Abstract

Numerical simulations of nonlinear pulse propagation in air show an initial pulse formed, absorbed by plasma generation, and subsequently replenished by power from the trailing edge. Here we show that this scenario implies that the length scale for filament propagation is relatively insensitive to the peak input power beyond the threshold for filament generation.

© Optical Society of America

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References

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  1. A. Braun, G. Korn, X. Liu, D. Du, J. Squier and G. Mourou. "Self-channeling of high-peak-power femtosecond laser pulses in air," Opt. Lett. 20, 73-5, 1995.
    [CrossRef] [PubMed]
  2. Xin Miao Zhao, P. Rambo and J.-C. Diels. "Filamentation of femtosecond uv pulses in air," In QELS 95. Summaries of Papers Presented at the Quantum Electronics and Laser Science Conference. Technical Digest Series Conference Edition, volume 16, pages 178-9, 1995.
  3. Xin Miao Zhao, J.-C. Diels, Cai Yi Wang and J. M. Elizondo. "Femtosecond ultraviolet laser pulse induced lightning discharges in gases," Quantum Electron. QE-31, 599-612, 1995.
  4. E. T. J. Nibbering, P. F. Curley, G. Grillon, B. S. Prade, M. A. Franco, F. Salin and A. Mysyrowicz. "Conical emission from self-guided femtosecond pulses in air," Opt. Lett. 21, 62-4, 1996.
    [CrossRef] [PubMed]
  5. A. Brodeur, C. Y. Chien, F. A. Ilkov, S. L. Chin, O. G. Kosareva and V. P. Kandidov. "Moving focus in the propagation of ultrashort laser pulses in air," Opt. Lett. 22, 304-6, 1997.
    [CrossRef] [PubMed]
  6. L. Woste, C. Wedekind, H. Wille, P. Rairoux, B. Stein, S. Nikolov, C. Werner, S. Niedermeier, F. Ronneberger, H. Schillinger and R. Sauerbrey. "Femtosecond atmospheric lamp," AT- Fachverlag, Stuttgart, Laser und Optoelectronik, 29, 51-3, 1997.
  7. M. Mlejnek, E. M. Wright and J. V. Moloney. "Dynamic spatial replenishment of femtosecond pulses propagating in air," Opt. Lett. 23, 382-4, 1998.
    [CrossRef]
  8. O. G. Kosareva, V. P. Kandidov, A. Brodeur, C. Y. Chien and S. L. Chin. "Conical emission from laser-plasma interactions in the filamentation of powerful ultrashort laser pulses in air," Opt. Lett. 22, 1332-4, 1997.
    [CrossRef]
  9. H. R. Lange, G. Grillon, J.-F. Ripoche, M. A. Franco, B. Lameuroux, B. S. Prade, A. Mysyrowicz, E. T. J. Nibbering and A. Chiron. "Anomalous long-range propagation of femtosecond laser pulses through air: moving focus or pulse self-guiding?" Opt. Lett. 23, 120-2, 1998.
    [CrossRef]
  10. M. Mlejnek, E. M. Wright and J. V. Moloney. "Moving-focus versus self-waveguiding model for long distance propagation of femtosecond pulses in air," To be published in Quantum Electron. (1999).

Other

A. Braun, G. Korn, X. Liu, D. Du, J. Squier and G. Mourou. "Self-channeling of high-peak-power femtosecond laser pulses in air," Opt. Lett. 20, 73-5, 1995.
[CrossRef] [PubMed]

Xin Miao Zhao, P. Rambo and J.-C. Diels. "Filamentation of femtosecond uv pulses in air," In QELS 95. Summaries of Papers Presented at the Quantum Electronics and Laser Science Conference. Technical Digest Series Conference Edition, volume 16, pages 178-9, 1995.

Xin Miao Zhao, J.-C. Diels, Cai Yi Wang and J. M. Elizondo. "Femtosecond ultraviolet laser pulse induced lightning discharges in gases," Quantum Electron. QE-31, 599-612, 1995.

E. T. J. Nibbering, P. F. Curley, G. Grillon, B. S. Prade, M. A. Franco, F. Salin and A. Mysyrowicz. "Conical emission from self-guided femtosecond pulses in air," Opt. Lett. 21, 62-4, 1996.
[CrossRef] [PubMed]

A. Brodeur, C. Y. Chien, F. A. Ilkov, S. L. Chin, O. G. Kosareva and V. P. Kandidov. "Moving focus in the propagation of ultrashort laser pulses in air," Opt. Lett. 22, 304-6, 1997.
[CrossRef] [PubMed]

L. Woste, C. Wedekind, H. Wille, P. Rairoux, B. Stein, S. Nikolov, C. Werner, S. Niedermeier, F. Ronneberger, H. Schillinger and R. Sauerbrey. "Femtosecond atmospheric lamp," AT- Fachverlag, Stuttgart, Laser und Optoelectronik, 29, 51-3, 1997.

M. Mlejnek, E. M. Wright and J. V. Moloney. "Dynamic spatial replenishment of femtosecond pulses propagating in air," Opt. Lett. 23, 382-4, 1998.
[CrossRef]

O. G. Kosareva, V. P. Kandidov, A. Brodeur, C. Y. Chien and S. L. Chin. "Conical emission from laser-plasma interactions in the filamentation of powerful ultrashort laser pulses in air," Opt. Lett. 22, 1332-4, 1997.
[CrossRef]

H. R. Lange, G. Grillon, J.-F. Ripoche, M. A. Franco, B. Lameuroux, B. S. Prade, A. Mysyrowicz, E. T. J. Nibbering and A. Chiron. "Anomalous long-range propagation of femtosecond laser pulses through air: moving focus or pulse self-guiding?" Opt. Lett. 23, 120-2, 1998.
[CrossRef]

M. Mlejnek, E. M. Wright and J. V. Moloney. "Moving-focus versus self-waveguiding model for long distance propagation of femtosecond pulses in air," To be published in Quantum Electron. (1999).

Supplementary Material (4)

» Media 1: MOV (2232 KB)     
» Media 2: MOV (2356 KB)     
» Media 3: MOV (2558 KB)     
» Media 4: MOV (2690 KB)     

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Figures (6)

Figure 1.
Figure 1.

Global maximum over time of the on-axis intensity as a function of propagation distance z for peak input power of ~ 4Pcr . The Rayleigh range was in this case ~ 2 m. (Dashed line … n 2 without the Raman contribution.)

Figure 2.
Figure 2.

Global maximum over time of the on-axis intensity as a function of propagation distance z for peak input power of ~ 6Pcr . The Rayleigh range was in this case ~ 2 m. (Dashed line … n 2 without the Raman contribution.)

Figure 3.
Figure 3.

Global maximum over time of the on-axis intensity as a function of propagation distance z for peak input power of ~ 6.5Pcr . The Rayleigh range was in this case ~ 2 m. Dashed line … n 2 without the Raman contribution.)

Figure 4.
Figure 4.

Global maximum over time of the on-axis intensity as a function of propagation distance z for peak input power of ~ 7Pcr . The Rayleigh range was in this case ~ 2 m. (Dashed line … n 2 without the Raman contribution.)

Figure 5.
Figure 5.

The intensity of The field for the case shown in Fig. 1 (Raman response included) at the propagation distance of 1 m.

Figure 6.
Figure 6.

The intensity of the field for the case shown in Fig. 1 (Raman response included) at the propagation distance of 2.8 m.

Equations (5)

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ε z = i 2 k ( 2 r 2 + 1 r r ) ε ik 2 2 ε t 2 σ 2 ( 1 + iωτ ) ρε β ( K ) 2 ε 2 K 2 ε
+ i k 0 ( 1 f ) n 2 ε 2 ε + i k 0 f n 2 [ dt R ( t t ) ε ( t ) 2 ] ε ,
R ( t ) = θ ( t ) Ω 2 e Γ t / 2 sin ( Λ t ) Λ , Λ = Ω 2 Γ 2 / 4 ,
ρ t = 1 n b 2 σ E g ρ ε 2 + β ( K ) ε 2 K Kħω a ρ 2 .
ε ( r , 0 , t ) = 2 P in π ω 0 2 exp ( r 2 ω 0 2 t 2 t p 2 ) ,

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