Abstract

An expression is derived for the reversible lengthening of optical pulse durations from the order of 50 fsec to the order of 500 fsec by a four-prism sequence and focusing elements. This temporal lengthening is caused by spatial dispersion of the different frequency components transverse to the direction of propagation at the symmetry plane of the prism sequence. Experimental measurements of the pulse lengthening agree well with calculated values.

© 1990 Optical Society of America

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References

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  1. M. Pessot, P. Maine, G. Mourou, Opt. Commun. 62, 419 (1987).
    [CrossRef]
  2. R. L. Fork, O. E. Martinez, J. P. Gordon, Opt. Lett. 9, 150 (1984).
    [CrossRef] [PubMed]
  3. R. L. Fork, Opt. Lett. 11, 629 (1986).
    [CrossRef] [PubMed]
  4. R. L. Fork, H. Avramopoulos, H. L. Fragnito, P. C. Becker, K. Schehrer, C. Hirlimann, Opt. Lett. 14, 1068 (1989).
    [CrossRef] [PubMed]
  5. R. L. Fork, P. C. Becker, J. Y. Bigot, H. L. Fragnito, C. V. Shank, AT&T Bell Laboratories, Holmdel, N.J. 07733 (personal communication).

1989

1987

M. Pessot, P. Maine, G. Mourou, Opt. Commun. 62, 419 (1987).
[CrossRef]

1986

1984

Avramopoulos, H.

Becker, P. C.

R. L. Fork, H. Avramopoulos, H. L. Fragnito, P. C. Becker, K. Schehrer, C. Hirlimann, Opt. Lett. 14, 1068 (1989).
[CrossRef] [PubMed]

R. L. Fork, P. C. Becker, J. Y. Bigot, H. L. Fragnito, C. V. Shank, AT&T Bell Laboratories, Holmdel, N.J. 07733 (personal communication).

Bigot, J. Y.

R. L. Fork, P. C. Becker, J. Y. Bigot, H. L. Fragnito, C. V. Shank, AT&T Bell Laboratories, Holmdel, N.J. 07733 (personal communication).

Fork, R. L.

Fragnito, H. L.

R. L. Fork, H. Avramopoulos, H. L. Fragnito, P. C. Becker, K. Schehrer, C. Hirlimann, Opt. Lett. 14, 1068 (1989).
[CrossRef] [PubMed]

R. L. Fork, P. C. Becker, J. Y. Bigot, H. L. Fragnito, C. V. Shank, AT&T Bell Laboratories, Holmdel, N.J. 07733 (personal communication).

Gordon, J. P.

Hirlimann, C.

Maine, P.

M. Pessot, P. Maine, G. Mourou, Opt. Commun. 62, 419 (1987).
[CrossRef]

Martinez, O. E.

Mourou, G.

M. Pessot, P. Maine, G. Mourou, Opt. Commun. 62, 419 (1987).
[CrossRef]

Pessot, M.

M. Pessot, P. Maine, G. Mourou, Opt. Commun. 62, 419 (1987).
[CrossRef]

Schehrer, K.

Shank, C. V.

R. L. Fork, P. C. Becker, J. Y. Bigot, H. L. Fragnito, C. V. Shank, AT&T Bell Laboratories, Holmdel, N.J. 07733 (personal communication).

Opt. Commun.

M. Pessot, P. Maine, G. Mourou, Opt. Commun. 62, 419 (1987).
[CrossRef]

Opt. Lett.

Other

R. L. Fork, P. C. Becker, J. Y. Bigot, H. L. Fragnito, C. V. Shank, AT&T Bell Laboratories, Holmdel, N.J. 07733 (personal communication).

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Figures (3)

Fig. 1
Fig. 1

Diagram of the focusing and spatial dispersion of the incident pulse by the spherical mirror M1 and the prism pair. The darker beam indicates the frequency component at the peak of the incident pulse spectrum, which is used as the reference beam in the derivation. The contribution to the group-velocity dispersion from the material of the prism pair must be included in evaluating the net group-velocity dispersion, as discussed in the text.

Fig. 2
Fig. 2

Diagram of the apparatus used to measure the temporal broadening. The beam transmitted through the beam splitter is spatially dispersed by the prism pair and focused by mirror M1. The focal plane of the mirror coincides with plane MM′. A second beam is reflected by the beam splitter and is not spatially dispersed by the prism pair. This reflected beam passes underneath the second prism and is focused by a lens onto the KDP crystal.

Fig. 3
Fig. 3

Profile of the temporally lengthened 50-fsec pulse at plane MM′ for three different positions of the translation stage T2. The points are experimental data for curve (a), 617.5 nm, curve (b), 620.0 nm, curve (c), 622.5 nm. The solid curves are plots of sech2(1.76t/τ) superimposed onto the data, where τ = 467 fsec.

Equations (11)

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E i ( t , r ) = E 0 exp [ b ( ρ 2 w i 2 + t 2 τ i 2 ) + i ( ω 0 t kz ) ] ,
e i ( Ω , r ) = E 0 τ i 2 b exp ( b ρ 2 w i 2 Ω 2 τ i 2 4 b ikz ) ,
Δ = 2 l d n d λ ( λ λ 0 ) cos β .
β = | d β d n d n d λ Δ λ | = 1 . 6 × 10 3 rad ,
Δ = Ω τ c w s 2 b ,
τ c 8 π / cb ω 0 2 w s d n d λ ,
e s ( Ω , r ) = E 0 w i w s τ i 2 b × exp [ b ρ 2 w s 2 Ω 2 ( τ c 2 + τ i 2 4 b ) Ω τ c x w s ikz ] .
E s ( t , r ) = E 0 w i τ i w s τ s exp [ b ( ρ 2 w s 2 x 2 τ c 2 w s 2 τ s 2 + t 2 τ s 2 ) + i ( ω 0 + 2 b x τ c w s τ s 2 ) t ikz ] ,
τ s τ i ( 1 + τ c 2 τ i 2 ) 1 / 2
δω = 2 b x τ c w s τ s 2 .
Φ ( x ) = 4 πδz ( x ) / λ .

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