Abstract

We investigate the dynamics of femtosecond laser pulses propagating in a hollow fiber filled with argon, through a full numerical solution of the nonlinear Schrödinger equation. The simulation results show that, if the intensity is low and no ionization takes place, the spatial profile of the beam does not change very much so that its propagation model may be simplified to a one-dimensional model. If the intensity is high and ionization takes place, the spatial dynamics as well as temporal dynamics become very complicated because of self-focusing and defocusing. It is found that, for the same value of the B integral, self-focusing inside a hollow fiber can be substantially suspended by a differential gas pressure technique, where the gas pressure is set to be a minimum at the entrance and then increased with the propagation distance. Numerical simulations show that using such a technique, the energy transmitted during propagation inside hollow fiber is significantly enhanced, and the spatial phase is also improved.

© 2003 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
  6. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in Fortran (Cambridge University, Cambridge, UK, 1992), pp. 701–740.
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    [CrossRef]
  8. E. Priori, G. Cerullo, M. Nisoli, S. Stagira, S. De Silvestri, P. Villoresi, L. Poletto, P. Ceccherini, and C. Altucci, “Nonadiabtic three-dimensional model of high-order harmonic generation in the few-optical-cycle regime,” Phys. Rev. A 61, 063801 (2000).
    [CrossRef]
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    [CrossRef]
  10. A. M. Perelemov, V. S. Popov, and M. V. Terent’ev, “Ionization of atoms in alternating electric field,” Sov. Phys. JETP 23, 924–934 (1966).
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    [CrossRef]
  12. Catalog (CVI Laser Corporation, Albuquerque, New Mexico, 1997).
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  15. M. Nurhuda, A. Suda, M. Hatayama, K. Nagasaka, and K. Midorikawa, “Propagation dynamics of femtosecond laser pulses in argon,” Phys. Rev. A 66, 023811 (2002).
    [CrossRef]

2002

M. Nurhuda, A. Suda, and K. Midorikawa, “Ionization-induced high order nonlinear susceptibility,” Phys. Rev. A 66, 041802 (2002).
[CrossRef]

M. Nurhuda, A. Suda, M. Hatayama, K. Nagasaka, and K. Midorikawa, “Propagation dynamics of femtosecond laser pulses in argon,” Phys. Rev. A 66, 023811 (2002).
[CrossRef]

2001

N. H. Shon, A. Suda, Y. Tamaki, and K. Midorikawa, “High-order harmonic and attosecond pulse generations: bulk media versus hollow waveguides,” Phys. Rev. A 63, 063806 (2001).
[CrossRef]

2000

1998

1996

M. Nisoli, S. De Silvestri, and O. Svelto, “Generation of high energy 10 fs pulses by a new pulse compression technique,” Appl. Phys. Lett. 68, 2793–2795 (1996).
[CrossRef]

1988

S. F. J. Larochelle, A. Talebpour, and S. L. Chin, “Coulomb effect in multiphoton ionization of rare-gas atom,” J. Phys. B 31, 1215–1224 (1988).
[CrossRef]

1966

A. M. Perelemov, V. S. Popov, and M. V. Terent’ev, “Ionization of atoms in alternating electric field,” Sov. Phys. JETP 23, 924–934 (1966).

Altucci, C.

E. Priori, G. Cerullo, M. Nisoli, S. Stagira, S. De Silvestri, P. Villoresi, L. Poletto, P. Ceccherini, and C. Altucci, “Nonadiabtic three-dimensional model of high-order harmonic generation in the few-optical-cycle regime,” Phys. Rev. A 61, 063801 (2000).
[CrossRef]

Brabec, T.

Ceccherini, P.

E. Priori, G. Cerullo, M. Nisoli, S. Stagira, S. De Silvestri, P. Villoresi, L. Poletto, P. Ceccherini, and C. Altucci, “Nonadiabtic three-dimensional model of high-order harmonic generation in the few-optical-cycle regime,” Phys. Rev. A 61, 063801 (2000).
[CrossRef]

Cerullo, G.

E. Priori, G. Cerullo, M. Nisoli, S. Stagira, S. De Silvestri, P. Villoresi, L. Poletto, P. Ceccherini, and C. Altucci, “Nonadiabtic three-dimensional model of high-order harmonic generation in the few-optical-cycle regime,” Phys. Rev. A 61, 063801 (2000).
[CrossRef]

Chin, S. L.

S. F. J. Larochelle, A. Talebpour, and S. L. Chin, “Coulomb effect in multiphoton ionization of rare-gas atom,” J. Phys. B 31, 1215–1224 (1988).
[CrossRef]

De Silvestri, S.

E. Priori, G. Cerullo, M. Nisoli, S. Stagira, S. De Silvestri, P. Villoresi, L. Poletto, P. Ceccherini, and C. Altucci, “Nonadiabtic three-dimensional model of high-order harmonic generation in the few-optical-cycle regime,” Phys. Rev. A 61, 063801 (2000).
[CrossRef]

M. Nisoli, S. De Silvestri, and O. Svelto, “Generation of high energy 10 fs pulses by a new pulse compression technique,” Appl. Phys. Lett. 68, 2793–2795 (1996).
[CrossRef]

Fibich, G.

Gaeta, A.

Hatayama, M.

M. Nurhuda, A. Suda, M. Hatayama, K. Nagasaka, and K. Midorikawa, “Propagation dynamics of femtosecond laser pulses in argon,” Phys. Rev. A 66, 023811 (2002).
[CrossRef]

M. Hatayama, A. Suda, M. Nurhuda, K. Nagasaka, and K. Midorikawa, “Spatiotemporal dynamics of high-intensity femtosecond laser pulses propagating in argon,” J. Opt. Soc. Am. B 20, 603–608 (2000).
[CrossRef]

Karasawa, N.

Larochelle, S. F. J.

S. F. J. Larochelle, A. Talebpour, and S. L. Chin, “Coulomb effect in multiphoton ionization of rare-gas atom,” J. Phys. B 31, 1215–1224 (1988).
[CrossRef]

Midorikawa, K.

M. Nurhuda, A. Suda, and K. Midorikawa, “Ionization-induced high order nonlinear susceptibility,” Phys. Rev. A 66, 041802 (2002).
[CrossRef]

M. Nurhuda, A. Suda, M. Hatayama, K. Nagasaka, and K. Midorikawa, “Propagation dynamics of femtosecond laser pulses in argon,” Phys. Rev. A 66, 023811 (2002).
[CrossRef]

N. H. Shon, A. Suda, Y. Tamaki, and K. Midorikawa, “High-order harmonic and attosecond pulse generations: bulk media versus hollow waveguides,” Phys. Rev. A 63, 063806 (2001).
[CrossRef]

M. Hatayama, A. Suda, M. Nurhuda, K. Nagasaka, and K. Midorikawa, “Spatiotemporal dynamics of high-intensity femtosecond laser pulses propagating in argon,” J. Opt. Soc. Am. B 20, 603–608 (2000).
[CrossRef]

Morita, R.

Nagasaka, K.

M. Nurhuda, A. Suda, M. Hatayama, K. Nagasaka, and K. Midorikawa, “Propagation dynamics of femtosecond laser pulses in argon,” Phys. Rev. A 66, 023811 (2002).
[CrossRef]

M. Hatayama, A. Suda, M. Nurhuda, K. Nagasaka, and K. Midorikawa, “Spatiotemporal dynamics of high-intensity femtosecond laser pulses propagating in argon,” J. Opt. Soc. Am. B 20, 603–608 (2000).
[CrossRef]

Nisoli, M.

E. Priori, G. Cerullo, M. Nisoli, S. Stagira, S. De Silvestri, P. Villoresi, L. Poletto, P. Ceccherini, and C. Altucci, “Nonadiabtic three-dimensional model of high-order harmonic generation in the few-optical-cycle regime,” Phys. Rev. A 61, 063801 (2000).
[CrossRef]

M. Nisoli, S. De Silvestri, and O. Svelto, “Generation of high energy 10 fs pulses by a new pulse compression technique,” Appl. Phys. Lett. 68, 2793–2795 (1996).
[CrossRef]

Nurhuda, M.

M. Nurhuda, A. Suda, and K. Midorikawa, “Ionization-induced high order nonlinear susceptibility,” Phys. Rev. A 66, 041802 (2002).
[CrossRef]

M. Nurhuda, A. Suda, M. Hatayama, K. Nagasaka, and K. Midorikawa, “Propagation dynamics of femtosecond laser pulses in argon,” Phys. Rev. A 66, 023811 (2002).
[CrossRef]

M. Hatayama, A. Suda, M. Nurhuda, K. Nagasaka, and K. Midorikawa, “Spatiotemporal dynamics of high-intensity femtosecond laser pulses propagating in argon,” J. Opt. Soc. Am. B 20, 603–608 (2000).
[CrossRef]

Perelemov, A. M.

A. M. Perelemov, V. S. Popov, and M. V. Terent’ev, “Ionization of atoms in alternating electric field,” Sov. Phys. JETP 23, 924–934 (1966).

Poletto, L.

E. Priori, G. Cerullo, M. Nisoli, S. Stagira, S. De Silvestri, P. Villoresi, L. Poletto, P. Ceccherini, and C. Altucci, “Nonadiabtic three-dimensional model of high-order harmonic generation in the few-optical-cycle regime,” Phys. Rev. A 61, 063801 (2000).
[CrossRef]

Popov, V. S.

A. M. Perelemov, V. S. Popov, and M. V. Terent’ev, “Ionization of atoms in alternating electric field,” Sov. Phys. JETP 23, 924–934 (1966).

Priori, E.

E. Priori, G. Cerullo, M. Nisoli, S. Stagira, S. De Silvestri, P. Villoresi, L. Poletto, P. Ceccherini, and C. Altucci, “Nonadiabtic three-dimensional model of high-order harmonic generation in the few-optical-cycle regime,” Phys. Rev. A 61, 063801 (2000).
[CrossRef]

Shigekawa, H.

Shon, N. H.

N. H. Shon, A. Suda, Y. Tamaki, and K. Midorikawa, “High-order harmonic and attosecond pulse generations: bulk media versus hollow waveguides,” Phys. Rev. A 63, 063806 (2001).
[CrossRef]

Stagira, S.

E. Priori, G. Cerullo, M. Nisoli, S. Stagira, S. De Silvestri, P. Villoresi, L. Poletto, P. Ceccherini, and C. Altucci, “Nonadiabtic three-dimensional model of high-order harmonic generation in the few-optical-cycle regime,” Phys. Rev. A 61, 063801 (2000).
[CrossRef]

Suda, A.

M. Nurhuda, A. Suda, and K. Midorikawa, “Ionization-induced high order nonlinear susceptibility,” Phys. Rev. A 66, 041802 (2002).
[CrossRef]

M. Nurhuda, A. Suda, M. Hatayama, K. Nagasaka, and K. Midorikawa, “Propagation dynamics of femtosecond laser pulses in argon,” Phys. Rev. A 66, 023811 (2002).
[CrossRef]

N. H. Shon, A. Suda, Y. Tamaki, and K. Midorikawa, “High-order harmonic and attosecond pulse generations: bulk media versus hollow waveguides,” Phys. Rev. A 63, 063806 (2001).
[CrossRef]

M. Hatayama, A. Suda, M. Nurhuda, K. Nagasaka, and K. Midorikawa, “Spatiotemporal dynamics of high-intensity femtosecond laser pulses propagating in argon,” J. Opt. Soc. Am. B 20, 603–608 (2000).
[CrossRef]

Svelto, O.

M. Nisoli, S. De Silvestri, and O. Svelto, “Generation of high energy 10 fs pulses by a new pulse compression technique,” Appl. Phys. Lett. 68, 2793–2795 (1996).
[CrossRef]

Talebpour, A.

S. F. J. Larochelle, A. Talebpour, and S. L. Chin, “Coulomb effect in multiphoton ionization of rare-gas atom,” J. Phys. B 31, 1215–1224 (1988).
[CrossRef]

Tamaki, Y.

N. H. Shon, A. Suda, Y. Tamaki, and K. Midorikawa, “High-order harmonic and attosecond pulse generations: bulk media versus hollow waveguides,” Phys. Rev. A 63, 063806 (2001).
[CrossRef]

Tempea, G.

Terent’ev, M. V.

A. M. Perelemov, V. S. Popov, and M. V. Terent’ev, “Ionization of atoms in alternating electric field,” Sov. Phys. JETP 23, 924–934 (1966).

Villoresi, P.

E. Priori, G. Cerullo, M. Nisoli, S. Stagira, S. De Silvestri, P. Villoresi, L. Poletto, P. Ceccherini, and C. Altucci, “Nonadiabtic three-dimensional model of high-order harmonic generation in the few-optical-cycle regime,” Phys. Rev. A 61, 063801 (2000).
[CrossRef]

Yamashita, M.

Appl. Phys. Lett.

M. Nisoli, S. De Silvestri, and O. Svelto, “Generation of high energy 10 fs pulses by a new pulse compression technique,” Appl. Phys. Lett. 68, 2793–2795 (1996).
[CrossRef]

J. Opt. Soc. Am. B

J. Phys. B

S. F. J. Larochelle, A. Talebpour, and S. L. Chin, “Coulomb effect in multiphoton ionization of rare-gas atom,” J. Phys. B 31, 1215–1224 (1988).
[CrossRef]

Opt. Lett.

Phys. Rev. A

N. H. Shon, A. Suda, Y. Tamaki, and K. Midorikawa, “High-order harmonic and attosecond pulse generations: bulk media versus hollow waveguides,” Phys. Rev. A 63, 063806 (2001).
[CrossRef]

E. Priori, G. Cerullo, M. Nisoli, S. Stagira, S. De Silvestri, P. Villoresi, L. Poletto, P. Ceccherini, and C. Altucci, “Nonadiabtic three-dimensional model of high-order harmonic generation in the few-optical-cycle regime,” Phys. Rev. A 61, 063801 (2000).
[CrossRef]

M. Nurhuda, A. Suda, and K. Midorikawa, “Ionization-induced high order nonlinear susceptibility,” Phys. Rev. A 66, 041802 (2002).
[CrossRef]

M. Nurhuda, A. Suda, M. Hatayama, K. Nagasaka, and K. Midorikawa, “Propagation dynamics of femtosecond laser pulses in argon,” Phys. Rev. A 66, 023811 (2002).
[CrossRef]

Sov. Phys. JETP

A. M. Perelemov, V. S. Popov, and M. V. Terent’ev, “Ionization of atoms in alternating electric field,” Sov. Phys. JETP 23, 924–934 (1966).

Other

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in Fortran (Cambridge University, Cambridge, UK, 1992), pp. 701–740.

Catalog (CVI Laser Corporation, Albuquerque, New Mexico, 1997).

G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, San Diego, Calif., 1995), pp. 29–55.

N. N. Akhmediev and A. Ankiewicz, Nonlinear Pulses and Beams (Chapmann & Hall, London, 1997), pp. 13–15.

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Figures (7)

Fig. 1
Fig. 1

Plot of spatiotemporal profiles of intensity as a function of propagation distance z. The horizontal axis represents the radial distance (from -0.125 mm to 0.125 mm), and the vertical axis is for time. The pulse energy used for simulation was 0.1 mJ, and the gas pressure was 2 atm.

Fig. 2
Fig. 2

Display showing the comparison between the results obtained from direct 3D numerical simulation of femtosecond laser propagation in a hollow waveguide (solid lines) with those from a 1D model (dotted line). (a) Energy transmittance; (b) the spectral and the phase profiles.

Fig. 3
Fig. 3

Display of the spatial and temporal profiles of intensity as a function of propagation distance. The laser energy used for simulation was 0.8 mJ, and the gas pressure was set to be static at 0.8 atm.

Fig. 4
Fig. 4

In (a), the occupation energy in the fundamental mode (n=1) and the next three lowest excited modes are shown. In (b), the right side, the energy transmittance and accumulated energy loss due to ionization and leakage are shown. Parameters used for simulation were the same as those shown in Fig. 3.

Fig. 5
Fig. 5

Display of spatial and temporal profile obtained at different propagation distances. The parameters used for the simulations were the same as those used in Fig. 3, except for the gas pressure, which was made to vary increasingly.

Fig. 6
Fig. 6

In (a), the left side, the occupation energy in the first three lowest modes is shown. In (b), the right, the energy transmittance, the accumulated ionization loss, and leakage are shown as a function of propagation distance. The parameters for simulation were the same as those shown in Fig. 5.

Fig. 7
Fig. 7

Spatiospectral profiles of the wave for constant gas pressure (upper left) and for differential gas pressure (lower left) at a distance of 50 cm from the exit are compared. Above each of these are the power spectra obtained by integrating over the circular area of 2 mm. On the right side are the spatial–spectral phase profiles of the waves. Above these are the on-axis spectral phase profiles.

Equations (16)

Equations on this page are rendered with MathJax. Learn more.

2E(r, z, t)-2c2zt E(r, z, t)
=10c22t2 PNL(r, z, t),
PNL(r, z, t)=Δχ(|E(r, z, t)|2)E(r, z, t)-η ωp20c2 E(r, z, t),
ρt=N0(1-ρ)Γ(I),
2c2zt E(r, z, t)=2E(r, z, t),
2c2zt E(r, z, t)=-10c22t2 PNL(r, z, t).
E(r, z, t)=exp(-iω0t)-E(r, z, ω-ω0)×exp[-i(ω-ω0)t]dω+c.c.=exp(-iω0t)E(r, z, t)+c.c.
E(r, z, ω-ω0)=nmbnm(z, ω-ω0)Jmλnra0,
bn0(z+Δz, ω-ω0)=exp(iβnΔz-αnΔz)×bn0(z, ω-ω0),
EH(r, z+Δz, t)
=F-1nbn0(z+Δz, ω-ω0)J0λnra0,
E(r, z, t)=R(r)-A(z, ω-ω0)exp[-i(ω-ω0)t]dω,
2R+[(ω)k02-k2]R=0,
2ik0A(z, ω-ω0)z+(k2-k02)A(z, ω-ω0)=0.
B=0Lp(x)dx=60cm atm.
p(x)=p02+xL (pL2-p02),

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