Abstract

A new class of tapered reflectivity mirrors with a super-Gaussian profile R ∝ exp(−krn) is introduced, and a geometrical-optics approach for analysis and design of unstable resonators made with these mirrors is presented. A super-Gaussian mirror, built by a special evaporation technique, has been tested in an unstable resonator of a pulsed Nd:YAG laser, demonstrating its effectiveness in generating diffraction-limited beams.

© 1988 Optical Society of America

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References

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  1. H. Zucker, Bell Syst. Tech. J. 49, 2349 (1970).
  2. Yu. A. Anan’ev, V. E. Sherstobitov, Sov. J. Quantum Electron. 1, 263 (1971).
    [CrossRef]
  3. Yu. A. Anan’ev, Sov. J. Quantum Electron. 1, 565 (1972).
    [CrossRef]
  4. L. W. Casperson, S. D. Lunnam, Appl. Opt. 14, 1193 (1975).
    [CrossRef] [PubMed]
  5. D. M. Walsh, L. V. Knight, Appl. Opt. 25, 2947 (1986).
    [CrossRef] [PubMed]
  6. J. M. Eggleston, G. Giuliani, R. L. Byer, J. Opt. Soc. Am. 71, 1264 (1981).
    [CrossRef]
  7. E. Armandillo, G. Giuliani, Opt. Lett. 10, 445 (1985).
    [CrossRef] [PubMed]
  8. P. Lavigne, N. McCarty, J. G. Demers, Appl. Opt. 24, 2581 (1985).
    [CrossRef] [PubMed]
  9. S. De Silvestri, P. Laporta, V. Magni, O. Svelto, Opt. Lett. 12, 84 (1987); S. De Silvestri, P. Laporta, V. Magni, J. Opt. Soc. Am. A 4, 1413 (1987).
    [CrossRef] [PubMed]
  10. A. Yariv, P. Yeh, Opt. Commun. 13, 370 (1975).
    [CrossRef]
  11. A. E. Siegman, Lasers (Oxford U. Press, Oxford, 1986), pp. 913–922.
  12. V. E. Sherstobitov, G. N. Vinokurov, Sov. J. Quantum Electron. 2, 224 (1972).
    [CrossRef]
  13. A. E. Siegman, R. Arrathoon, IEEE J. Quantum Electron. QE-3, 156 (1967).
    [CrossRef]
  14. Ref. 11, pp. 738–739.
  15. A. Parent, N. McCarthy, P. Lavigne, IEEE J. Quantum Electron. QE-23, 222 (1987).
    [CrossRef]
  16. W. F. Krupke, W. R. Sooy, IEEE J. Quantum Electron. QE-5, 575 (1969).
    [CrossRef]
  17. N. McCarthy, P. Lavigne, Appl. Opt. 23, 3845 (1984).
    [CrossRef] [PubMed]
  18. N. McCarthy, P. Lavigne, Opt. Lett. 10, 553 (1985).
    [CrossRef] [PubMed]
  19. A. Chester, IEEE J. Quantum Electron. QE-9, 209 (1973).
    [CrossRef]
  20. N. McCarthy, P. Lavigne, Appl. Opt. 22, 2704 (1983).
    [CrossRef] [PubMed]

1987 (2)

1986 (1)

1985 (3)

1984 (1)

1983 (1)

1981 (1)

1975 (2)

1973 (1)

A. Chester, IEEE J. Quantum Electron. QE-9, 209 (1973).
[CrossRef]

1972 (2)

V. E. Sherstobitov, G. N. Vinokurov, Sov. J. Quantum Electron. 2, 224 (1972).
[CrossRef]

Yu. A. Anan’ev, Sov. J. Quantum Electron. 1, 565 (1972).
[CrossRef]

1971 (1)

Yu. A. Anan’ev, V. E. Sherstobitov, Sov. J. Quantum Electron. 1, 263 (1971).
[CrossRef]

1970 (1)

H. Zucker, Bell Syst. Tech. J. 49, 2349 (1970).

1969 (1)

W. F. Krupke, W. R. Sooy, IEEE J. Quantum Electron. QE-5, 575 (1969).
[CrossRef]

1967 (1)

A. E. Siegman, R. Arrathoon, IEEE J. Quantum Electron. QE-3, 156 (1967).
[CrossRef]

Anan’ev, Yu. A.

Yu. A. Anan’ev, Sov. J. Quantum Electron. 1, 565 (1972).
[CrossRef]

Yu. A. Anan’ev, V. E. Sherstobitov, Sov. J. Quantum Electron. 1, 263 (1971).
[CrossRef]

Armandillo, E.

Arrathoon, R.

A. E. Siegman, R. Arrathoon, IEEE J. Quantum Electron. QE-3, 156 (1967).
[CrossRef]

Byer, R. L.

Casperson, L. W.

Chester, A.

A. Chester, IEEE J. Quantum Electron. QE-9, 209 (1973).
[CrossRef]

De Silvestri, S.

Demers, J. G.

Eggleston, J. M.

Giuliani, G.

Knight, L. V.

Krupke, W. F.

W. F. Krupke, W. R. Sooy, IEEE J. Quantum Electron. QE-5, 575 (1969).
[CrossRef]

Laporta, P.

Lavigne, P.

Lunnam, S. D.

Magni, V.

McCarthy, N.

McCarty, N.

Parent, A.

A. Parent, N. McCarthy, P. Lavigne, IEEE J. Quantum Electron. QE-23, 222 (1987).
[CrossRef]

Sherstobitov, V. E.

V. E. Sherstobitov, G. N. Vinokurov, Sov. J. Quantum Electron. 2, 224 (1972).
[CrossRef]

Yu. A. Anan’ev, V. E. Sherstobitov, Sov. J. Quantum Electron. 1, 263 (1971).
[CrossRef]

Siegman, A. E.

A. E. Siegman, R. Arrathoon, IEEE J. Quantum Electron. QE-3, 156 (1967).
[CrossRef]

A. E. Siegman, Lasers (Oxford U. Press, Oxford, 1986), pp. 913–922.

Sooy, W. R.

W. F. Krupke, W. R. Sooy, IEEE J. Quantum Electron. QE-5, 575 (1969).
[CrossRef]

Svelto, O.

Vinokurov, G. N.

V. E. Sherstobitov, G. N. Vinokurov, Sov. J. Quantum Electron. 2, 224 (1972).
[CrossRef]

Walsh, D. M.

Yariv, A.

A. Yariv, P. Yeh, Opt. Commun. 13, 370 (1975).
[CrossRef]

Yeh, P.

A. Yariv, P. Yeh, Opt. Commun. 13, 370 (1975).
[CrossRef]

Zucker, H.

H. Zucker, Bell Syst. Tech. J. 49, 2349 (1970).

Appl. Opt. (5)

Bell Syst. Tech. J. (1)

H. Zucker, Bell Syst. Tech. J. 49, 2349 (1970).

IEEE J. Quantum Electron. (4)

A. Parent, N. McCarthy, P. Lavigne, IEEE J. Quantum Electron. QE-23, 222 (1987).
[CrossRef]

W. F. Krupke, W. R. Sooy, IEEE J. Quantum Electron. QE-5, 575 (1969).
[CrossRef]

A. E. Siegman, R. Arrathoon, IEEE J. Quantum Electron. QE-3, 156 (1967).
[CrossRef]

A. Chester, IEEE J. Quantum Electron. QE-9, 209 (1973).
[CrossRef]

J. Opt. Soc. Am. (1)

Opt. Commun. (1)

A. Yariv, P. Yeh, Opt. Commun. 13, 370 (1975).
[CrossRef]

Opt. Lett. (3)

Sov. J. Quantum Electron. (3)

Yu. A. Anan’ev, V. E. Sherstobitov, Sov. J. Quantum Electron. 1, 263 (1971).
[CrossRef]

Yu. A. Anan’ev, Sov. J. Quantum Electron. 1, 565 (1972).
[CrossRef]

V. E. Sherstobitov, G. N. Vinokurov, Sov. J. Quantum Electron. 2, 224 (1972).
[CrossRef]

Other (2)

A. E. Siegman, Lasers (Oxford U. Press, Oxford, 1986), pp. 913–922.

Ref. 11, pp. 738–739.

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Figures (3)

Fig. 1
Fig. 1

Intensity super-Gaussian reflectivity profiles normalized to the peak reflectivity as a function of the radius normalized to the spot size wm. The parameter n is the order of the curve.

Fig. 2
Fig. 2

Experimental reflectivity profile of a super-Gaussian mirror (open circles) and interpolating curve (solid line) of order n = 2.8, spot size wm = 2.2 mm, and peak reflectivity 0.44.

Fig. 3
Fig. 3

(a) Near-field and (b) far-field intensity profiles of the output beam.

Equations (7)

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R = R 0 exp [ 2 ( r / w m ) n ] ,
σu ( r ) = ( 1 / M ) ρ ( r / M ) u ( r / M ) .
u 0 ( r ) = A exp [ ( r / w i ) n ] ,
w i = w m ( M n 1 ) 1 / n .
w r = w i / M .
γ = 1 ( R 0 / M 2 ) .
M ˆ 2 1 M ˆ 2 λL π w m 2 | g 1 | ,

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