SD2 and ST2 characterizing the movement of the optical-axis on mirror P1 with A = 43.87°. The perturbation source is the misalignment of mirror P1

Fig. 3
Fig. 3

Determinant of M' versues L/R.

Fig. 4
Fig. 4

Stability map of the nonplanar ring resonators and the track of the singular points. In the shaded regions 1-5, the resonator has the effective modes. The dashed line is the track of the singular points.

Fig. 5
Fig. 5

Quantitatively defined the unsuitable regions (the shaded regions) for a nonplanar ring resonator with any sensitivity factors larger than 100.

Equations (8)

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

M ( R j , A j ) = [ 1 0 0 0 2 δ j z sin ( A j ) 2 R j cos ( A j ) 1 0 0 2 δ j z tan ( A j ) R j + 2 ( θ j x + δ j x R j ) 0 0 1 0 0 0 0 2 cos ( A j ) R j 1 2 ( θ j y + δ j y R j ) 0 0 0 0 1 ] ,
M j = R ( φ j ) M ( R j , A j ) T ( L j ) .
M = M j .
V = [ r x r x ' r y r y ' 1 ] T ,
M V = V .
[ M 11 1 M 12 M 13 M 14 M 21 M 22 1 M 23 M 24 M 31 M 32 M 33 1 M 34 M 41 M 42 M 43 M 44 1 ] [ r x r x ' r y r y ' ] = [ M 15 M 25 M 35 M 45 ] .
SD 1 ( x y ) i ( x y ) j = 1 L [ r ( x y ) i θ ( x y ) j ] ,   ST 1 ( x y ) i ( x y ) j = [ r ( x y ) i θ ( x y ) j ] .
SD 2 ( x y ) i ( x y z ) j = [ r ( x y ) i δ ( x y z ) j ] ,   ST 2 ( x y ) i ( x y z ) j = L [ r ( x y ) i δ ( x y z ) j ] .

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