Reanalysis of generalized sensitivity factors for optical-axis perturbation in nonplanar ring resonators

doi:10.1364/OE.21.002297

Reanalysis of generalized sensitivity factors for optical-axis perturbation in nonplanar ring resonators

Jie Yuan, Meixiong Chen, Yingying Li, Zhongqi Tan, and Zhiguo Wang »View Author Affiliations

Optics Express, Vol. 21, Issue 2, pp. 2297-2306 (2013)
http://dx.doi.org/10.1364/OE.21.002297

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Abstract

By utilizing the novel coordinate system for Gaussian beam reflection and the generalized ray matrix for spherical mirror reflection, the generalized sensitivity factors SD1, ST1, SD2 and ST2 influenced by both the radial and axial displacements of a spherical mirror in a nonplanar ring resonator have been obtained. Besides, the singular points of different kinds of non-planar ring resonators under the conditions of incident angle A ranging from 0° to 45° or total coordinate rotation angle ρ ranging from 0°to 360°have also been obtained through the analysis of the determinant of the coefficient matrix of the linear equations. The analysis in this paper is important to the cavity design of non-planar ring resonators and it could be helpful to avoid the violent movement of the optical-axis to small misalignment of the mirrors in non-planar ring resonators.

OCIS Codes
(070.2590) Fourier optics and signal processing : ABCD transforms
(080.2730) Geometric optics : Matrix methods in paraxial optics
(140.3370) Lasers and laser optics : Laser gyroscopes
(140.3410) Lasers and laser optics : Laser resonators
(140.4780) Lasers and laser optics : Optical resonators

ToC Category:
Lasers and Laser Optics

History
Original Manuscript: May 7, 2012
Manuscript Accepted: January 3, 2013
Published: January 23, 2013

Citation
Jie Yuan, Meixiong Chen, Yingying Li, Zhongqi Tan, and Zhiguo Wang, "Reanalysis of generalized sensitivity factors for optical-axis perturbation in nonplanar ring resonators," Opt. Express 21, 2297-2306 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-2-2297

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References

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]
A. E. Siegman, Lasers (University Science, 1986).
G. A. Massey and A. E. Siegman, “Reflection and refraction of Gaussian light beams at tilted ellipsoidal surfaces,” Appl. Opt.8(5), 975–978 (1969). [CrossRef] [PubMed]
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. 4, Chap. 3, 229–327, (North-Holland, 1985).
S.-C. Sheng, “Optical-axis perturbation singularity in an out-of-plane ring resonator,” Opt. Lett.19(10), 683–685 (1994). [CrossRef] [PubMed]
J. Yuan and X. W. Long, “Optical-axis perturbation in nonplanar ring resonators,” Opt. Commun.281(5), 1204–1210 (2008). [CrossRef]
D. D. Wen, D. Li, and J. L. Zhao, “Generalized sensitivity factors for optical-axis perturbation in nonplanar ring resonators,” Opt. Express19(20), 19752–19757 (2011). [CrossRef] [PubMed]
J. Yuan, M. Chen, Z. Kang, and X. Long, “Novel coordinate system for Gaussian beam reflection,” Opt. Lett.37(11), 2082–2084 (2012). [CrossRef] [PubMed]
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]
J. Yuan, X. Long, L. Liang, B. Zhang, F. Wang, and H. Zhao, “Nonplanar ring resonator modes: generalized Gaussian beams,” Appl. Opt.46(15), 2980–2989 (2007). [CrossRef] [PubMed]
G. J. Martin, “Multioscillator ring laser gyro using compensated optical wedge,” U.S. patent 5,907,402 (25 May 1999).
J. Yuan, X. W. Long, B. Zhang, F. Wang, and H. C. Zhao, “Optical axis perturbation in folded planar ring resonators,” Appl. Opt.46(25), 6314–6322 (2007). [CrossRef] [PubMed]
A. H. Paxton and W. P. Latham., “Unstable resonators with 90 ° beam rotation,” Appl. Opt.25(17), 2939–2946 (1986). [CrossRef] [PubMed]
J. Yuan, X. W. Long, and L. M. Liang, “Optical-axis perturbation in triaxial ring resonator,” Appl. Opt.47(5), 628–631 (2008). [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]
Y. X. Zhao, M. G. Sceats, and A. D. Stokes, “Application of ray tracing to the design of a monolithic nonplanar ring laser,” Appl. Opt.30(36), 5235–5238 (1991). [CrossRef] [PubMed]
H. T. Tuan and S. L. Huang, “Analysis of reentrant two-mirror nonplanar ring laser cavity,” J. Opt. Soc. Am. A22(11), 2476–2482 (2005). [CrossRef] [PubMed]
S. Gangopadhyay and S. Sarkar, “ABCD matrix for reflection and refraction of Gaussian light beams at surfaces of hyperboloid of revolution and efficiency computation for laser diode to single-mode fiber coupling by way of a hyperbolic lens on the fiber tip,” Appl. Opt.36(33), 8582–8586 (1997). [CrossRef] [PubMed]
H. Z. Liu, L. R. Liu, R. W. Xu, and Z. Luan, “ABCD matrix for reflection and refraction of Gaussian beams at the surface of a parabola of revolution,” Appl. Opt.44(23), 4809–4813 (2005). [CrossRef] [PubMed]

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[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(1), 61–104 (1985). [CrossRef]

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

[3] A. E. Siegman, Lasers (University Science, 1986).

[4] G. A. Massey and A. E. Siegman, “Reflection and refraction of Gaussian light beams at tilted ellipsoidal surfaces,” Appl. Opt.8(5), 975–978 (1969). [CrossRef] [PubMed]

[5] 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. 4, Chap. 3, 229–327, (North-Holland, 1985).

[6] S.-C. Sheng, “Optical-axis perturbation singularity in an out-of-plane ring resonator,” Opt. Lett.19(10), 683–685 (1994). [CrossRef] [PubMed]

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

[8] D. D. Wen, D. Li, and J. L. Zhao, “Generalized sensitivity factors for optical-axis perturbation in nonplanar ring resonators,” Opt. Express19(20), 19752–19757 (2011). [CrossRef] [PubMed]

[9] J. Yuan, M. Chen, Z. Kang, and X. Long, “Novel coordinate system for Gaussian beam reflection,” Opt. Lett.37(11), 2082–2084 (2012). [CrossRef] [PubMed]

[10] 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]

[11] J. Yuan, X. Long, L. Liang, B. Zhang, F. Wang, and H. Zhao, “Nonplanar ring resonator modes: generalized Gaussian beams,” Appl. Opt.46(15), 2980–2989 (2007). [CrossRef] [PubMed]

[12] G. J. Martin, “Multioscillator ring laser gyro using compensated optical wedge,” U.S. patent 5,907,402 (25 May 1999).

[13] J. Yuan, X. W. Long, B. Zhang, F. Wang, and H. C. Zhao, “Optical axis perturbation in folded planar ring resonators,” Appl. Opt.46(25), 6314–6322 (2007). [CrossRef] [PubMed]

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

[15] J. Yuan, X. W. Long, and L. M. Liang, “Optical-axis perturbation in triaxial ring resonator,” Appl. Opt.47(5), 628–631 (2008). [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] Y. X. Zhao, M. G. Sceats, and A. D. Stokes, “Application of ray tracing to the design of a monolithic nonplanar ring laser,” Appl. Opt.30(36), 5235–5238 (1991). [CrossRef] [PubMed]

[18] H. T. Tuan and S. L. Huang, “Analysis of reentrant two-mirror nonplanar ring laser cavity,” J. Opt. Soc. Am. A22(11), 2476–2482 (2005). [CrossRef] [PubMed]

[19] S. Gangopadhyay and S. Sarkar, “ABCD matrix for reflection and refraction of Gaussian light beams at surfaces of hyperboloid of revolution and efficiency computation for laser diode to single-mode fiber coupling by way of a hyperbolic lens on the fiber tip,” Appl. Opt.36(33), 8582–8586 (1997). [CrossRef] [PubMed]

[20] H. Z. Liu, L. R. Liu, R. W. Xu, and Z. Luan, “ABCD matrix for reflection and refraction of Gaussian beams at the surface of a parabola of revolution,” Appl. Opt.44(23), 4809–4813 (2005). [CrossRef] [PubMed]

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Reanalysis of generalized sensitivity factors for optical-axis perturbation in nonplanar ring resonators