Abstract

The effect of mirror misalignment of spherical resonators is investigated experimentally and compared to first-order perturbation theory. An expression D is derived, which characterizes the misalignment sensitivity of any spherical resonator. It is proved experimentally that this misalignment sensitivity depends on the effective resonator length L* and the gi parameters only.

© 1980 Optical Society of America

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References

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  1. R. B. Chesler, D. Maydam, J. Appl. Phys. 43, 2254 (1972).
    [CrossRef]
  2. R. L. Sanderson, W. Streifer, Appl. Opt. 8, 2241 (1969).
    [CrossRef] [PubMed]
  3. H. Ogura, Y. Yoshida, Y. Furuhama, J. Ikenone, Jpn. J. Appl. Phys. 5, 225 (1966).
    [CrossRef]
  4. C. Santana, L. B. Felsen, Appl. Opt. 17, 2352 (1978).
    [CrossRef] [PubMed]
  5. J. L. Remo, Opt. Lett. 3, 193 (1978).
    [CrossRef] [PubMed]
  6. A. G. Fox, T. Li, Proc. IEEE 51, 80 (1963).
    [CrossRef]
  7. H. Ogura, Y. Yoshida, J. Ikenone, J. Phys. Soc. Jpn. 20, 598 (1965).
    [CrossRef]
  8. J. Kotik, M. C. Newstein, J. Appl. Phys. 32, 178 (1961).
    [CrossRef]
  9. N. K. Berger, N. A. Deryugin, Yu. N. Lukyanov, Yu. E. Studenikin, Opt. Spectrosc. USSR 43, 176 (1977).
  10. M. Kogelnik, T. Li, Proc. IEEE 54, 1312 (1966).
    [CrossRef]
  11. W. Müller, “Optimierung eines TEM00 Nd-Lasers und Bestimmung der Beugungsverluste,” Diploma Thesis, Department of Physics, U. Kaiserslautern (1974).
  12. V. P. Kalinin, V. V. Lyubimov, Opt. Spectrosc. USSR 22, 64 (1964).
  13. I. A. Rom-Kricherskaya, A. M. Ratner, A. V. Mescheryakov, Opt. Spectrosc. USSR 19, 149 (1965).
  14. R. J. Freiberg, A. S. Halsted, Appl. Opt. 8, 355 (1969).
    [CrossRef] [PubMed]
  15. W. Koechner, Solid State Laser Engineering (Springer, New York, 1976), Chap. 5.1.8.
  16. J. Junghans, M. Keller, H. Weber, Appl. Opt. 13, 2793 (1974).
    [CrossRef] [PubMed]
  17. D. Slepian, Bell Syst. Tech. J. 43, 3009 (1964).
  18. H. U. Leuenberger, “Investigation on the Conditions for Generation of Reproducible Emission of Solid State Lasers,” Dissertation, Institute of Applied Physics, U. Berne (February1975).
  19. R. Hauck, H. P. Kortz, H. Weber, Verh. Dtsch. Phys. Ges. 14, 615 (1979).

1979 (1)

R. Hauck, H. P. Kortz, H. Weber, Verh. Dtsch. Phys. Ges. 14, 615 (1979).

1978 (2)

1977 (1)

N. K. Berger, N. A. Deryugin, Yu. N. Lukyanov, Yu. E. Studenikin, Opt. Spectrosc. USSR 43, 176 (1977).

1974 (1)

1972 (1)

R. B. Chesler, D. Maydam, J. Appl. Phys. 43, 2254 (1972).
[CrossRef]

1969 (2)

1966 (2)

H. Ogura, Y. Yoshida, Y. Furuhama, J. Ikenone, Jpn. J. Appl. Phys. 5, 225 (1966).
[CrossRef]

M. Kogelnik, T. Li, Proc. IEEE 54, 1312 (1966).
[CrossRef]

1965 (2)

H. Ogura, Y. Yoshida, J. Ikenone, J. Phys. Soc. Jpn. 20, 598 (1965).
[CrossRef]

I. A. Rom-Kricherskaya, A. M. Ratner, A. V. Mescheryakov, Opt. Spectrosc. USSR 19, 149 (1965).

1964 (2)

D. Slepian, Bell Syst. Tech. J. 43, 3009 (1964).

V. P. Kalinin, V. V. Lyubimov, Opt. Spectrosc. USSR 22, 64 (1964).

1963 (1)

A. G. Fox, T. Li, Proc. IEEE 51, 80 (1963).
[CrossRef]

1961 (1)

J. Kotik, M. C. Newstein, J. Appl. Phys. 32, 178 (1961).
[CrossRef]

Berger, N. K.

N. K. Berger, N. A. Deryugin, Yu. N. Lukyanov, Yu. E. Studenikin, Opt. Spectrosc. USSR 43, 176 (1977).

Chesler, R. B.

R. B. Chesler, D. Maydam, J. Appl. Phys. 43, 2254 (1972).
[CrossRef]

Deryugin, N. A.

N. K. Berger, N. A. Deryugin, Yu. N. Lukyanov, Yu. E. Studenikin, Opt. Spectrosc. USSR 43, 176 (1977).

Felsen, L. B.

Fox, A. G.

A. G. Fox, T. Li, Proc. IEEE 51, 80 (1963).
[CrossRef]

Freiberg, R. J.

Furuhama, Y.

H. Ogura, Y. Yoshida, Y. Furuhama, J. Ikenone, Jpn. J. Appl. Phys. 5, 225 (1966).
[CrossRef]

Halsted, A. S.

Hauck, R.

R. Hauck, H. P. Kortz, H. Weber, Verh. Dtsch. Phys. Ges. 14, 615 (1979).

Ikenone, J.

H. Ogura, Y. Yoshida, Y. Furuhama, J. Ikenone, Jpn. J. Appl. Phys. 5, 225 (1966).
[CrossRef]

H. Ogura, Y. Yoshida, J. Ikenone, J. Phys. Soc. Jpn. 20, 598 (1965).
[CrossRef]

Junghans, J.

Kalinin, V. P.

V. P. Kalinin, V. V. Lyubimov, Opt. Spectrosc. USSR 22, 64 (1964).

Keller, M.

Koechner, W.

W. Koechner, Solid State Laser Engineering (Springer, New York, 1976), Chap. 5.1.8.

Kogelnik, M.

M. Kogelnik, T. Li, Proc. IEEE 54, 1312 (1966).
[CrossRef]

Kortz, H. P.

R. Hauck, H. P. Kortz, H. Weber, Verh. Dtsch. Phys. Ges. 14, 615 (1979).

Kotik, J.

J. Kotik, M. C. Newstein, J. Appl. Phys. 32, 178 (1961).
[CrossRef]

Leuenberger, H. U.

H. U. Leuenberger, “Investigation on the Conditions for Generation of Reproducible Emission of Solid State Lasers,” Dissertation, Institute of Applied Physics, U. Berne (February1975).

Li, T.

M. Kogelnik, T. Li, Proc. IEEE 54, 1312 (1966).
[CrossRef]

A. G. Fox, T. Li, Proc. IEEE 51, 80 (1963).
[CrossRef]

Lukyanov, Yu. N.

N. K. Berger, N. A. Deryugin, Yu. N. Lukyanov, Yu. E. Studenikin, Opt. Spectrosc. USSR 43, 176 (1977).

Lyubimov, V. V.

V. P. Kalinin, V. V. Lyubimov, Opt. Spectrosc. USSR 22, 64 (1964).

Maydam, D.

R. B. Chesler, D. Maydam, J. Appl. Phys. 43, 2254 (1972).
[CrossRef]

Mescheryakov, A. V.

I. A. Rom-Kricherskaya, A. M. Ratner, A. V. Mescheryakov, Opt. Spectrosc. USSR 19, 149 (1965).

Müller, W.

W. Müller, “Optimierung eines TEM00 Nd-Lasers und Bestimmung der Beugungsverluste,” Diploma Thesis, Department of Physics, U. Kaiserslautern (1974).

Newstein, M. C.

J. Kotik, M. C. Newstein, J. Appl. Phys. 32, 178 (1961).
[CrossRef]

Ogura, H.

H. Ogura, Y. Yoshida, Y. Furuhama, J. Ikenone, Jpn. J. Appl. Phys. 5, 225 (1966).
[CrossRef]

H. Ogura, Y. Yoshida, J. Ikenone, J. Phys. Soc. Jpn. 20, 598 (1965).
[CrossRef]

Ratner, A. M.

I. A. Rom-Kricherskaya, A. M. Ratner, A. V. Mescheryakov, Opt. Spectrosc. USSR 19, 149 (1965).

Remo, J. L.

Rom-Kricherskaya, I. A.

I. A. Rom-Kricherskaya, A. M. Ratner, A. V. Mescheryakov, Opt. Spectrosc. USSR 19, 149 (1965).

Sanderson, R. L.

Santana, C.

Slepian, D.

D. Slepian, Bell Syst. Tech. J. 43, 3009 (1964).

Streifer, W.

Studenikin, Yu. E.

N. K. Berger, N. A. Deryugin, Yu. N. Lukyanov, Yu. E. Studenikin, Opt. Spectrosc. USSR 43, 176 (1977).

Weber, H.

R. Hauck, H. P. Kortz, H. Weber, Verh. Dtsch. Phys. Ges. 14, 615 (1979).

J. Junghans, M. Keller, H. Weber, Appl. Opt. 13, 2793 (1974).
[CrossRef] [PubMed]

Yoshida, Y.

H. Ogura, Y. Yoshida, Y. Furuhama, J. Ikenone, Jpn. J. Appl. Phys. 5, 225 (1966).
[CrossRef]

H. Ogura, Y. Yoshida, J. Ikenone, J. Phys. Soc. Jpn. 20, 598 (1965).
[CrossRef]

Appl. Opt. (4)

Bell Syst. Tech. J. (1)

D. Slepian, Bell Syst. Tech. J. 43, 3009 (1964).

J. Appl. Phys. (2)

R. B. Chesler, D. Maydam, J. Appl. Phys. 43, 2254 (1972).
[CrossRef]

J. Kotik, M. C. Newstein, J. Appl. Phys. 32, 178 (1961).
[CrossRef]

J. Phys. Soc. Jpn. (1)

H. Ogura, Y. Yoshida, J. Ikenone, J. Phys. Soc. Jpn. 20, 598 (1965).
[CrossRef]

Jpn. J. Appl. Phys. (1)

H. Ogura, Y. Yoshida, Y. Furuhama, J. Ikenone, Jpn. J. Appl. Phys. 5, 225 (1966).
[CrossRef]

Opt. Lett. (1)

Opt. Spectrosc. USSR (3)

N. K. Berger, N. A. Deryugin, Yu. N. Lukyanov, Yu. E. Studenikin, Opt. Spectrosc. USSR 43, 176 (1977).

V. P. Kalinin, V. V. Lyubimov, Opt. Spectrosc. USSR 22, 64 (1964).

I. A. Rom-Kricherskaya, A. M. Ratner, A. V. Mescheryakov, Opt. Spectrosc. USSR 19, 149 (1965).

Proc. IEEE (2)

M. Kogelnik, T. Li, Proc. IEEE 54, 1312 (1966).
[CrossRef]

A. G. Fox, T. Li, Proc. IEEE 51, 80 (1963).
[CrossRef]

Verh. Dtsch. Phys. Ges. (1)

R. Hauck, H. P. Kortz, H. Weber, Verh. Dtsch. Phys. Ges. 14, 615 (1979).

Other (3)

W. Müller, “Optimierung eines TEM00 Nd-Lasers und Bestimmung der Beugungsverluste,” Diploma Thesis, Department of Physics, U. Kaiserslautern (1974).

H. U. Leuenberger, “Investigation on the Conditions for Generation of Reproducible Emission of Solid State Lasers,” Dissertation, Institute of Applied Physics, U. Berne (February1975).

W. Koechner, Solid State Laser Engineering (Springer, New York, 1976), Chap. 5.1.8.

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Figures (4)

Fig. 1
Fig. 1

Misaligned spherical resonator. A tilt of mirror S2 by α2 shifts the resonator axis by Θ2 and results in displacement Δ12 and Δ22 of the intensity patterns on both mirrors.

Fig. 2
Fig. 2

Lines of constant misalignment sensitivity D/D0 in the g1,g2 diagram. D0 = (2πL*/λ)1/2.

Fig. 3
Fig. 3

Total loss factor V2 vs tilt angle α2: (L* = 125.8 cm, g1 = 1.32, g2 = 0.75).

Fig. 4
Fig. 4

Experimental values of angle α0i vs misalignment sensitivity Di: ○,×, and + represent the work of Freiberg and Halsted14; ao-19-4-598-i001 represents this work.

Equations (19)

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V i = V 0 [ 1 - ( α i / α 0 i ) 2 ] ,
W i 2 = λ L * π ( g j g i ( 1 - g 1 g 2 ) ) 1 / 2 .
Θ i = α i 1 - g i 1 - g 1 g 2 ,
Δ i i = α i g j L * / ( 1 - g 1 g 2 ) ,
Δ i j = α j L * / ( 1 - g 1 g 2 )             i j .
V = 1 - [ 1 + 2 ( Δ / w ) 2 ( a / w ) 2 ] · exp [ - 2 ( a / w ) 2 ] ,
V i = ( V i i · V j i ) 1 / 2             i j ,
V j i = 1 - [ 1 + 2 ( Δ j i w j ) 2 ( a j w j ) 2 ] · exp [ - 2 ( a j w j ) 2 ] .
V i V 0 - { [ ( Δ j i w j ) ( a j w j ) ] 2 · exp [ - 2 ( a j w j ) 2 ] + [ ( Δ i i w i ) ( a i w i ) ] 2 · exp [ - 2 ( a i w i ) 2 ] } .
V 0 = 1 - 1 2 { exp [ - 2 ( a i w i ) 2 ] + exp [ - 2 ( a j w j ) 2 ] } .
a i = S w i ,             S = 1.2.
V i = V 0 ( 1 - α i 2 S 2 exp 2 S 2 - 1 D i 2 )
V 0 = 1 - exp ( - 2 S 2 ) ] , D i 2 = π L * λ ( g j g i ) 1 / 2 1 + g 1 g 2 ( 1 - g 1 g 2 ) 3 / 2 .
α 0 i = [ exp ( 2 S 2 ) - 1 ] 1 / 2 S D i .
D = [ ( π L * λ ) 1 + g 1 g 2 ( 1 - g 1 g 2 ) 3 / 2 g 1 + g 2 ( g 1 g 2 ) 1 / 2 ] 1 / 2 ,
D 0 = ( 2 π L * λ ) 1 / 2 .
V 0 = 1 - exp ( - 2 π F )
V 0 = ( 1 - 16 π 2 ) F exp ( - 4 π F ) , F = a 2 / λ L * .
α min = 2 × 10 - 5 rad = 4 sec

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