Abstract

The chirp acquired by a Gaussian ultrashort pulse due to angular dispersion, unlike that of plane waves, increases nonlinearly with propagation distance and eventually asymptotes to a constant. However, this interesting result has never been directly measured. In this Letter, we use two-dimensional spectral interferometry to measure the propagation dependence of the chirp for Gaussian ultrashort pulses and beams with angular dispersion. The measured chirp as a function of propagation distance agreed well with theory. This work verifies both an equation and a measurement technique that will be useful for predicting or determining the pulse’s chirp in ultrafast optics experiments that contain angular dispersion.

© 2009 Optical Society of America

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References

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2008 (1)

2007 (1)

2006 (2)

2005 (1)

2004 (1)

K. Osvay, A. P. Kovacs, Z. Heiner, G. Kurdi, J. Klebniczki, and M. Csatari, IEEE J. Sel. Areas Commun. 10, 213 (2004).

2003 (2)

2002 (1)

2000 (1)

1999 (1)

1996 (2)

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[Crossref] [PubMed]

L. Lepetit, G. Cheriaus, and M. Joffre, J. Nonlinear Opt. Phys. Mater. 5, 465 (1996).
[Crossref]

1993 (1)

Z. L. Horvath, Z. Benko, and A. Kovacs, Opt. Eng. (Bellingham) 32, 2491 (1993).
[Crossref]

1990 (1)

1989 (1)

O. E. Martinez, IEEE J. Quantum Electron. 25, 2464 (1989).
[Crossref]

1988 (1)

1986 (2)

1973 (1)

C. Froehly, A. Lacourt, and J. C. Vienot, Nouv. Rev. Opt. 4, 183 (1973).
[Crossref]

Akturk, S.

Amir, W.

Belabas, N.

Benko, Z.

Z. L. Horvath, Z. Benko, and A. Kovacs, Opt. Eng. (Bellingham) 32, 2491 (1993).
[Crossref]

Bowlan, P.

Cheriaus, G.

L. Lepetit, G. Cheriaus, and M. Joffre, J. Nonlinear Opt. Phys. Mater. 5, 465 (1996).
[Crossref]

Coughlan, M. A.

Csatari, M.

K. Osvay, A. P. Kovacs, Z. Heiner, G. Kurdi, J. Klebniczki, and M. Csatari, IEEE J. Sel. Areas Commun. 10, 213 (2004).

Dorrer, C.

Durfee, C. G.

Feuerhake, M.

Froehly, C.

C. Froehly, A. Lacourt, and J. C. Vienot, Nouv. Rev. Opt. 4, 183 (1973).
[Crossref]

Gabolde, P.

Gu, X.

Heiner, Z.

K. Osvay, A. P. Kovacs, Z. Heiner, G. Kurdi, J. Klebniczki, and M. Csatari, IEEE J. Sel. Areas Commun. 10, 213 (2004).

Heritage, J. P.

Horvath, Z. L.

Z. L. Horvath, Z. Benko, and A. Kovacs, Opt. Eng. (Bellingham) 32, 2491 (1993).
[Crossref]

Jasapara, J.

Jean-Pierre, L.

Joffre, M.

C. Dorrer, M. Joffre, L. Jean-Pierre, and N. Belabas, J. Opt. Soc. Am. B 17, 1795 (2000).
[Crossref]

L. Lepetit, G. Cheriaus, and M. Joffre, J. Nonlinear Opt. Phys. Mater. 5, 465 (1996).
[Crossref]

Kimmel, M.

Kirschner, E. M.

Klebniczki, J.

K. Osvay, A. P. Kovacs, Z. Heiner, G. Kurdi, J. Klebniczki, and M. Csatari, IEEE J. Sel. Areas Commun. 10, 213 (2004).

Kovacs, A.

Z. L. Horvath, Z. Benko, and A. Kovacs, Opt. Eng. (Bellingham) 32, 2491 (1993).
[Crossref]

Kovacs, A. P.

K. Osvay, A. P. Kovacs, Z. Heiner, G. Kurdi, J. Klebniczki, and M. Csatari, IEEE J. Sel. Areas Commun. 10, 213 (2004).

Kovács, A. P.

Kuhnle, G.

Kurdi, G.

K. Osvay, A. P. Kovacs, Z. Heiner, G. Kurdi, J. Klebniczki, and M. Csatari, IEEE J. Sel. Areas Commun. 10, 213 (2004).

K. Varjú, A. P. Kovács, K. Osvay, and G. Kurdi, Opt. Lett. 27, 2034 (2002).
[Crossref]

Lacourt, A.

C. Froehly, A. Lacourt, and J. C. Vienot, Nouv. Rev. Opt. 4, 183 (1973).
[Crossref]

Lepetit, L.

L. Lepetit, G. Cheriaus, and M. Joffre, J. Nonlinear Opt. Phys. Mater. 5, 465 (1996).
[Crossref]

Levis, R. J.

Li, D.

Liu, J.

Luo, Q.

Lv, X.

Martinez, O. E.

O. E. Martinez, IEEE J. Quantum Electron. 25, 2464 (1989).
[Crossref]

O. E. Martinez, Opt. Commun. 59, 229 (1986).
[Crossref]

O. E. Martinez, J. Opt. Soc. Am. B 3, 929 (1986).
[Crossref]

Mueller, M.

Oron, D.

O'Shea, P.

Osvay, K.

K. Osvay, A. P. Kovacs, Z. Heiner, G. Kurdi, J. Klebniczki, and M. Csatari, IEEE J. Sel. Areas Commun. 10, 213 (2004).

K. Varjú, A. P. Kovács, K. Osvay, and G. Kurdi, Opt. Lett. 27, 2034 (2002).
[Crossref]

Planchon, T. A.

Rudolph, W.

Silberberg, Y.

Simon, P.

Squier, J. A.

Szatmari, S.

Tal, E.

Trebino, R.

Varjú, K.

Vienot, J. C.

C. Froehly, A. Lacourt, and J. C. Vienot, Nouv. Rev. Opt. 4, 183 (1973).
[Crossref]

Weiner, A. M.

Zeng, S.

Appl. Opt. (1)

IEEE J. Quantum Electron. (1)

O. E. Martinez, IEEE J. Quantum Electron. 25, 2464 (1989).
[Crossref]

IEEE J. Sel. Areas Commun. (1)

K. Osvay, A. P. Kovacs, Z. Heiner, G. Kurdi, J. Klebniczki, and M. Csatari, IEEE J. Sel. Areas Commun. 10, 213 (2004).

J. Nonlinear Opt. Phys. Mater. (1)

L. Lepetit, G. Cheriaus, and M. Joffre, J. Nonlinear Opt. Phys. Mater. 5, 465 (1996).
[Crossref]

J. Opt. Soc. Am. B (4)

Nouv. Rev. Opt. (1)

C. Froehly, A. Lacourt, and J. C. Vienot, Nouv. Rev. Opt. 4, 183 (1973).
[Crossref]

Opt. Commun. (1)

O. E. Martinez, Opt. Commun. 59, 229 (1986).
[Crossref]

Opt. Eng. (Bellingham) (1)

Z. L. Horvath, Z. Benko, and A. Kovacs, Opt. Eng. (Bellingham) 32, 2491 (1993).
[Crossref]

Opt. Express (3)

Opt. Lett. (6)

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Figures (4)

Fig. 1
Fig. 1

Schematic of the interferometer and the imaging spectrometer. (Left) The beam was spilt into a reference beam and an angularly dispersed beam, which were recombined with a second beam splitter, spatially flipped by 90° using a periscope, and then sent to the imaging spectrometer. The delay stage temporally separated the unknown and reference pulses by 1 ps to yield spectral fringes. (Right) The imaging spectrometer used cylindrical and spherical lenses to image the vertical dimension onto the camera. The cylindrical lens was translated to vary the imaging plane so that the spectral phase of the angularly dispersed beam could be measured at different distances from the prism.

Fig. 2
Fig. 2

(Left) The 2DSI trace taken of the pulse 1.9 m after the prism. (Right) Retrieved spectrum and spectral phase from the interferogram at the left. The thin solid curve shows the curve fit used to extract the chirp.

Fig. 3
Fig. 3

Chirp as a function of propagation distance z. The incidence angle is γ = 60.2 ° .

Fig. 4
Fig. 4

Chirp as a function of propagation distance z at different incident angles ( γ = 58.5 ° , 60.5°, 62.5°; a smaller incident angle provides larger angular dispersion). The theoretical curves use the Gaussian-beam model.

Equations (2)

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φ p ( 2 ) = k β 2 z .
φ g ( 2 ) = d ( d + α 2 z ) + z R 2 ( d + α 2 z ) 2 + z R 2 k β 2 z .

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