Abstract

We use collinear spatially resolved spectral interferometery to characterize the nonlinear phase changes experienced by an intense ultrashort pulse propagating in glass. The measurement yields the spectrally dependent wavefront, allowing us to measure the spatial and chromatic aberrations of the nonlinearly induced lens. For these conditions, we find that while the shape of the spatial wavefront follows the beam profile as expected, the spectral dependence of the lensing power is determined by the self-phase modulation. The simultaneous measurement of the nonlinear spatiospectral phase demonstrates how the nonlinear spectral phase is coupled to self-focusing.

© 2009 Optical Society of America

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K. Osvay and M. Gorbe, Opt. Lett. 32, 3095 (2007).
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S. L. Chin and F. Theberge, Appl. Phys. B 86, 477 (2007).
[CrossRef]

2006 (3)

2005 (2)

2004 (1)

2003 (3)

V. P. Kandidov and O. G. Kosareva, Appl. Phys. B 77, 149 (2003).
[CrossRef]

X. J. Fang and T. Kobayashi, Appl. Phys. B 77, 167 (2003).
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J. Kasparian, M. Rodriguez, G. Mjean, J. Yu, and E. Salmon, Science 301, 61 (2003).
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2002 (1)

A. C. Bernstein and T. S. Luk, Appl. Phys. B 75, 119 (2002).
[CrossRef]

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A. Brodeur and S. L. Chin, Phys. Rev. Lett. 80, 4406 (1998).
[CrossRef]

1997 (1)

1995 (3)

L. Lepetit, G. Cheriaux, and M. Joffre, J. Opt. Soc. Am. B 12, 2467 (1995).
[CrossRef]

A. P. Kovacs and K. Osvay, Opt. Lett. 20, 788 (1995).
[CrossRef] [PubMed]

E. T. J. Nibbering, M. A. Franco, B. S. Prade, G. Grillon, C. Le Blanc, and A. Mysyrowicz, Opt. Commun. 119, 479 (1995).
[CrossRef]

1989 (1)

1983 (1)

1982 (1)

1977 (1)

W. L. Smith, P. Liu, and N. Bloembergen, Phys. Rev. A 15, 2396 (1977).
[CrossRef]

Akturk, S.

Amir, W.

Barthelemy, A.

Bernstein, A. C.

A. C. Bernstein and T. S. Luk, Appl. Phys. B 75, 119 (2002).
[CrossRef]

Bloembergen, N.

W. L. Smith, P. Liu, and N. Bloembergen, Phys. Rev. A 15, 2396 (1977).
[CrossRef]

Bowlan, P.

Briscoe, E.

Brodeur, A.

A. Brodeur and S. L. Chin, Phys. Rev. Lett. 80, 4406 (1998).
[CrossRef]

Cheriaux, G.

Childress, C.

Chin, S. L.

S. L. Chin and F. Theberge, Appl. Phys. B 86, 477 (2007).
[CrossRef]

A. Brodeur and S. L. Chin, Phys. Rev. Lett. 80, 4406 (1998).
[CrossRef]

Durfee, C. G.

Eisenmann, S.

Fang, X. J.

X. J. Fang and T. Kobayashi, Appl. Phys. B 77, 167 (2003).
[CrossRef]

Fibich, G.

Field, J. J.

J. J. Field, T. A. Planchon, W. Amir, C. G. Durfee, and J. A. Squier, Opt. Commun. 278, 368 (2007).
[CrossRef] [PubMed]

Fork, R. L.

Foster, M. A.

Franco, M. A.

E. T. J. Nibbering, M. A. Franco, B. S. Prade, G. Grillon, C. Le Blanc, and A. Mysyrowicz, Opt. Commun. 119, 479 (1995).
[CrossRef]

Gabolde, P.

Gaeta, A. L.

Gorbe, M.

Gordon, D. F.

Grillon, G.

E. T. J. Nibbering, M. A. Franco, B. S. Prade, G. Grillon, C. Le Blanc, and A. Mysyrowicz, Opt. Commun. 119, 479 (1995).
[CrossRef]

Grow, T. D.

Ilan, B.

Ina, H.

Ishaaya, A. A.

Joffre, M.

Kandidov, V. P.

V. P. Kandidov and O. G. Kosareva, Appl. Phys. B 77, 149 (2003).
[CrossRef]

Kasparian, J.

J. Kasparian, M. Rodriguez, G. Mjean, J. Yu, and E. Salmon, Science 301, 61 (2003).
[CrossRef] [PubMed]

Kobayashi, S.

Kobayashi, T.

X. J. Fang and T. Kobayashi, Appl. Phys. B 77, 167 (2003).
[CrossRef]

Kosareva, O. G.

V. P. Kandidov and O. G. Kosareva, Appl. Phys. B 77, 149 (2003).
[CrossRef]

Kovacs, A. P.

Le Blanc, C.

E. T. J. Nibbering, M. A. Franco, B. S. Prade, G. Grillon, C. Le Blanc, and A. Mysyrowicz, Opt. Commun. 119, 479 (1995).
[CrossRef]

Lepetit, L.

Liu, P.

W. L. Smith, P. Liu, and N. Bloembergen, Phys. Rev. A 15, 2396 (1977).
[CrossRef]

Luk, T. S.

A. C. Bernstein and T. S. Luk, Appl. Phys. B 75, 119 (2002).
[CrossRef]

Mcbresham, K.

Meshulach, D.

Mjean, G.

J. Kasparian, M. Rodriguez, G. Mjean, J. Yu, and E. Salmon, Science 301, 61 (2003).
[CrossRef] [PubMed]

Muller, M.

Mysyrowicz, A.

E. T. J. Nibbering, M. A. Franco, B. S. Prade, G. Grillon, C. Le Blanc, and A. Mysyrowicz, Opt. Commun. 119, 479 (1995).
[CrossRef]

Nibbering, E. T. J.

E. T. J. Nibbering, M. A. Franco, B. S. Prade, G. Grillon, C. Le Blanc, and A. Mysyrowicz, Opt. Commun. 119, 479 (1995).
[CrossRef]

Osvay, K.

Peano, J. R.

Planchon, T. A.

Prade, B. S.

E. T. J. Nibbering, M. A. Franco, B. S. Prade, G. Grillon, C. Le Blanc, and A. Mysyrowicz, Opt. Commun. 119, 479 (1995).
[CrossRef]

Reynaud, F.

Rodriguez, M.

J. Kasparian, M. Rodriguez, G. Mjean, J. Yu, and E. Salmon, Science 301, 61 (2003).
[CrossRef] [PubMed]

Salin, F.

Salmon, E.

J. Kasparian, M. Rodriguez, G. Mjean, J. Yu, and E. Salmon, Science 301, 61 (2003).
[CrossRef] [PubMed]

Shank, C. V.

Shreenath, A.

Smith, W. L.

W. L. Smith, P. Liu, and N. Bloembergen, Phys. Rev. A 15, 2396 (1977).
[CrossRef]

Sprangle, P.

Squier, J.

Squier, J. A.

Takeda, M.

Theberge, F.

S. L. Chin and F. Theberge, Appl. Phys. B 86, 477 (2007).
[CrossRef]

Ting, A.

Trebino, R.

Yelin, D.

Yu, J.

J. Kasparian, M. Rodriguez, G. Mjean, J. Yu, and E. Salmon, Science 301, 61 (2003).
[CrossRef] [PubMed]

Zigler, A.

Appl. Opt. (1)

Appl. Phys. B (4)

S. L. Chin and F. Theberge, Appl. Phys. B 86, 477 (2007).
[CrossRef]

X. J. Fang and T. Kobayashi, Appl. Phys. B 77, 167 (2003).
[CrossRef]

A. C. Bernstein and T. S. Luk, Appl. Phys. B 75, 119 (2002).
[CrossRef]

V. P. Kandidov and O. G. Kosareva, Appl. Phys. B 77, 149 (2003).
[CrossRef]

J. Microsc. (1)

W. Amir and C. G. Durfee, J. Microsc. 230, 4 (2008).
[CrossRef] [PubMed]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. B (2)

Opt. Commun. (2)

E. T. J. Nibbering, M. A. Franco, B. S. Prade, G. Grillon, C. Le Blanc, and A. Mysyrowicz, Opt. Commun. 119, 479 (1995).
[CrossRef]

J. J. Field, T. A. Planchon, W. Amir, C. G. Durfee, and J. A. Squier, Opt. Commun. 278, 368 (2007).
[CrossRef] [PubMed]

Opt. Express (4)

Opt. Lett. (7)

Phys. Rev. A (1)

W. L. Smith, P. Liu, and N. Bloembergen, Phys. Rev. A 15, 2396 (1977).
[CrossRef]

Phys. Rev. Lett. (1)

A. Brodeur and S. L. Chin, Phys. Rev. Lett. 80, 4406 (1998).
[CrossRef]

Science (1)

J. Kasparian, M. Rodriguez, G. Mjean, J. Yu, and E. Salmon, Science 301, 61 (2003).
[CrossRef] [PubMed]

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Figures (4)

Fig. 1
Fig. 1

Spatially resolved spectral interferometry setup. The f = 250 mm lens relay images planes from inside the interferometer to the entrance slit of the spectrometer. (B.S., 98R beam splitter)

Fig. 2
Fig. 2

(a) Plot of the spatiospectral phase and (b) lineouts for several angular frequencies. The data were taken with 40 μ J of energy, a chirped temporal width of 100 fs FWHM, and a beam diameter of 1 mm FWHM. A 6 - mm -thick window of BK7 glass was placed in both arms of the interferometer.

Fig. 3
Fig. 3

(a) Measurement and (b) simulation of the spatiospectral phase after nonlinear propagation through 6 mm BK7 for a near-transform-limited 35 fs (FWHM), 1 mm (FWHM) beam diameter, and 40 μ J pulse. The nonlinear phase surface near the center of the pulse develops a saddle shape. The spatial phase cross sections follow the input-beam profile. The phase has been set to zero, where the intensity drops below 1% of the peak value.

Fig. 4
Fig. 4

Lineouts of spectrum and phase for (a) a chirped pulse 100 fs FWHM at Y = 0 , for (b) a short pulse 35 fs FWHM at Y = 0 . Optical power as a function of frequency for (c) the chirped pulse and for (d) the short pulse.

Equations (1)

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f NL = π w 4 4 n 2 P 0 L ,

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