Abstract

An analytical method of matching the mode of an input laser to the lowest-order mode of a passive resonant ring laser gyro is described, as are the steps in determining the location and focal length of cylindrical mode matching lenses. Results were obtained with no mode matching, with a compromise spherical lens, with horizontal mode matching only, and with the proper cylindrical mode matching lenses. Compared with no mode matching, the latter case shows that the amplitude of the lowest-order mode is increased ∼2.5 times. In addition, the number and intensity of higher-order modes are reduced to near zero, and the relative intensity of the lowest-order mode to the higher-order mode increased from ∼5 to ∼60 times greater.

© 1983 Optical Society of America

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References

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  1. T. T. Saito, J. Gossner, “Mode Sensitivity and Matching for a Passive Ring Resonant Gyroscope with Equal Curvature Mirrors,” in Proceedings, 19th Science and Engineering Symposium, 27–29 Oct. 1981, co-sponsored by Air Force Systems Command Naval Material Command.
  2. J. D. Keating, G. L. Shaw, “Programs to Locate and Describe the Mode Matching Lenses for the PRRLG,” Aug.1982, Frank J. Seiler Research Laboratory Technical Memorandum FJSRLTM-82-0011.
  3. D. Presonas, Roto-Lok Corp.; private communication (1982).
  4. A. E. Siegman, An Introduction to Lasers and Masers (McGraw-Hill, New York, 1971), Chap. 8.
  5. W. W. Rigrod, Bell Sys. Tech. J. 44, 907 (1965).

1965

W. W. Rigrod, Bell Sys. Tech. J. 44, 907 (1965).

Gossner, J.

T. T. Saito, J. Gossner, “Mode Sensitivity and Matching for a Passive Ring Resonant Gyroscope with Equal Curvature Mirrors,” in Proceedings, 19th Science and Engineering Symposium, 27–29 Oct. 1981, co-sponsored by Air Force Systems Command Naval Material Command.

Keating, J. D.

J. D. Keating, G. L. Shaw, “Programs to Locate and Describe the Mode Matching Lenses for the PRRLG,” Aug.1982, Frank J. Seiler Research Laboratory Technical Memorandum FJSRLTM-82-0011.

Presonas, D.

D. Presonas, Roto-Lok Corp.; private communication (1982).

Rigrod, W. W.

W. W. Rigrod, Bell Sys. Tech. J. 44, 907 (1965).

Saito, T. T.

T. T. Saito, J. Gossner, “Mode Sensitivity and Matching for a Passive Ring Resonant Gyroscope with Equal Curvature Mirrors,” in Proceedings, 19th Science and Engineering Symposium, 27–29 Oct. 1981, co-sponsored by Air Force Systems Command Naval Material Command.

Shaw, G. L.

J. D. Keating, G. L. Shaw, “Programs to Locate and Describe the Mode Matching Lenses for the PRRLG,” Aug.1982, Frank J. Seiler Research Laboratory Technical Memorandum FJSRLTM-82-0011.

Siegman, A. E.

A. E. Siegman, An Introduction to Lasers and Masers (McGraw-Hill, New York, 1971), Chap. 8.

Bell Sys. Tech. J.

W. W. Rigrod, Bell Sys. Tech. J. 44, 907 (1965).

Other

T. T. Saito, J. Gossner, “Mode Sensitivity and Matching for a Passive Ring Resonant Gyroscope with Equal Curvature Mirrors,” in Proceedings, 19th Science and Engineering Symposium, 27–29 Oct. 1981, co-sponsored by Air Force Systems Command Naval Material Command.

J. D. Keating, G. L. Shaw, “Programs to Locate and Describe the Mode Matching Lenses for the PRRLG,” Aug.1982, Frank J. Seiler Research Laboratory Technical Memorandum FJSRLTM-82-0011.

D. Presonas, Roto-Lok Corp.; private communication (1982).

A. E. Siegman, An Introduction to Lasers and Masers (McGraw-Hill, New York, 1971), Chap. 8.

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Figures (9)

Fig. 1
Fig. 1

Diagram of the passive resonate ring laser gyro.

Fig. 2
Fig. 2

Resonator description.

Fig. 3
Fig. 3

Locating equal spot sizes.

Fig. 4
Fig. 4

Data for horizontal mode matching.

Fig. 5
Fig. 5

Data for vertical mode matching.

Fig. 6
Fig. 6

Resonator scan with no mode matching lens.

Fig. 7
Fig. 7

Resonator scan with f = 100-cm spherical mode matching lens.

Fig. 8
Fig. 8

Resonator scan with horizontal mode matching lens only.

Fig. 9
Fig. 9

Resonator scan with mode matching in both planes.

Equations (7)

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W 2 = W 0 2 + ( λ π W 0 ) 2 Z 2 .
( W O L 2 W O R 2 ) Z 2 2 X W O L 2 Z + ( X 2 W O L 2 ) + ( π λ ) 2 ( W O L W O R ) 2 ( W O R 2 W O L 2 ) = 0 .
1 f = 1 q 1 1 q 2 .
1 q n = 1 R n = j λ π W n 2 ,
R n = Z n [ 1 + ( π W 0 n 2 λ Z n ) 2 ]
1 f = 1 q 1 1 q 2 = 1 R 1 j λ π W 1 2 1 R 2 j λ π W 2 2 .
1 f = 1 R 1 1 R 2 or f = R 1 R 2 R 2 R 1 .

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