Abstract

We measured the tilting of a femtosecond laser wave packet in a birefringent rutile crystal. The measurements were carried out with a linear interferometric technique that, in contrast to nonlinear correlation techniques, allows measurement at very low power. A 23-fs delay between the left and the right parts of a 30-fs, 800-nm wave packet with 20° divergence was measured for a 1-mm-thick rutile crystal, in agreement with theoretical predictions.

© 1997 Optical Society of America

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References

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  1. M. Trippenbach and Y. B. Band, Phys. Rev. Lett. 76, 1457–1460 (1996); Y. B. Band and M. Trippenbach, J. Opt. Soc. Am. B 13, 1403–1411 (1996).
    [CrossRef]
  2. M. J. Weber, Handbook of Laser Science and Technology (CRC, New York, 1986), Vol. 4, p. 233.
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    [CrossRef]
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    [CrossRef] [PubMed]
  5. Z. Bor, K. Osway, B. Racz, and B. Szabo, Opt. Commun. 78, 109–112 (1990).
    [CrossRef]
  6. C. Radzewicz, G. W. Pearson, and J. S. Krasinski, Opt. Commun. 102, 464–468 (1993).
    [CrossRef]
  7. Z. Bor, Opt. Commun. 14, 119 (1989); Z. L. Horvath and Z. Bor, Opt. Commun. 108, 333 (1994).
    [CrossRef]
  8. R. L. Fork, O. E. Martinez, and J. P. Gordon, Opt. Lett. 9, 150 (1984).
    [CrossRef] [PubMed]

1993

C. Radzewicz, G. W. Pearson, and J. S. Krasinski, Opt. Commun. 102, 464–468 (1993).
[CrossRef]

1990

Z. Bor, K. Osway, B. Racz, and B. Szabo, Opt. Commun. 78, 109–112 (1990).
[CrossRef]

1989

1988

1984

Bor, Z.

Z. Bor, K. Osway, B. Racz, and B. Szabo, Opt. Commun. 78, 109–112 (1990).
[CrossRef]

Z. Bor, Z. Gogolak, and G. Szabo, Opt. Lett. 14, 862–864 (1989).
[CrossRef] [PubMed]

Fork, R. L.

Gogolak, Z.

Gordon, J. P.

Hirlimann, C. A.

Knox, W. H.

Krasinski, J. S.

C. Radzewicz, G. W. Pearson, and J. S. Krasinski, Opt. Commun. 102, 464–468 (1993).
[CrossRef]

Li, K. D.

Martinez, O. E.

Osway, K.

Z. Bor, K. Osway, B. Racz, and B. Szabo, Opt. Commun. 78, 109–112 (1990).
[CrossRef]

Pearson, G. W.

C. Radzewicz, G. W. Pearson, and J. S. Krasinski, Opt. Commun. 102, 464–468 (1993).
[CrossRef]

Pearson, N. M.

Racz, B.

Z. Bor, K. Osway, B. Racz, and B. Szabo, Opt. Commun. 78, 109–112 (1990).
[CrossRef]

Radzewicz, C.

C. Radzewicz, G. W. Pearson, and J. S. Krasinski, Opt. Commun. 102, 464–468 (1993).
[CrossRef]

Szabo, B.

Z. Bor, K. Osway, B. Racz, and B. Szabo, Opt. Commun. 78, 109–112 (1990).
[CrossRef]

Szabo, G.

Opt. Commun.

Z. Bor, K. Osway, B. Racz, and B. Szabo, Opt. Commun. 78, 109–112 (1990).
[CrossRef]

C. Radzewicz, G. W. Pearson, and J. S. Krasinski, Opt. Commun. 102, 464–468 (1993).
[CrossRef]

Opt. Lett.

Other

Z. Bor, Opt. Commun. 14, 119 (1989); Z. L. Horvath and Z. Bor, Opt. Commun. 108, 333 (1994).
[CrossRef]

M. Trippenbach and Y. B. Band, Phys. Rev. Lett. 76, 1457–1460 (1996); Y. B. Band and M. Trippenbach, J. Opt. Soc. Am. B 13, 1403–1411 (1996).
[CrossRef]

M. J. Weber, Handbook of Laser Science and Technology (CRC, New York, 1986), Vol. 4, p. 233.

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Figures (6)

Fig. 1
Fig. 1

(a) Schematic representation of a WP propagating in a positive uniaxial crystal. The initial WP is shown on the left. Velocities in the crystal are shown as arrows. The dots in the WP's represent their centers. The propagated WP is tilted, time broadened by dispersion, and moved off axis owing to the walkoff. The effects of diffraction are not shown. (b) Diagram of our experimental situation. The initial WP is shown on the left. Velocities in the crystals are shown as arrows. The dots in the WP's represent their centers. The WP is tilted, time broadened by dispersion, and moved off axis owing to the walkoff. The effects of diffraction are not shown.

Fig. 2
Fig. 2

Michelson interferometer used in the experiment. L1–L4 are lens objectives, M1 and M2 are flat mirrors, C1 and C2 are rutile crystals, and BS1 is a 50% beam splitter. Ellipses drawn with dashes indicate the WP's propagating in the system.

Fig. 3
Fig. 3

Set of images of the interference patterns taken by the TV camera for a set of path differences between arm 1 and arm 2. The numbers next to the pictures are positions of mirror M1 in micrometers.

Fig. 4
Fig. 4

Calculated path-length difference for the extraordinary ray in a 1-mm-thick rutile crystal with respect to the central ray for the range of incidence angles used in the experiment.

Fig. 5
Fig. 5

(a) Visibility of fringes in three different regions of the beam corresponding to incidence angles of 6°, 16°, and 26° (left, central, and right parts of the beam). (b) Visibility of the fringes with one of the crystals rotated by 180° as described in the text. Here the triangles, squares, and circles correspond to the left, center, and right, respectively.

Fig. 6
Fig. 6

Calculated (dotted curve) and measured (symbols) time-delay differences versus incidence angle for our experimental configuration.

Equations (1)

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zA(x, t)=-β1 t-i2β2 2t2+16β3 3t3++γx x+γy y-i2γxx 2x2-i2γyy 2y2+iγxt xt+iγyt yt+iγxy xyA(x, t).

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