Abstract

New optical combinations of axicons and axicons with spherical mirrors and lenses suitable for laser machining are presented. Linear and annular focusing, coaxially and radially to the laser beam, are possible. Most combinations allow continuous adjustment of exit beam parameters, focal line length, focal ring diameter, and magnification, by varying the relative position of one of the axicons. Potential new laser applications are also discussed in relation to these optical devices.

© 1978 Optical Society of America

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References

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  1. J. H. McLeod, J. Opt. Soc. Am. 44, 592 (1954).
    [CrossRef]
  2. J. H. McLeod, J. Opt. Soc. Am. 50, 166 (1960).
    [CrossRef]
  3. G. S. Bahen, J. A. Jordan, Nucl. Instrum. Methods 90, 181 (1970).
    [CrossRef]
  4. G. S. Baken, Appl. Opt. 13, 1291 (1974).
    [CrossRef]
  5. W. R. Edmunds, Appl. Opt. 12, 1940 (1973).
    [CrossRef]
  6. C. Mclntyre et al., Proc. IEEE 58, 1491 (1970).
    [CrossRef]
  7. S. Fujuiwara, J. Opt. Soc. Am. 52, 287 (1962).
    [CrossRef]
  8. J. W. Y. Lit, E. Brannen, J. Opt. Soc. Am. 60, 370 (1970).
    [CrossRef]
  9. J. W. Y. Lit, J. Opt. Soc. Am. 60, 1001 (1970).
    [CrossRef]
  10. J. W. Y. Lit, R. Tremblay, J. Opt. Soc. Am. 63, 445 (1973).
    [CrossRef]
  11. J. L. Rayces, J. Opt. Soc. Am. 48, 576 (1958).
    [CrossRef]
  12. W. R. Edmunds, Appl. Opt. 13, 1762 (1974).
    [CrossRef]
  13. P. A. Bélanger, M. Rioux, Can. J. Phys. 54, 1774 (1976).
    [CrossRef]
  14. P. A. Bélanger, M. Rioux, Appl. Opt. 17, 000 (1978).
    [CrossRef]
  15. M. Abramowitz, I. Stegun, Handbook of Mathematical Functions (Dover, New York, 1965).
  16. L. W. Casperson, M. S. Shekhani, Appl. Opt. 13, 104 (1974).
    [CrossRef] [PubMed]
  17. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975), p. 416.
  18. R. B. Barber, “Laser Optical Apparatus for Cutting Holes,” U.S. Patent3,419,321 (December1968).

1978 (1)

P. A. Bélanger, M. Rioux, Appl. Opt. 17, 000 (1978).
[CrossRef]

1976 (1)

P. A. Bélanger, M. Rioux, Can. J. Phys. 54, 1774 (1976).
[CrossRef]

1974 (3)

1973 (2)

1970 (4)

G. S. Bahen, J. A. Jordan, Nucl. Instrum. Methods 90, 181 (1970).
[CrossRef]

C. Mclntyre et al., Proc. IEEE 58, 1491 (1970).
[CrossRef]

J. W. Y. Lit, E. Brannen, J. Opt. Soc. Am. 60, 370 (1970).
[CrossRef]

J. W. Y. Lit, J. Opt. Soc. Am. 60, 1001 (1970).
[CrossRef]

1962 (1)

1960 (1)

1958 (1)

1954 (1)

Abramowitz, M.

M. Abramowitz, I. Stegun, Handbook of Mathematical Functions (Dover, New York, 1965).

Bahen, G. S.

G. S. Bahen, J. A. Jordan, Nucl. Instrum. Methods 90, 181 (1970).
[CrossRef]

Baken, G. S.

Barber, R. B.

R. B. Barber, “Laser Optical Apparatus for Cutting Holes,” U.S. Patent3,419,321 (December1968).

Bélanger, P. A.

P. A. Bélanger, M. Rioux, Appl. Opt. 17, 000 (1978).
[CrossRef]

P. A. Bélanger, M. Rioux, Can. J. Phys. 54, 1774 (1976).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975), p. 416.

Brannen, E.

Casperson, L. W.

Edmunds, W. R.

Fujuiwara, S.

Jordan, J. A.

G. S. Bahen, J. A. Jordan, Nucl. Instrum. Methods 90, 181 (1970).
[CrossRef]

Lit, J. W. Y.

McLeod, J. H.

Mclntyre, C.

C. Mclntyre et al., Proc. IEEE 58, 1491 (1970).
[CrossRef]

Rayces, J. L.

Rioux, M.

P. A. Bélanger, M. Rioux, Appl. Opt. 17, 000 (1978).
[CrossRef]

P. A. Bélanger, M. Rioux, Can. J. Phys. 54, 1774 (1976).
[CrossRef]

Shekhani, M. S.

Stegun, I.

M. Abramowitz, I. Stegun, Handbook of Mathematical Functions (Dover, New York, 1965).

Tremblay, R.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975), p. 416.

Appl. Opt. (5)

Can. J. Phys. (1)

P. A. Bélanger, M. Rioux, Can. J. Phys. 54, 1774 (1976).
[CrossRef]

J. Opt. Soc. Am. (7)

Nucl. Instrum. Methods (1)

G. S. Bahen, J. A. Jordan, Nucl. Instrum. Methods 90, 181 (1970).
[CrossRef]

Proc. IEEE (1)

C. Mclntyre et al., Proc. IEEE 58, 1491 (1970).
[CrossRef]

Other (3)

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975), p. 416.

R. B. Barber, “Laser Optical Apparatus for Cutting Holes,” U.S. Patent3,419,321 (December1968).

M. Abramowitz, I. Stegun, Handbook of Mathematical Functions (Dover, New York, 1965).

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Figures (10)

Fig. 1
Fig. 1

Transmitting axicon; L = a/[(n − 1)α].

Fig. 2
Fig. 2

Reflective axicon; L = a/(tan2α).

Fig. 3
Fig. 3

Section of an axicon for line focusing.

Fig. 4
Fig. 4

Ring formation produced by a combination of a lens and a converging or diverging axicon.

Fig. 5
Fig. 5

Changing ring diameters by combinations of a lens and two axicons. dmax depends on the diameter of the right side axicon used.

Fig. 6
Fig. 6

A 10.6-μm laser beam incident from right is focused by the axicon combination of Fig. 5. (a) The interaction of a single laser pulse on a carbon target, (b) A multiple exposure shows various ring diameters occurring when various axicon distances are used.

Fig. 7
Fig. 7

Holes of various diameters punched out by an axicon-based optical device.

Fig. 8
Fig. 8

Radial focusing using a conical reflector.

Fig. 9
Fig. 9

Infrared laser light from a TEA CO2 laser is radially focused on a ceramic rod, located on the optical axis.

Fig. 10
Fig. 10

The axicon beam expander.

Equations (10)

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L a / [ ( n 1 ) α ] , for α < 10 ° ,
L a / tan 2 α .
R 0 ( n 1 ) α F ,
Δ = 1.22 ( F λ ) / a ] .
I M = 0.14 a E λ F R 0 ,
Δ = 1.05 ( F λ ) / W ] .
I M = 0.24 W E λ F R 0 ,
R 0 d α ( n 1 ) 1 α , α < 10 ° ,
R 0 = d 1 d 0 .
M 1 + 2 d α a ( n 1 1 α ) , α < 10 ° ,

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