Abstract

We experimentally demonstrate an efficient way to control and stabilize single optical filaments initiated by ultrashort laser pulses in a rare gas medium. This is done by the application of a stationary two-dimensional phase mask to the laser beam prior to focusing. Simple circular phase-step patterns of a given radius and relative phase are sufficient to stabilize the pointing of the filament output and to optimize the spectral bandwidth of the light without any resulting loss of input laser power.

© 2006 Optical Society of America

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  1. C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, Appl. Phys. B 79, 673 (2004).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  5. M. Rodriguez, R. Bourayou, G. Méjean, J. Kasparian, J. Yu, E. Salmon, A. Scholz, B. Stecklum, J. Eislöffel, U. Laux, A. P. Hatzes, R. Sauerbrey, L. Wöste, and J. P. Wolf, Phys. Rev. E 69, 036607 (2004).
    [CrossRef]
  6. A. Iwasaki, N. Akozbek, B. Ferland, Q. Luo, G. Roy, C. M. Bowden, and S. L. Chin, Appl. Phys. B 76, 231 (2003).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  10. D. J. Jones, S. T. Cundiff, T. M. Fortier, J. L. Hall, and J. Ye, in Few-Cycle Laser Pulse Generation and Its Applications, F.X.Kärtner, ed. (Springer-Verlag, 2004), pp. 317-342.
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    [CrossRef] [PubMed]
  12. T. Pfeifer, R. Kemmer, R. Spitzenpfeil, D. Walter, C. Winterfeldt, G. Gerber, and C. Spielmann, Opt. Lett. 30, 1497 (2005).
    [CrossRef] [PubMed]

2005 (3)

2004 (4)

G. Méchain, A. Couairon, M. Franco, B. Prade, and A. Mysyrowicz, Phys. Rev. Lett. 93, 035003 (2004).
[CrossRef] [PubMed]

G. Fibich, S. Eisenmann, B. Ilan, and A. Zigler, Opt. Lett. 29, 1772 (2004).
[CrossRef] [PubMed]

M. Rodriguez, R. Bourayou, G. Méjean, J. Kasparian, J. Yu, E. Salmon, A. Scholz, B. Stecklum, J. Eislöffel, U. Laux, A. P. Hatzes, R. Sauerbrey, L. Wöste, and J. P. Wolf, Phys. Rev. E 69, 036607 (2004).
[CrossRef]

C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, Appl. Phys. B 79, 673 (2004).
[CrossRef]

2003 (1)

A. Iwasaki, N. Akozbek, B. Ferland, Q. Luo, G. Roy, C. M. Bowden, and S. L. Chin, Appl. Phys. B 76, 231 (2003).
[CrossRef]

1999 (1)

A. Chiron, B. Lamouroux, R. Lange, J. F. Ripoche, M. Franco, B. Prade, G. Bonnaud, G. Riazuelo, and A. Mysyrowicz, Eur. Phys. J. D 6, 383 (1999).
[CrossRef]

1995 (1)

1979 (1)

C. V. Shank, R. L. Fork, R. F. Leheny, and J. Shah, Phys. Rev. Lett. 42, 112 (1979).
[CrossRef]

Akozbek, N.

A. Iwasaki, N. Akozbek, B. Ferland, Q. Luo, G. Roy, C. M. Bowden, and S. L. Chin, Appl. Phys. B 76, 231 (2003).
[CrossRef]

Biegert, J.

C. P. Hauri, A. Guandalini, P. Eckle, W. Kornelis, J. Biegert, and U. Keller, Opt. Express 13, 7541 (2005).
[CrossRef] [PubMed]

C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, Appl. Phys. B 79, 673 (2004).
[CrossRef]

Bonnaud, G.

A. Chiron, B. Lamouroux, R. Lange, J. F. Ripoche, M. Franco, B. Prade, G. Bonnaud, G. Riazuelo, and A. Mysyrowicz, Eur. Phys. J. D 6, 383 (1999).
[CrossRef]

Bourayou, R.

M. Rodriguez, R. Bourayou, G. Méjean, J. Kasparian, J. Yu, E. Salmon, A. Scholz, B. Stecklum, J. Eislöffel, U. Laux, A. P. Hatzes, R. Sauerbrey, L. Wöste, and J. P. Wolf, Phys. Rev. E 69, 036607 (2004).
[CrossRef]

Bowden, C. M.

A. Iwasaki, N. Akozbek, B. Ferland, Q. Luo, G. Roy, C. M. Bowden, and S. L. Chin, Appl. Phys. B 76, 231 (2003).
[CrossRef]

Braun, A.

Chin, S. L.

A. Iwasaki, N. Akozbek, B. Ferland, Q. Luo, G. Roy, C. M. Bowden, and S. L. Chin, Appl. Phys. B 76, 231 (2003).
[CrossRef]

Chiron, A.

A. Chiron, B. Lamouroux, R. Lange, J. F. Ripoche, M. Franco, B. Prade, G. Bonnaud, G. Riazuelo, and A. Mysyrowicz, Eur. Phys. J. D 6, 383 (1999).
[CrossRef]

Cook, K.

Couairon, A.

G. Méchain, A. Couairon, M. Franco, B. Prade, and A. Mysyrowicz, Phys. Rev. Lett. 93, 035003 (2004).
[CrossRef] [PubMed]

C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, Appl. Phys. B 79, 673 (2004).
[CrossRef]

Cundiff, S. T.

D. J. Jones, S. T. Cundiff, T. M. Fortier, J. L. Hall, and J. Ye, in Few-Cycle Laser Pulse Generation and Its Applications, F.X.Kärtner, ed. (Springer-Verlag, 2004), pp. 317-342.

Du, D.

Eckle, P.

Eisenmann, S.

Eislöffel, J.

M. Rodriguez, R. Bourayou, G. Méjean, J. Kasparian, J. Yu, E. Salmon, A. Scholz, B. Stecklum, J. Eislöffel, U. Laux, A. P. Hatzes, R. Sauerbrey, L. Wöste, and J. P. Wolf, Phys. Rev. E 69, 036607 (2004).
[CrossRef]

Ferland, B.

A. Iwasaki, N. Akozbek, B. Ferland, Q. Luo, G. Roy, C. M. Bowden, and S. L. Chin, Appl. Phys. B 76, 231 (2003).
[CrossRef]

Fibich, G.

Fork, R. L.

C. V. Shank, R. L. Fork, R. F. Leheny, and J. Shah, Phys. Rev. Lett. 42, 112 (1979).
[CrossRef]

Fortier, T. M.

D. J. Jones, S. T. Cundiff, T. M. Fortier, J. L. Hall, and J. Ye, in Few-Cycle Laser Pulse Generation and Its Applications, F.X.Kärtner, ed. (Springer-Verlag, 2004), pp. 317-342.

Franco, M.

G. Méchain, A. Couairon, M. Franco, B. Prade, and A. Mysyrowicz, Phys. Rev. Lett. 93, 035003 (2004).
[CrossRef] [PubMed]

A. Chiron, B. Lamouroux, R. Lange, J. F. Ripoche, M. Franco, B. Prade, G. Bonnaud, G. Riazuelo, and A. Mysyrowicz, Eur. Phys. J. D 6, 383 (1999).
[CrossRef]

Gerber, G.

Guandalini, A.

Hall, J. L.

D. J. Jones, S. T. Cundiff, T. M. Fortier, J. L. Hall, and J. Ye, in Few-Cycle Laser Pulse Generation and Its Applications, F.X.Kärtner, ed. (Springer-Verlag, 2004), pp. 317-342.

Hatzes, A. P.

M. Rodriguez, R. Bourayou, G. Méjean, J. Kasparian, J. Yu, E. Salmon, A. Scholz, B. Stecklum, J. Eislöffel, U. Laux, A. P. Hatzes, R. Sauerbrey, L. Wöste, and J. P. Wolf, Phys. Rev. E 69, 036607 (2004).
[CrossRef]

Hauri, C. P.

C. P. Hauri, A. Guandalini, P. Eckle, W. Kornelis, J. Biegert, and U. Keller, Opt. Express 13, 7541 (2005).
[CrossRef] [PubMed]

C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, Appl. Phys. B 79, 673 (2004).
[CrossRef]

Heinrich, A.

C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, Appl. Phys. B 79, 673 (2004).
[CrossRef]

Helbing, F. W.

C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, Appl. Phys. B 79, 673 (2004).
[CrossRef]

Ilan, B.

Iwasaki, A.

A. Iwasaki, N. Akozbek, B. Ferland, Q. Luo, G. Roy, C. M. Bowden, and S. L. Chin, Appl. Phys. B 76, 231 (2003).
[CrossRef]

Jones, D. J.

D. J. Jones, S. T. Cundiff, T. M. Fortier, J. L. Hall, and J. Ye, in Few-Cycle Laser Pulse Generation and Its Applications, F.X.Kärtner, ed. (Springer-Verlag, 2004), pp. 317-342.

Kar, A. K.

Kasparian, J.

M. Rodriguez, R. Bourayou, G. Méjean, J. Kasparian, J. Yu, E. Salmon, A. Scholz, B. Stecklum, J. Eislöffel, U. Laux, A. P. Hatzes, R. Sauerbrey, L. Wöste, and J. P. Wolf, Phys. Rev. E 69, 036607 (2004).
[CrossRef]

Keller, U.

C. P. Hauri, A. Guandalini, P. Eckle, W. Kornelis, J. Biegert, and U. Keller, Opt. Express 13, 7541 (2005).
[CrossRef] [PubMed]

C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, Appl. Phys. B 79, 673 (2004).
[CrossRef]

Kemmer, R.

Korn, G.

Kornelis, W.

C. P. Hauri, A. Guandalini, P. Eckle, W. Kornelis, J. Biegert, and U. Keller, Opt. Express 13, 7541 (2005).
[CrossRef] [PubMed]

C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, Appl. Phys. B 79, 673 (2004).
[CrossRef]

Lamb, R. A.

Lamouroux, B.

A. Chiron, B. Lamouroux, R. Lange, J. F. Ripoche, M. Franco, B. Prade, G. Bonnaud, G. Riazuelo, and A. Mysyrowicz, Eur. Phys. J. D 6, 383 (1999).
[CrossRef]

Lange, R.

A. Chiron, B. Lamouroux, R. Lange, J. F. Ripoche, M. Franco, B. Prade, G. Bonnaud, G. Riazuelo, and A. Mysyrowicz, Eur. Phys. J. D 6, 383 (1999).
[CrossRef]

Laux, U.

M. Rodriguez, R. Bourayou, G. Méjean, J. Kasparian, J. Yu, E. Salmon, A. Scholz, B. Stecklum, J. Eislöffel, U. Laux, A. P. Hatzes, R. Sauerbrey, L. Wöste, and J. P. Wolf, Phys. Rev. E 69, 036607 (2004).
[CrossRef]

Leheny, R. F.

C. V. Shank, R. L. Fork, R. F. Leheny, and J. Shah, Phys. Rev. Lett. 42, 112 (1979).
[CrossRef]

Liu, X.

Luo, Q.

A. Iwasaki, N. Akozbek, B. Ferland, Q. Luo, G. Roy, C. M. Bowden, and S. L. Chin, Appl. Phys. B 76, 231 (2003).
[CrossRef]

Méchain, G.

G. Méchain, A. Couairon, M. Franco, B. Prade, and A. Mysyrowicz, Phys. Rev. Lett. 93, 035003 (2004).
[CrossRef] [PubMed]

Méjean, G.

M. Rodriguez, R. Bourayou, G. Méjean, J. Kasparian, J. Yu, E. Salmon, A. Scholz, B. Stecklum, J. Eislöffel, U. Laux, A. P. Hatzes, R. Sauerbrey, L. Wöste, and J. P. Wolf, Phys. Rev. E 69, 036607 (2004).
[CrossRef]

Mourou, G.

Mysyrowicz, A.

G. Méchain, A. Couairon, M. Franco, B. Prade, and A. Mysyrowicz, Phys. Rev. Lett. 93, 035003 (2004).
[CrossRef] [PubMed]

C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, Appl. Phys. B 79, 673 (2004).
[CrossRef]

A. Chiron, B. Lamouroux, R. Lange, J. F. Ripoche, M. Franco, B. Prade, G. Bonnaud, G. Riazuelo, and A. Mysyrowicz, Eur. Phys. J. D 6, 383 (1999).
[CrossRef]

Pfeifer, T.

Prade, B.

G. Méchain, A. Couairon, M. Franco, B. Prade, and A. Mysyrowicz, Phys. Rev. Lett. 93, 035003 (2004).
[CrossRef] [PubMed]

A. Chiron, B. Lamouroux, R. Lange, J. F. Ripoche, M. Franco, B. Prade, G. Bonnaud, G. Riazuelo, and A. Mysyrowicz, Eur. Phys. J. D 6, 383 (1999).
[CrossRef]

Riazuelo, G.

A. Chiron, B. Lamouroux, R. Lange, J. F. Ripoche, M. Franco, B. Prade, G. Bonnaud, G. Riazuelo, and A. Mysyrowicz, Eur. Phys. J. D 6, 383 (1999).
[CrossRef]

Ripoche, J. F.

A. Chiron, B. Lamouroux, R. Lange, J. F. Ripoche, M. Franco, B. Prade, G. Bonnaud, G. Riazuelo, and A. Mysyrowicz, Eur. Phys. J. D 6, 383 (1999).
[CrossRef]

Rodriguez, M.

M. Rodriguez, R. Bourayou, G. Méjean, J. Kasparian, J. Yu, E. Salmon, A. Scholz, B. Stecklum, J. Eislöffel, U. Laux, A. P. Hatzes, R. Sauerbrey, L. Wöste, and J. P. Wolf, Phys. Rev. E 69, 036607 (2004).
[CrossRef]

Roy, G.

A. Iwasaki, N. Akozbek, B. Ferland, Q. Luo, G. Roy, C. M. Bowden, and S. L. Chin, Appl. Phys. B 76, 231 (2003).
[CrossRef]

Salmon, E.

M. Rodriguez, R. Bourayou, G. Méjean, J. Kasparian, J. Yu, E. Salmon, A. Scholz, B. Stecklum, J. Eislöffel, U. Laux, A. P. Hatzes, R. Sauerbrey, L. Wöste, and J. P. Wolf, Phys. Rev. E 69, 036607 (2004).
[CrossRef]

Sauerbrey, R.

M. Rodriguez, R. Bourayou, G. Méjean, J. Kasparian, J. Yu, E. Salmon, A. Scholz, B. Stecklum, J. Eislöffel, U. Laux, A. P. Hatzes, R. Sauerbrey, L. Wöste, and J. P. Wolf, Phys. Rev. E 69, 036607 (2004).
[CrossRef]

Scholz, A.

M. Rodriguez, R. Bourayou, G. Méjean, J. Kasparian, J. Yu, E. Salmon, A. Scholz, B. Stecklum, J. Eislöffel, U. Laux, A. P. Hatzes, R. Sauerbrey, L. Wöste, and J. P. Wolf, Phys. Rev. E 69, 036607 (2004).
[CrossRef]

Shah, J.

C. V. Shank, R. L. Fork, R. F. Leheny, and J. Shah, Phys. Rev. Lett. 42, 112 (1979).
[CrossRef]

Shank, C. V.

C. V. Shank, R. L. Fork, R. F. Leheny, and J. Shah, Phys. Rev. Lett. 42, 112 (1979).
[CrossRef]

Spielmann, C.

Spitzenpfeil, R.

Squier, J.

Stecklum, B.

M. Rodriguez, R. Bourayou, G. Méjean, J. Kasparian, J. Yu, E. Salmon, A. Scholz, B. Stecklum, J. Eislöffel, U. Laux, A. P. Hatzes, R. Sauerbrey, L. Wöste, and J. P. Wolf, Phys. Rev. E 69, 036607 (2004).
[CrossRef]

Walter, D.

Winterfeldt, C.

Wolf, J. P.

M. Rodriguez, R. Bourayou, G. Méjean, J. Kasparian, J. Yu, E. Salmon, A. Scholz, B. Stecklum, J. Eislöffel, U. Laux, A. P. Hatzes, R. Sauerbrey, L. Wöste, and J. P. Wolf, Phys. Rev. E 69, 036607 (2004).
[CrossRef]

Wöste, L.

M. Rodriguez, R. Bourayou, G. Méjean, J. Kasparian, J. Yu, E. Salmon, A. Scholz, B. Stecklum, J. Eislöffel, U. Laux, A. P. Hatzes, R. Sauerbrey, L. Wöste, and J. P. Wolf, Phys. Rev. E 69, 036607 (2004).
[CrossRef]

Ye, J.

D. J. Jones, S. T. Cundiff, T. M. Fortier, J. L. Hall, and J. Ye, in Few-Cycle Laser Pulse Generation and Its Applications, F.X.Kärtner, ed. (Springer-Verlag, 2004), pp. 317-342.

Yu, J.

M. Rodriguez, R. Bourayou, G. Méjean, J. Kasparian, J. Yu, E. Salmon, A. Scholz, B. Stecklum, J. Eislöffel, U. Laux, A. P. Hatzes, R. Sauerbrey, L. Wöste, and J. P. Wolf, Phys. Rev. E 69, 036607 (2004).
[CrossRef]

Zigler, A.

Appl. Phys. B (2)

C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, Appl. Phys. B 79, 673 (2004).
[CrossRef]

A. Iwasaki, N. Akozbek, B. Ferland, Q. Luo, G. Roy, C. M. Bowden, and S. L. Chin, Appl. Phys. B 76, 231 (2003).
[CrossRef]

Eur. Phys. J. D (1)

A. Chiron, B. Lamouroux, R. Lange, J. F. Ripoche, M. Franco, B. Prade, G. Bonnaud, G. Riazuelo, and A. Mysyrowicz, Eur. Phys. J. D 6, 383 (1999).
[CrossRef]

Opt. Express (2)

Opt. Lett. (3)

Phys. Rev. E (1)

M. Rodriguez, R. Bourayou, G. Méjean, J. Kasparian, J. Yu, E. Salmon, A. Scholz, B. Stecklum, J. Eislöffel, U. Laux, A. P. Hatzes, R. Sauerbrey, L. Wöste, and J. P. Wolf, Phys. Rev. E 69, 036607 (2004).
[CrossRef]

Phys. Rev. Lett. (2)

C. V. Shank, R. L. Fork, R. F. Leheny, and J. Shah, Phys. Rev. Lett. 42, 112 (1979).
[CrossRef]

G. Méchain, A. Couairon, M. Franco, B. Prade, and A. Mysyrowicz, Phys. Rev. Lett. 93, 035003 (2004).
[CrossRef] [PubMed]

Other (1)

D. J. Jones, S. T. Cundiff, T. M. Fortier, J. L. Hall, and J. Ye, in Few-Cycle Laser Pulse Generation and Its Applications, F.X.Kärtner, ed. (Springer-Verlag, 2004), pp. 317-342.

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Figures (3)

Fig. 1
Fig. 1

Experimental setup. The spatial phase of the laser pulse is modified by a circular phase mask created with a two-dimensional spatial light modulator before being focused into the gas cell for optical filamentation. The output characteristics of the laser after filamentation (beam stability and pulse spectrum) are recorded.

Fig. 2
Fig. 2

Controlling the supercontinuum spectrum after filamentation by a circular phase mask. (a) Variation of the phase for a constant radius r = 2.9 mm . The integrated spectrum in the blue ( 450 650 nm ) (solid curve) and the red spectral region ( 850 1000 nm ) (dashed curve) are plotted versus the phase step. (b) Blue (solid) and red (dashed) integrated spectral content versus radius of the phase step for a constant phase of 0.85 π . An optimum occurs near a phase and radius of 0.85 π and r = 3.9 mm , respectively. (c) The spectrum obtained without (dashed line) and with application of the optimal phase mask (solid line). (d) Predicted bandwidth-limited laser-pulse shapes and FWHM durations for the spectra shown in (c).

Fig. 3
Fig. 3

Stabilization of pointing fluctuations in the laser beam after filamentation. (a) Position of the beam after the filament for the case of no phase mask applied (open squares), and phase mask of 0.85 π applied with a radius of 2.7 mm (solid dots) and 2.9 mm (crosses). (b) Position of x (solid curve) and y positions (dashed curves) versus frame number of image acquired with CCD camera after filamentation. The curves are offset along the vertical axis. The mean standard deviation σ ¯ of the x and y positions is decreased by factors of 4 and 3 for the case of radii of 2.7 and 2.9 mm , respectively.

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