Abstract

I use a matrix approach to determine the optical-axis perturbation sensitivity of an out-of-plane stable ring resonator. It is found to have a singularity for certain design parameters. On one side of the singularity the cavity behaves abnormally: the longer the mirror radius, the larger the mode volume and, surprisingly, the less the perturbation sensitivity. This is opposite the behavior of conventional stable resonators, a finding that is important to the cavity designs of out-of-plane ring lasers.

© 1994 Optical Society of America

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References

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  1. A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), Chap. 15.
  2. A. H. Paxton, W. P. Latham, Appl. Opt. 25, 2939 (1986).
    [CrossRef] [PubMed]
  3. G. B. Al’tshuler, E. D. Isyanova, V. B. Karasev, A. L. Levit, V. M. Ovchinnikov, S. F. Sharlai, Sov. J. Quantum Electron. 7, 857 (1977).
    [CrossRef]
  4. E. F. Ischenko, E. F. Reshetin, J. Appl. Spectrosc. (USSR) 30, 304 (1979).
    [CrossRef]
  5. E. D. Isyanova, A. L. Levit, V. M. Ovehinnikov, J. Appl. Spectrosc. (USSR) 36, 287 (1982).
    [CrossRef]
  6. A. L. Levit, V. M. Ovchinnikov, J. Appl. Spectrosc. (USSR) 40, 657 (1984).
    [CrossRef]
  7. A. L. Levit, V. M. Ovchinnikov, Sov. J. Opt. Technol. 50, 423 (1984).
  8. M. L. Stitch, M. Bass, Laser Handbook (North-Holland, Amsterdam, 1985), Vol. 4, Chap. 3.
  9. T. J. Kane, R. L. Byer, Opt. Lett. 10, 65 (1985).
    [CrossRef] [PubMed]
  10. A. C. Nilsson, E. K. Gustafson, R. L. Byer, IEEE J. Quantum Electron. 25, 767 (1989).
    [CrossRef]

1989 (1)

A. C. Nilsson, E. K. Gustafson, R. L. Byer, IEEE J. Quantum Electron. 25, 767 (1989).
[CrossRef]

1986 (1)

1985 (1)

1984 (2)

A. L. Levit, V. M. Ovchinnikov, J. Appl. Spectrosc. (USSR) 40, 657 (1984).
[CrossRef]

A. L. Levit, V. M. Ovchinnikov, Sov. J. Opt. Technol. 50, 423 (1984).

1982 (1)

E. D. Isyanova, A. L. Levit, V. M. Ovehinnikov, J. Appl. Spectrosc. (USSR) 36, 287 (1982).
[CrossRef]

1979 (1)

E. F. Ischenko, E. F. Reshetin, J. Appl. Spectrosc. (USSR) 30, 304 (1979).
[CrossRef]

1977 (1)

G. B. Al’tshuler, E. D. Isyanova, V. B. Karasev, A. L. Levit, V. M. Ovchinnikov, S. F. Sharlai, Sov. J. Quantum Electron. 7, 857 (1977).
[CrossRef]

Al’tshuler, G. B.

G. B. Al’tshuler, E. D. Isyanova, V. B. Karasev, A. L. Levit, V. M. Ovchinnikov, S. F. Sharlai, Sov. J. Quantum Electron. 7, 857 (1977).
[CrossRef]

Bass, M.

M. L. Stitch, M. Bass, Laser Handbook (North-Holland, Amsterdam, 1985), Vol. 4, Chap. 3.

Byer, R. L.

A. C. Nilsson, E. K. Gustafson, R. L. Byer, IEEE J. Quantum Electron. 25, 767 (1989).
[CrossRef]

T. J. Kane, R. L. Byer, Opt. Lett. 10, 65 (1985).
[CrossRef] [PubMed]

Gustafson, E. K.

A. C. Nilsson, E. K. Gustafson, R. L. Byer, IEEE J. Quantum Electron. 25, 767 (1989).
[CrossRef]

Ischenko, E. F.

E. F. Ischenko, E. F. Reshetin, J. Appl. Spectrosc. (USSR) 30, 304 (1979).
[CrossRef]

Isyanova, E. D.

E. D. Isyanova, A. L. Levit, V. M. Ovehinnikov, J. Appl. Spectrosc. (USSR) 36, 287 (1982).
[CrossRef]

G. B. Al’tshuler, E. D. Isyanova, V. B. Karasev, A. L. Levit, V. M. Ovchinnikov, S. F. Sharlai, Sov. J. Quantum Electron. 7, 857 (1977).
[CrossRef]

Kane, T. J.

Karasev, V. B.

G. B. Al’tshuler, E. D. Isyanova, V. B. Karasev, A. L. Levit, V. M. Ovchinnikov, S. F. Sharlai, Sov. J. Quantum Electron. 7, 857 (1977).
[CrossRef]

Latham, W. P.

Levit, A. L.

A. L. Levit, V. M. Ovchinnikov, J. Appl. Spectrosc. (USSR) 40, 657 (1984).
[CrossRef]

A. L. Levit, V. M. Ovchinnikov, Sov. J. Opt. Technol. 50, 423 (1984).

E. D. Isyanova, A. L. Levit, V. M. Ovehinnikov, J. Appl. Spectrosc. (USSR) 36, 287 (1982).
[CrossRef]

G. B. Al’tshuler, E. D. Isyanova, V. B. Karasev, A. L. Levit, V. M. Ovchinnikov, S. F. Sharlai, Sov. J. Quantum Electron. 7, 857 (1977).
[CrossRef]

Nilsson, A. C.

A. C. Nilsson, E. K. Gustafson, R. L. Byer, IEEE J. Quantum Electron. 25, 767 (1989).
[CrossRef]

Ovchinnikov, V. M.

A. L. Levit, V. M. Ovchinnikov, Sov. J. Opt. Technol. 50, 423 (1984).

A. L. Levit, V. M. Ovchinnikov, J. Appl. Spectrosc. (USSR) 40, 657 (1984).
[CrossRef]

G. B. Al’tshuler, E. D. Isyanova, V. B. Karasev, A. L. Levit, V. M. Ovchinnikov, S. F. Sharlai, Sov. J. Quantum Electron. 7, 857 (1977).
[CrossRef]

Ovehinnikov, V. M.

E. D. Isyanova, A. L. Levit, V. M. Ovehinnikov, J. Appl. Spectrosc. (USSR) 36, 287 (1982).
[CrossRef]

Paxton, A. H.

Reshetin, E. F.

E. F. Ischenko, E. F. Reshetin, J. Appl. Spectrosc. (USSR) 30, 304 (1979).
[CrossRef]

Sharlai, S. F.

G. B. Al’tshuler, E. D. Isyanova, V. B. Karasev, A. L. Levit, V. M. Ovchinnikov, S. F. Sharlai, Sov. J. Quantum Electron. 7, 857 (1977).
[CrossRef]

Siegman, A. E.

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

Stitch, M. L.

M. L. Stitch, M. Bass, Laser Handbook (North-Holland, Amsterdam, 1985), Vol. 4, Chap. 3.

Appl. Opt. (1)

IEEE J. Quantum Electron. (1)

A. C. Nilsson, E. K. Gustafson, R. L. Byer, IEEE J. Quantum Electron. 25, 767 (1989).
[CrossRef]

J. Appl. Spectrosc. (3)

E. F. Ischenko, E. F. Reshetin, J. Appl. Spectrosc. (USSR) 30, 304 (1979).
[CrossRef]

E. D. Isyanova, A. L. Levit, V. M. Ovehinnikov, J. Appl. Spectrosc. (USSR) 36, 287 (1982).
[CrossRef]

A. L. Levit, V. M. Ovchinnikov, J. Appl. Spectrosc. (USSR) 40, 657 (1984).
[CrossRef]

Opt. Lett. (1)

Sov. J. Opt. Technol. (1)

A. L. Levit, V. M. Ovchinnikov, Sov. J. Opt. Technol. 50, 423 (1984).

Sov. J. Quantum Electron. (1)

G. B. Al’tshuler, E. D. Isyanova, V. B. Karasev, A. L. Levit, V. M. Ovchinnikov, S. F. Sharlai, Sov. J. Quantum Electron. 7, 857 (1977).
[CrossRef]

Other (2)

M. L. Stitch, M. Bass, Laser Handbook (North-Holland, Amsterdam, 1985), Vol. 4, Chap. 3.

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

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Figures (6)

Fig. 1
Fig. 1

One single segment of a general resonator.

Fig. 2
Fig. 2

Four-equal-sided out-of-plane ring cavity used in the analysis, where the fold angle is β = 104° and all the incidence angles are equal, θ12 = θ23 = θ34 = θ41 = 31.62°

Fig. 3
Fig. 3

Optical-axis perturbation sensitivity S versus L/R for misalignment of mirror P2 in its sagittal plane.

Fig. 4
Fig. 4

Normalized Gaussian beam size parameter 4L/kw2 versus L/R; w is the Gaussian beam radius and k = 2π/λ.

Fig. 5
Fig. 5

Planar ring cavity optical-axis perturbation sensitivity versus L/R for misalignment of mirror P2 in its sagittal plane.

Fig. 6
Fig. 6

Planar cavity spot size parameter versus L/R.

Equations (6)

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[ r 0 r 0 1 ] = [ A B 0 C D § 0 0 1 ] [ r i r i 1 ] ,
M i = [ - cos θ i - L i cos θ i 0 sin θ i L i sin θ i 0 2 cos θ i R i cos i 2 L i cos θ i R i cos i - cos θ i - d x i cos θ i - 2 sin θ i cos i R i - 2 L i sin θ i cos i R i + sin θ i d y i sin θ i 0 0 1 0 0 0 sin θ i L i sin θ i 0 cos θ i L i cos θ i 0 - 2 sin θ i R i cos i - 2 L i sin θ i R i cos i + sin θ i d x i sin θ i - 2 cos θ i cos i R i - 2 L i cos θ i cos i R i + cos θ i d y i cos θ i 0 0 0 0 0 1 ] ,
M = M i .
[ r x r x 1 r y r y 1 ] = M [ r x r x 1 r y r y 1 ] .
[ M 11 - 1 M 12 M 14 M 15 M 21 M 22 - 1 M 24 M 25 M 41 M 42 M 44 - 1 M 45 M 51 M 52 M 54 M 55 - 1 ] × [ r x r x r y r y ] = - [ M 13 + M 16 M 23 + M 26 M 43 + M 46 M 53 + M 56 ] .
S ( x y ) i ( x y ) j = 1 L [ r ( x y ) i Δ ( x y ) j ] ,

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