Abstract

We show that pairs of prisms can have negative group-velocity dispersion in the absence of any negative material dispersion. A prism arrangement is described that limits losses to Brewster-surface reflections, avoids transverse displacement of the temporally dispersed rays, permits continuous adjustment of the dispersion through zero, and yields a transmitted beam collinear with the incident beam.

© 1984 Optical Society of America

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References

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  1. R. L. Fork, C. V. Shank, R. Yen, C. A. Hirlimann, IEEE J. Quantum Electron. QE-19, 500 (1983).
    [CrossRef]
  2. E. B. Treacy, IEEE J. Quantum Electron. QE-5, 454 (1969).
    [CrossRef]
  3. R. L. Fork, B. I. Greene, C. V. Shank, Appl. Phys. Lett. 38, 671 (1981).
    [CrossRef]
  4. J. P. Gordon, R. L. Fork, Opt. Lett. 9, 153 (1984).
    [CrossRef] [PubMed]
  5. O. E. Martinez, R. L. Fork, J. P. Gordon, Opt. Lett. (to be published).
  6. O. E. Martinez, J. P. Gordon, R. L. Fork, J. Opt. Soc. Am. B (to be published).
  7. F. A. Jenkins, H. E. White, Fundamentals of Optics (McGraw-Hill, New York, 1957), p. 21.
  8. D. Marcuse, Appl. Opt. 19, 1653 (1980).
    [CrossRef] [PubMed]
  9. For our idealized example, l sin β need only be of the order of the beam diameter; however, actual systems require that the incident beam also pass at least a beam diameter inside the apex of the first prism. We account for this by taking l sin β as twice the beam diameter.
  10. The use of a prism translation of this type to adjust the amount of positive material dispersion in a laser was previously reported. See, e.g., W. Dietel, J. J. Fontaine, J. C. Diels, Opt. Lett. 8, 4 (1983).
    [CrossRef] [PubMed]

1984 (1)

1983 (2)

1981 (1)

R. L. Fork, B. I. Greene, C. V. Shank, Appl. Phys. Lett. 38, 671 (1981).
[CrossRef]

1980 (1)

1969 (1)

E. B. Treacy, IEEE J. Quantum Electron. QE-5, 454 (1969).
[CrossRef]

Diels, J. C.

Dietel, W.

Fontaine, J. J.

Fork, R. L.

J. P. Gordon, R. L. Fork, Opt. Lett. 9, 153 (1984).
[CrossRef] [PubMed]

R. L. Fork, C. V. Shank, R. Yen, C. A. Hirlimann, IEEE J. Quantum Electron. QE-19, 500 (1983).
[CrossRef]

R. L. Fork, B. I. Greene, C. V. Shank, Appl. Phys. Lett. 38, 671 (1981).
[CrossRef]

O. E. Martinez, J. P. Gordon, R. L. Fork, J. Opt. Soc. Am. B (to be published).

O. E. Martinez, R. L. Fork, J. P. Gordon, Opt. Lett. (to be published).

Gordon, J. P.

J. P. Gordon, R. L. Fork, Opt. Lett. 9, 153 (1984).
[CrossRef] [PubMed]

O. E. Martinez, J. P. Gordon, R. L. Fork, J. Opt. Soc. Am. B (to be published).

O. E. Martinez, R. L. Fork, J. P. Gordon, Opt. Lett. (to be published).

Greene, B. I.

R. L. Fork, B. I. Greene, C. V. Shank, Appl. Phys. Lett. 38, 671 (1981).
[CrossRef]

Hirlimann, C. A.

R. L. Fork, C. V. Shank, R. Yen, C. A. Hirlimann, IEEE J. Quantum Electron. QE-19, 500 (1983).
[CrossRef]

Jenkins, F. A.

F. A. Jenkins, H. E. White, Fundamentals of Optics (McGraw-Hill, New York, 1957), p. 21.

Marcuse, D.

Martinez, O. E.

O. E. Martinez, J. P. Gordon, R. L. Fork, J. Opt. Soc. Am. B (to be published).

O. E. Martinez, R. L. Fork, J. P. Gordon, Opt. Lett. (to be published).

Shank, C. V.

R. L. Fork, C. V. Shank, R. Yen, C. A. Hirlimann, IEEE J. Quantum Electron. QE-19, 500 (1983).
[CrossRef]

R. L. Fork, B. I. Greene, C. V. Shank, Appl. Phys. Lett. 38, 671 (1981).
[CrossRef]

Treacy, E. B.

E. B. Treacy, IEEE J. Quantum Electron. QE-5, 454 (1969).
[CrossRef]

White, H. E.

F. A. Jenkins, H. E. White, Fundamentals of Optics (McGraw-Hill, New York, 1957), p. 21.

Yen, R.

R. L. Fork, C. V. Shank, R. Yen, C. A. Hirlimann, IEEE J. Quantum Electron. QE-19, 500 (1983).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

R. L. Fork, B. I. Greene, C. V. Shank, Appl. Phys. Lett. 38, 671 (1981).
[CrossRef]

IEEE J. Quantum Electron. (2)

R. L. Fork, C. V. Shank, R. Yen, C. A. Hirlimann, IEEE J. Quantum Electron. QE-19, 500 (1983).
[CrossRef]

E. B. Treacy, IEEE J. Quantum Electron. QE-5, 454 (1969).
[CrossRef]

Opt. Lett. (2)

Other (4)

O. E. Martinez, R. L. Fork, J. P. Gordon, Opt. Lett. (to be published).

O. E. Martinez, J. P. Gordon, R. L. Fork, J. Opt. Soc. Am. B (to be published).

F. A. Jenkins, H. E. White, Fundamentals of Optics (McGraw-Hill, New York, 1957), p. 21.

For our idealized example, l sin β need only be of the order of the beam diameter; however, actual systems require that the incident beam also pass at least a beam diameter inside the apex of the first prism. We account for this by taking l sin β as twice the beam diameter.

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Figures (3)

Fig. 1
Fig. 1

Four-prism sequence having negative dispersion. The prisms are used at minimum deviation and oriented so that the rays enter and leave at Brewster’s angle. The arrangement is symmetric about the plane MM′.

Fig. 2
Fig. 2

Construction for calculating the paths CDE, EFG, and BH. (a) Path CDE and path AB are equal because AC and BE are both possible wave fronts. (b) Path CJ is both parallel and equal to AB by construction. It follows that the optical path length of CDE is equal to l cos β.

Fig. 3
Fig. 3

Colliding-pulse laser with adjustable negative dispersion. Each prism can be translated along a line normal to its base, as indicated, for example, for prism II.

Equations (13)

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D = L 1 d T d λ = ( λ c L ) d 2 P d λ 2
P = l cos β .
P = 2 l cos β ,
d P / d β = 2 l sin β ,
d 2 P / d β 2 = 2 l cos β .
d 2 P d λ 2 = [ d 2 n d λ 2 d β d n + ( d n d λ ) 2 d 2 β d n 2 ] d P d β + ( d n d λ ) 2 ( d β d n ) 2 d 2 P d β 2 .
d ϕ 2 / d n = ( cos ϕ 2 ) 1 [ sin ( ϕ 2 ) + cos ( ϕ 2 ) tan ( ϕ 1 ) ] ,
d 2 ϕ 2 d n 2 = tan ϕ 2 ( d ϕ 2 d n ) 2 tan 2 ϕ 1 n ( d ϕ 2 d n ) .
d β / d n = 2 ,
d 2 β / d n 2 = 4 + 2 / n 3 .
d 2 P d λ 2 = 4 l { [ d 2 n d λ 2 + ( 2 n 1 n 3 ) ( d n d λ ) 2 ] sin β 2 ( d n d λ ) 2 cos β } .
d 2 P / d λ 2 = 1 . 0354 l ( 7 . 48 × 10 3 ) ,
d 3 P d λ 3 4 l ( d 3 n d λ 3 sin β 6 d n d λ d 2 n d λ 2 cos β ) .

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