Abstract

We investigate beam pointing dynamics in filamentation in gases driven by high repetition rate femtosecond laser pulses. Upon sudden exposure of a gas to a kilohertz train of filamenting pulses, successive filaments are steered from their original direction to a new stable direction whose equilibrium is determined by a balance among buoyant, viscous, and diffusive processes in the gas. The beam mode is preserved. Results are shown for Xe and air, but are broadly applicable to all configurations employing intense, high repetition rate femtosecond laser pulses in gases.

© 2013 Optical Society of America

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  1. A. Couairon and A. Mysyrowicz, “Femtosecond filamentation in transparent media,” Phys. Rep.441(2–4), 47–189 (2007).
    [CrossRef]
  2. N. Aközbek, A. Iwasaki, A. Becker, M. Scalora, S. L. Chin, and C. M. Bowden, “Third-harmonic generation and self-channeling in air using high-power femtosecond laser pulses,” Phys. Rev. Lett.89(14), 143901 (2002).
    [CrossRef] [PubMed]
  3. N. Kortsalioudakis, M. Tatarakis, N. Vakakis, S. D. Moustaizis, M. Franco, B. Prade, A. Mysyrowicz, N. A. Papadogiannis, A. Couairon, and S. Tzortzakis, “Enhanced harmonic conversion efficiency in the self-guided propagation of femtosecond ultraviolet laser pulses in argon,” Appl. Phys. B80(2), 211–214 (2005).
    [CrossRef]
  4. P. B. Corkum, C. Rolland, and T. Srinivasan-Rao, “Supercontinuum generation in gases,” Phys. Rev. Lett.57(18), 2268–2271 (1986).
    [CrossRef] [PubMed]
  5. C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, “Generation of intense, carrier-envelope phase-locked few-cycle laser pulses through filamentation,” Appl. Phys. B79(6), 673–677 (2004).
    [CrossRef]
  6. G. Stibenz, N. Zhavoronkov, and G. Steinmeyer, “Self-compression of millijoule pulses to 7.8 fs duration in a white-light filament,” Opt. Lett.31(2), 274–276 (2006).
    [CrossRef] [PubMed]
  7. D. C. Smith, “High-power laser propagation: Thermal blooming,” Proc. IEEE65(12), 1679–1714 (1977).
    [CrossRef]
  8. V. V. Vorob’ev, “Thermal blooming of laser beams in the atmosphere,” Prog. Quantum Electron.15(1–2), 1–152 (1991).
    [CrossRef]
  9. Y.-H. Cheng, J. K. Wahlstrand, N. Jhajj, and H. M. Milchberg, “The effect of long timescale gas dynamics on femtosecond filamentation,” Opt. Express21(4), 4740–4751 (2013).
    [CrossRef] [PubMed]
  10. J. K. Wahlstrand, Y.-H. Cheng, and H. M. Milchberg, “High field optical nonlinearity and the Kramers-Kronig relations,” Phys. Rev. Lett.109(11), 113904 (2012).
    [CrossRef] [PubMed]
  11. M. Takeda, H. Ina, and S. Kobayashi, “Fourier-transform method of fringe pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am.72(1), 156–160 (1982).
    [CrossRef]
  12. A. Dalgarno and A. E. Kingston, “The refractive indices and Verdet constants of the inert gases,” Proc. R. Soc. London A Math. Phys. Sci.259(1298), 424–431 (1960).
    [CrossRef]
  13. M. Mlejnek, E. M. Wright, and J. V. Moloney, “Dynamic spatial replenishment of femtosecond pulses propagating in air,” Opt. Lett.23(5), 382–384 (1998).
    [CrossRef] [PubMed]
  14. http://webbook.nist.gov/chemistry/fluid/

2013

2012

J. K. Wahlstrand, Y.-H. Cheng, and H. M. Milchberg, “High field optical nonlinearity and the Kramers-Kronig relations,” Phys. Rev. Lett.109(11), 113904 (2012).
[CrossRef] [PubMed]

2007

A. Couairon and A. Mysyrowicz, “Femtosecond filamentation in transparent media,” Phys. Rep.441(2–4), 47–189 (2007).
[CrossRef]

2006

2005

N. Kortsalioudakis, M. Tatarakis, N. Vakakis, S. D. Moustaizis, M. Franco, B. Prade, A. Mysyrowicz, N. A. Papadogiannis, A. Couairon, and S. Tzortzakis, “Enhanced harmonic conversion efficiency in the self-guided propagation of femtosecond ultraviolet laser pulses in argon,” Appl. Phys. B80(2), 211–214 (2005).
[CrossRef]

2004

C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, “Generation of intense, carrier-envelope phase-locked few-cycle laser pulses through filamentation,” Appl. Phys. B79(6), 673–677 (2004).
[CrossRef]

2002

N. Aközbek, A. Iwasaki, A. Becker, M. Scalora, S. L. Chin, and C. M. Bowden, “Third-harmonic generation and self-channeling in air using high-power femtosecond laser pulses,” Phys. Rev. Lett.89(14), 143901 (2002).
[CrossRef] [PubMed]

1998

1991

V. V. Vorob’ev, “Thermal blooming of laser beams in the atmosphere,” Prog. Quantum Electron.15(1–2), 1–152 (1991).
[CrossRef]

1986

P. B. Corkum, C. Rolland, and T. Srinivasan-Rao, “Supercontinuum generation in gases,” Phys. Rev. Lett.57(18), 2268–2271 (1986).
[CrossRef] [PubMed]

1982

1977

D. C. Smith, “High-power laser propagation: Thermal blooming,” Proc. IEEE65(12), 1679–1714 (1977).
[CrossRef]

1960

A. Dalgarno and A. E. Kingston, “The refractive indices and Verdet constants of the inert gases,” Proc. R. Soc. London A Math. Phys. Sci.259(1298), 424–431 (1960).
[CrossRef]

Aközbek, N.

N. Aközbek, A. Iwasaki, A. Becker, M. Scalora, S. L. Chin, and C. M. Bowden, “Third-harmonic generation and self-channeling in air using high-power femtosecond laser pulses,” Phys. Rev. Lett.89(14), 143901 (2002).
[CrossRef] [PubMed]

Becker, A.

N. Aközbek, A. Iwasaki, A. Becker, M. Scalora, S. L. Chin, and C. M. Bowden, “Third-harmonic generation and self-channeling in air using high-power femtosecond laser pulses,” Phys. Rev. Lett.89(14), 143901 (2002).
[CrossRef] [PubMed]

Biegert, J.

C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, “Generation of intense, carrier-envelope phase-locked few-cycle laser pulses through filamentation,” Appl. Phys. B79(6), 673–677 (2004).
[CrossRef]

Bowden, C. M.

N. Aközbek, A. Iwasaki, A. Becker, M. Scalora, S. L. Chin, and C. M. Bowden, “Third-harmonic generation and self-channeling in air using high-power femtosecond laser pulses,” Phys. Rev. Lett.89(14), 143901 (2002).
[CrossRef] [PubMed]

Cheng, Y.-H.

Y.-H. Cheng, J. K. Wahlstrand, N. Jhajj, and H. M. Milchberg, “The effect of long timescale gas dynamics on femtosecond filamentation,” Opt. Express21(4), 4740–4751 (2013).
[CrossRef] [PubMed]

J. K. Wahlstrand, Y.-H. Cheng, and H. M. Milchberg, “High field optical nonlinearity and the Kramers-Kronig relations,” Phys. Rev. Lett.109(11), 113904 (2012).
[CrossRef] [PubMed]

Chin, S. L.

N. Aközbek, A. Iwasaki, A. Becker, M. Scalora, S. L. Chin, and C. M. Bowden, “Third-harmonic generation and self-channeling in air using high-power femtosecond laser pulses,” Phys. Rev. Lett.89(14), 143901 (2002).
[CrossRef] [PubMed]

Corkum, P. B.

P. B. Corkum, C. Rolland, and T. Srinivasan-Rao, “Supercontinuum generation in gases,” Phys. Rev. Lett.57(18), 2268–2271 (1986).
[CrossRef] [PubMed]

Couairon, A.

A. Couairon and A. Mysyrowicz, “Femtosecond filamentation in transparent media,” Phys. Rep.441(2–4), 47–189 (2007).
[CrossRef]

N. Kortsalioudakis, M. Tatarakis, N. Vakakis, S. D. Moustaizis, M. Franco, B. Prade, A. Mysyrowicz, N. A. Papadogiannis, A. Couairon, and S. Tzortzakis, “Enhanced harmonic conversion efficiency in the self-guided propagation of femtosecond ultraviolet laser pulses in argon,” Appl. Phys. B80(2), 211–214 (2005).
[CrossRef]

C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, “Generation of intense, carrier-envelope phase-locked few-cycle laser pulses through filamentation,” Appl. Phys. B79(6), 673–677 (2004).
[CrossRef]

Dalgarno, A.

A. Dalgarno and A. E. Kingston, “The refractive indices and Verdet constants of the inert gases,” Proc. R. Soc. London A Math. Phys. Sci.259(1298), 424–431 (1960).
[CrossRef]

Franco, M.

N. Kortsalioudakis, M. Tatarakis, N. Vakakis, S. D. Moustaizis, M. Franco, B. Prade, A. Mysyrowicz, N. A. Papadogiannis, A. Couairon, and S. Tzortzakis, “Enhanced harmonic conversion efficiency in the self-guided propagation of femtosecond ultraviolet laser pulses in argon,” Appl. Phys. B80(2), 211–214 (2005).
[CrossRef]

Hauri, C. P.

C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, “Generation of intense, carrier-envelope phase-locked few-cycle laser pulses through filamentation,” Appl. Phys. B79(6), 673–677 (2004).
[CrossRef]

Heinrich, A.

C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, “Generation of intense, carrier-envelope phase-locked few-cycle laser pulses through filamentation,” Appl. Phys. B79(6), 673–677 (2004).
[CrossRef]

Helbing, F. W.

C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, “Generation of intense, carrier-envelope phase-locked few-cycle laser pulses through filamentation,” Appl. Phys. B79(6), 673–677 (2004).
[CrossRef]

Ina, H.

Iwasaki, A.

N. Aközbek, A. Iwasaki, A. Becker, M. Scalora, S. L. Chin, and C. M. Bowden, “Third-harmonic generation and self-channeling in air using high-power femtosecond laser pulses,” Phys. Rev. Lett.89(14), 143901 (2002).
[CrossRef] [PubMed]

Jhajj, N.

Keller, U.

C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, “Generation of intense, carrier-envelope phase-locked few-cycle laser pulses through filamentation,” Appl. Phys. B79(6), 673–677 (2004).
[CrossRef]

Kingston, A. E.

A. Dalgarno and A. E. Kingston, “The refractive indices and Verdet constants of the inert gases,” Proc. R. Soc. London A Math. Phys. Sci.259(1298), 424–431 (1960).
[CrossRef]

Kobayashi, S.

Kornelis, W.

C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, “Generation of intense, carrier-envelope phase-locked few-cycle laser pulses through filamentation,” Appl. Phys. B79(6), 673–677 (2004).
[CrossRef]

Kortsalioudakis, N.

N. Kortsalioudakis, M. Tatarakis, N. Vakakis, S. D. Moustaizis, M. Franco, B. Prade, A. Mysyrowicz, N. A. Papadogiannis, A. Couairon, and S. Tzortzakis, “Enhanced harmonic conversion efficiency in the self-guided propagation of femtosecond ultraviolet laser pulses in argon,” Appl. Phys. B80(2), 211–214 (2005).
[CrossRef]

Milchberg, H. M.

Y.-H. Cheng, J. K. Wahlstrand, N. Jhajj, and H. M. Milchberg, “The effect of long timescale gas dynamics on femtosecond filamentation,” Opt. Express21(4), 4740–4751 (2013).
[CrossRef] [PubMed]

J. K. Wahlstrand, Y.-H. Cheng, and H. M. Milchberg, “High field optical nonlinearity and the Kramers-Kronig relations,” Phys. Rev. Lett.109(11), 113904 (2012).
[CrossRef] [PubMed]

Mlejnek, M.

Moloney, J. V.

Moustaizis, S. D.

N. Kortsalioudakis, M. Tatarakis, N. Vakakis, S. D. Moustaizis, M. Franco, B. Prade, A. Mysyrowicz, N. A. Papadogiannis, A. Couairon, and S. Tzortzakis, “Enhanced harmonic conversion efficiency in the self-guided propagation of femtosecond ultraviolet laser pulses in argon,” Appl. Phys. B80(2), 211–214 (2005).
[CrossRef]

Mysyrowicz, A.

A. Couairon and A. Mysyrowicz, “Femtosecond filamentation in transparent media,” Phys. Rep.441(2–4), 47–189 (2007).
[CrossRef]

N. Kortsalioudakis, M. Tatarakis, N. Vakakis, S. D. Moustaizis, M. Franco, B. Prade, A. Mysyrowicz, N. A. Papadogiannis, A. Couairon, and S. Tzortzakis, “Enhanced harmonic conversion efficiency in the self-guided propagation of femtosecond ultraviolet laser pulses in argon,” Appl. Phys. B80(2), 211–214 (2005).
[CrossRef]

C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, “Generation of intense, carrier-envelope phase-locked few-cycle laser pulses through filamentation,” Appl. Phys. B79(6), 673–677 (2004).
[CrossRef]

Papadogiannis, N. A.

N. Kortsalioudakis, M. Tatarakis, N. Vakakis, S. D. Moustaizis, M. Franco, B. Prade, A. Mysyrowicz, N. A. Papadogiannis, A. Couairon, and S. Tzortzakis, “Enhanced harmonic conversion efficiency in the self-guided propagation of femtosecond ultraviolet laser pulses in argon,” Appl. Phys. B80(2), 211–214 (2005).
[CrossRef]

Prade, B.

N. Kortsalioudakis, M. Tatarakis, N. Vakakis, S. D. Moustaizis, M. Franco, B. Prade, A. Mysyrowicz, N. A. Papadogiannis, A. Couairon, and S. Tzortzakis, “Enhanced harmonic conversion efficiency in the self-guided propagation of femtosecond ultraviolet laser pulses in argon,” Appl. Phys. B80(2), 211–214 (2005).
[CrossRef]

Rolland, C.

P. B. Corkum, C. Rolland, and T. Srinivasan-Rao, “Supercontinuum generation in gases,” Phys. Rev. Lett.57(18), 2268–2271 (1986).
[CrossRef] [PubMed]

Scalora, M.

N. Aközbek, A. Iwasaki, A. Becker, M. Scalora, S. L. Chin, and C. M. Bowden, “Third-harmonic generation and self-channeling in air using high-power femtosecond laser pulses,” Phys. Rev. Lett.89(14), 143901 (2002).
[CrossRef] [PubMed]

Smith, D. C.

D. C. Smith, “High-power laser propagation: Thermal blooming,” Proc. IEEE65(12), 1679–1714 (1977).
[CrossRef]

Srinivasan-Rao, T.

P. B. Corkum, C. Rolland, and T. Srinivasan-Rao, “Supercontinuum generation in gases,” Phys. Rev. Lett.57(18), 2268–2271 (1986).
[CrossRef] [PubMed]

Steinmeyer, G.

Stibenz, G.

Takeda, M.

Tatarakis, M.

N. Kortsalioudakis, M. Tatarakis, N. Vakakis, S. D. Moustaizis, M. Franco, B. Prade, A. Mysyrowicz, N. A. Papadogiannis, A. Couairon, and S. Tzortzakis, “Enhanced harmonic conversion efficiency in the self-guided propagation of femtosecond ultraviolet laser pulses in argon,” Appl. Phys. B80(2), 211–214 (2005).
[CrossRef]

Tzortzakis, S.

N. Kortsalioudakis, M. Tatarakis, N. Vakakis, S. D. Moustaizis, M. Franco, B. Prade, A. Mysyrowicz, N. A. Papadogiannis, A. Couairon, and S. Tzortzakis, “Enhanced harmonic conversion efficiency in the self-guided propagation of femtosecond ultraviolet laser pulses in argon,” Appl. Phys. B80(2), 211–214 (2005).
[CrossRef]

Vakakis, N.

N. Kortsalioudakis, M. Tatarakis, N. Vakakis, S. D. Moustaizis, M. Franco, B. Prade, A. Mysyrowicz, N. A. Papadogiannis, A. Couairon, and S. Tzortzakis, “Enhanced harmonic conversion efficiency in the self-guided propagation of femtosecond ultraviolet laser pulses in argon,” Appl. Phys. B80(2), 211–214 (2005).
[CrossRef]

Vorob’ev, V. V.

V. V. Vorob’ev, “Thermal blooming of laser beams in the atmosphere,” Prog. Quantum Electron.15(1–2), 1–152 (1991).
[CrossRef]

Wahlstrand, J. K.

Y.-H. Cheng, J. K. Wahlstrand, N. Jhajj, and H. M. Milchberg, “The effect of long timescale gas dynamics on femtosecond filamentation,” Opt. Express21(4), 4740–4751 (2013).
[CrossRef] [PubMed]

J. K. Wahlstrand, Y.-H. Cheng, and H. M. Milchberg, “High field optical nonlinearity and the Kramers-Kronig relations,” Phys. Rev. Lett.109(11), 113904 (2012).
[CrossRef] [PubMed]

Wright, E. M.

Zhavoronkov, N.

Appl. Phys. B

N. Kortsalioudakis, M. Tatarakis, N. Vakakis, S. D. Moustaizis, M. Franco, B. Prade, A. Mysyrowicz, N. A. Papadogiannis, A. Couairon, and S. Tzortzakis, “Enhanced harmonic conversion efficiency in the self-guided propagation of femtosecond ultraviolet laser pulses in argon,” Appl. Phys. B80(2), 211–214 (2005).
[CrossRef]

C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, “Generation of intense, carrier-envelope phase-locked few-cycle laser pulses through filamentation,” Appl. Phys. B79(6), 673–677 (2004).
[CrossRef]

J. Opt. Soc. Am.

Opt. Express

Opt. Lett.

Phys. Rep.

A. Couairon and A. Mysyrowicz, “Femtosecond filamentation in transparent media,” Phys. Rep.441(2–4), 47–189 (2007).
[CrossRef]

Phys. Rev. Lett.

N. Aközbek, A. Iwasaki, A. Becker, M. Scalora, S. L. Chin, and C. M. Bowden, “Third-harmonic generation and self-channeling in air using high-power femtosecond laser pulses,” Phys. Rev. Lett.89(14), 143901 (2002).
[CrossRef] [PubMed]

P. B. Corkum, C. Rolland, and T. Srinivasan-Rao, “Supercontinuum generation in gases,” Phys. Rev. Lett.57(18), 2268–2271 (1986).
[CrossRef] [PubMed]

J. K. Wahlstrand, Y.-H. Cheng, and H. M. Milchberg, “High field optical nonlinearity and the Kramers-Kronig relations,” Phys. Rev. Lett.109(11), 113904 (2012).
[CrossRef] [PubMed]

Proc. IEEE

D. C. Smith, “High-power laser propagation: Thermal blooming,” Proc. IEEE65(12), 1679–1714 (1977).
[CrossRef]

Proc. R. Soc. London A Math. Phys. Sci.

A. Dalgarno and A. E. Kingston, “The refractive indices and Verdet constants of the inert gases,” Proc. R. Soc. London A Math. Phys. Sci.259(1298), 424–431 (1960).
[CrossRef]

Prog. Quantum Electron.

V. V. Vorob’ev, “Thermal blooming of laser beams in the atmosphere,” Prog. Quantum Electron.15(1–2), 1–152 (1991).
[CrossRef]

Other

http://webbook.nist.gov/chemistry/fluid/

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Figures (4)

Fig. 1
Fig. 1

Experimental setup: the pump and probe travel collinearly through the gas cell. The probe beam is relay imaged from the axial center of the plasma where the density hole is produced.

Fig. 2
Fig. 2

Two-dimensional plots of gas density in 1 atm xenon and air created by 1 kHz pulse trains with 0.12 mJ and 1.5 mJ per pulse respectively. The image was taken in between pulses in the pulse train. The deep center region was created largely by the pulse prior to the probe, while the larger, shallower background is due to the accumulation of heat from earlier pulses in the train.

Fig. 3
Fig. 3

Top panel: Image of deflected white light supercontinuum spot as a function of pulse number in the 1 kHz pulse train. Lower panels: Hole parameters as a function of pulse number in the pulse train. The fast shutter is opened just before pulse 1. Equilibrium is approached by about the 250th pulse (at 250 ms).The inset in the second panel is a typical relative density profile extracted from the interferogram.

Fig. 4
Fig. 4

Far field beam deflection angle versus pulse number in 1 kHz plus train. Blue squares: measurement; red squares: ray optics calculation using measured gas density profiles.

Equations (3)

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d 2 x d z 2 = dΔn dx
Δn=Δ n 0 exp(β x 2 γ z 2 )
dx dz | z= dx dz | z= =Δθ= dΔn( x( z ),z ) dx dz 4π Δ n 0 β x 0 γ e β x 0 2

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