Abstract

We present the procedure for measuring self-phase modulation of ultrashort laser pulses focused in gases by use of the spectral phase interferometry for direct electric-field reconstruction (SPIDER) technique. We tested the device, which employs a noncollinear type I frequency mixing scheme, by measuring the phase induced by group-velocity dispersion either in a piece of glass or in the compressor of the laser system. Both results were validated by comparison with the expected values. The phase that resulted from self-phase modulation in H2 gas or atmospheric air was then measured and compared with calculations based on a Gaussian beam assumption. A new estimate of the nonlinear index of refraction of H2 at 800 nm was deduced. The data recorded in atmospheric air are in good agreement with the reported value of the nonlinear index measured with spectral methods.

© 2002 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

1999 (3)

1998 (2)

1997 (1)

1993 (1)

1989 (1)

K. Naganuma, K. Mogi, and H. Yamada, “General method for ultrashort light pulse chirp measurement,” IEEE J. Quantum Electron. 25, 1225–1233 (1989).
[CrossRef]

1967 (2)

H. P. Weber, “Method for pulsewidth measurement of ultrashort light pulses using nonlinear optics,” J. Appl. Phys. 38, 2231–2234 (1967).
[CrossRef]

J. A. Giordmaine, P. M. Rentzepis, S. L. Shapiro, and K. W. Wecht, “Two-photon excitation of fluorescence by picosecond light pulses,” Appl. Phys. Lett. 11, 216–218 (1967).
[CrossRef]

Chambaret, J.-P.

Clement, T. S.

de Beauvoir, B.

Diddams, S. A.

Dorrer, C.

Eaton, H. K.

Franco, M. A.

Gallmann, L.

Giordmaine, J. A.

J. A. Giordmaine, P. M. Rentzepis, S. L. Shapiro, and K. W. Wecht, “Two-photon excitation of fluorescence by picosecond light pulses,” Appl. Phys. Lett. 11, 216–218 (1967).
[CrossRef]

Grillon, G.

Iaconis, C.

Kane, D. J.

Keller, U.

Le Blanc, C.

Matuschek, N.

Mogi, K.

K. Naganuma, K. Mogi, and H. Yamada, “General method for ultrashort light pulse chirp measurement,” IEEE J. Quantum Electron. 25, 1225–1233 (1989).
[CrossRef]

Mysyrowicz, A.

Naganuma, K.

K. Naganuma, K. Mogi, and H. Yamada, “General method for ultrashort light pulse chirp measurement,” IEEE J. Quantum Electron. 25, 1225–1233 (1989).
[CrossRef]

Nibbering, E. T. J.

Prade, B. S.

Ranc, S.

Rentzepis, P. M.

J. A. Giordmaine, P. M. Rentzepis, S. L. Shapiro, and K. W. Wecht, “Two-photon excitation of fluorescence by picosecond light pulses,” Appl. Phys. Lett. 11, 216–218 (1967).
[CrossRef]

Rousseau, J.-P.

Rousseau, P.

Salin, F.

Shapiro, S. L.

J. A. Giordmaine, P. M. Rentzepis, S. L. Shapiro, and K. W. Wecht, “Two-photon excitation of fluorescence by picosecond light pulses,” Appl. Phys. Lett. 11, 216–218 (1967).
[CrossRef]

Steinmeyer, G.

Sutter, D. H.

Trebino, R.

Walmsley, I. A.

Weber, H. P.

H. P. Weber, “Method for pulsewidth measurement of ultrashort light pulses using nonlinear optics,” J. Appl. Phys. 38, 2231–2234 (1967).
[CrossRef]

Wecht, K. W.

J. A. Giordmaine, P. M. Rentzepis, S. L. Shapiro, and K. W. Wecht, “Two-photon excitation of fluorescence by picosecond light pulses,” Appl. Phys. Lett. 11, 216–218 (1967).
[CrossRef]

Yamada, H.

K. Naganuma, K. Mogi, and H. Yamada, “General method for ultrashort light pulse chirp measurement,” IEEE J. Quantum Electron. 25, 1225–1233 (1989).
[CrossRef]

Zozulya, A. A.

Appl. Phys. Lett. (1)

J. A. Giordmaine, P. M. Rentzepis, S. L. Shapiro, and K. W. Wecht, “Two-photon excitation of fluorescence by picosecond light pulses,” Appl. Phys. Lett. 11, 216–218 (1967).
[CrossRef]

IEEE J. Quantum Electron. (2)

K. Naganuma, K. Mogi, and H. Yamada, “General method for ultrashort light pulse chirp measurement,” IEEE J. Quantum Electron. 25, 1225–1233 (1989).
[CrossRef]

C. Iaconis and I. A. Walmsley, “Self-referencing spectral interferometry for measuring ultrashort optical pulses,” IEEE J. Quantum Electron. 35, 501–509 (1999).
[CrossRef]

J. Appl. Phys. (1)

H. P. Weber, “Method for pulsewidth measurement of ultrashort light pulses using nonlinear optics,” J. Appl. Phys. 38, 2231–2234 (1967).
[CrossRef]

J. Opt. Soc. Am. A (1)

J. Opt. Soc. Am. B (1)

Opt. Lett. (4)

Other (1)

J. C. Diels and W. Rudolph, Ultrashort Laser Pulse Phenomena (Academic, San Diego, Calif., 1996).

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Figures (5)

Fig. 1
Fig. 1

Experimental apparatus for the characterization of short laser pulses based on spectral phase interferometry: M1–M6, mirrors; BSs, beam splitters, L1, L2, lenses; PC, personal computer.

Fig. 2
Fig. 2

Measured spectral phase induced by a silica plate of 1.5-cm thickness (solid curve) and calculated phase (dashed curve).

Fig. 3
Fig. 3

Same as in Fig. 2 but with a large chirp parameter φ=5.72×10-26 s2 produced by the grating compressor of the laser.

Fig. 4
Fig. 4

(a) Measured profile of the temporal phase (open squares) that results from the self-phase modulation that occurs in H2 gas. The measurement was performed with a 110-µJ laser energy and a gas pressure of 5.75×105 Pa. The phase is compared with the measured intensity temporal profile (filled circles) of width τp=145 fs(FWHM). (b) Variation of the phase over the full time domain.

Fig. 5
Fig. 5

Same as in Fig. 4, with H2 replaced by atmospheric air (pressure, 9.6×104 Pa).

Equations (3)

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dφ=n¯2 2πλ I(x, y, z)dz=n¯2 2πλ 2P exp[-2(x2+y2)/w2(z)]πw2(z) dz,
dφaverage=x, y dφdxdyπw2(z)=n¯2 2πλ x, y I(x, y, z)dxdyπw2(z) dz=n¯2 2πλ Pπw2(z) dz.
φaverage(t)=(4π3/2log 2) n¯2Eλ2τp exp(-4 log 2×t2/τp2),

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