Generalized sensitivity factors for optical-axis perturbation in nonplanar ring resonators

doi:10.1364/OE.19.019752

Generalized sensitivity factors for optical-axis perturbation in nonplanar ring resonators

Dandan Wen, Dong Li, and Jianlin Zhao »View Author Affiliations

Optics Express, Vol. 19, Issue 20, pp. 19752-19757 (2011)
http://dx.doi.org/10.1364/OE.19.019752

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Abstract
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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.

OCIS Codes
(140.3370) Lasers and laser optics : Laser gyroscopes
(140.3410) Lasers and laser optics : Laser resonators
(140.3560) Lasers and laser optics : Lasers, ring
(140.4780) Lasers and laser optics : Optical resonators

ToC Category:
Lasers and Laser Optics

History
Original Manuscript: July 26, 2011
Revised Manuscript: September 7, 2011
Manuscript Accepted: September 7, 2011
Published: September 23, 2011

Citation
Dandan Wen, Dong Li, and Jianlin Zhao, "Generalized sensitivity factors for optical-axis perturbation in nonplanar ring resonators," Opt. Express 19, 19752-19757 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-20-19752

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References

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.
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]
A. E. Siegman, “Laser beams and resonators: beyond the 1960s,” IEEE J. Sel. Top. Quantum Electron.6(6), 1389–1399 (2000). [CrossRef]
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]
R. Rodloff, “A laser gyro with optimized resonator geometry,” IEEE J. Quantum Electron.23(4), 438–445 (1987). [CrossRef]
J. Yuan and X. W. Long, “Optical-axis perturbation in nonplanar ring resonators,” Opt. Commun.281(5), 1204–1210 (2008). [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]
I. W. Smith, “Optical resonator axis stability and instability from ﬁrst principles,” Proc. SPIE412, 203–206 (1983).
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]
S.-C. Sheng, “Optical-axis perturbation singularity in an out-of-plane ring resonator,” Opt. Lett.19(10), 683–685 (1994). [CrossRef] [PubMed]
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. SPIE554, 159–163 (1985).
A. E. Siegman, Lasers (University Science, 1986).
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. Express19(7), 6762–6776 (2011). [CrossRef] [PubMed]
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]
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]

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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. SPIE412, 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. SPIE554, 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. Express19(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]

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Generalized sensitivity factors for optical-axis perturbation in nonplanar ring resonators