Abstract

The three-dimensional (3-D) pulse propagation code, pulsed ultrashort laser simulation emulator (PULSE), has been used to model the interaction of thermal blooming, diffraction, and nonlinear self-focusing in the atmosphere. PULSE is a derivative of the free-electron laser (FEL) simulation code, free-electron laser experiment (FELEX) [Nucl. Instrum. Methods Phys. Res. A 250, 449 (1986)] that was used for many years to model the 3-D interaction of optical pulses with electron beams. This code has now been modified to model nonlinear material interactions. In its current configuration, an electromagnetic pulse is modeled on a Cartesian grid, thereby allowing for arbitrary amplitude and phase modulations in the transverse (x, y) and longitudinal (z) directions. The code includes models for thermal blooming (in a laminar transverse wind field), diffraction, Kerr self-focusing and self-phase modulation, plasma defocusing and absorption, and multiphoton and avalanche ionization. Simulation of picosecond length pulses indicate that the defocusing effects of thermal blooming and diffraction can be effectively eliminated by Kerr self-focusing. Simulation results show that the beam arrives at the target with a spot size comparable to (or less than) its initial spot size. For propagation distances of many kilometers, this can result in order-of-magnitude increases of the on-target intensity at range, which can significantly reduce the average power requirement of the laser required to provide a given irradiance level.

© 2003 Optical Society of America

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References

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  1. B. D. McVey, “3-D simulations of free-electron laser physics,” Nucl. Instrum. Methods Phys. Res. A 250, 449-455 (1986).
    [CrossRef]
  2. M. Mlejnek, E. M. Wright, and J. V. Moloney, “Dynamic spatial replenishment of femtosecond pulses propagating in air,” Opt. Lett. 23, 382-384 (1998).
    [CrossRef]
  3. N. Ako¨zbek, C. M. Bowden, and S. L. Chin, “Propagation dynamics of ultra-short high-power laser pulses in air: supercontinuum generation and transverse ring formation,” J. Mod. Opt. 49, 475-486 (2002).
    [CrossRef]
  4. S. Tzortzakis, L. Bergé, A. Couairon, M. Franco, B. Prade, and A. Mysyrowicz, “Breakup and fusion of self-guided femtosecond light pulses in air,” Phys. Rev. Lett. 86, 5470-5473 (2001).
    [CrossRef] [PubMed]
  5. J. F. Schonfeld, “Instability in saturated full-field compensation for thermal blooming,” J. Opt. Soc. Am. B 9, 1794-1799 (1992).
    [CrossRef]
  6. F. G. Smith, “Atmospheric propagation of radiation,” in The Infrared and Electro-Optical Systems Handbook, Vol. 2, J. S. Accetta and D. L. Shurnaker, eds. (SPIE Press, Bellingham, Wash., 1993), p. 88.
  7. Integrating over the intensity profile of a Gaussian and dividing by the area gives (1 − e−2)/2=1/2.3.
  8. Linearization of Beer’s law I=I0 exp(−αz)∼I0(1−αz).
  9. The thermal diffusivity for air χ can be expressed in term of the thermal conductivity κT as χ=κT/(ρatmCp)∼ 0.2 cm2/s. Since χ/Dbeam≪vwind, one is in the convection dominated regime.
  10. R. W. Boyd, Nonlinear Optics (Academic, San Diego, Calif., 1992), Eq. 4.1.15.
  11. R. L. Sutherland gives n2 = 1 × 10−18 at 1.06 μm; see Handbook of Nonlinear Optics (Marcel Dekker, Monticello, N.Y., 1996).
  12. n0, Cp, and ρatm for air are taken from the CRC Handbook of Chemistry and Physics, 68th ed. (CRC Press, Boca Raton, Fla., 1987).
  13. This extinction value taken from a FASCODE run for mid-latitude summer with 23-km visibility assuming a Beer’s law dependence.
  14. L. V. Keldysh, “Ionization in the field of a strong electromagnetic wave,” Sov. Phys. JETP 20, 1307-1314 (1965).
  15. D. S. Clark and N. J. Fisch, “Regime for a self-ionizing Raman laser amplifier,” Phys. Plasmas 9, 2772–2780 (2002).
    [CrossRef]

2002 (2)

N. Ako¨zbek, C. M. Bowden, and S. L. Chin, “Propagation dynamics of ultra-short high-power laser pulses in air: supercontinuum generation and transverse ring formation,” J. Mod. Opt. 49, 475-486 (2002).
[CrossRef]

D. S. Clark and N. J. Fisch, “Regime for a self-ionizing Raman laser amplifier,” Phys. Plasmas 9, 2772–2780 (2002).
[CrossRef]

2001 (1)

S. Tzortzakis, L. Bergé, A. Couairon, M. Franco, B. Prade, and A. Mysyrowicz, “Breakup and fusion of self-guided femtosecond light pulses in air,” Phys. Rev. Lett. 86, 5470-5473 (2001).
[CrossRef] [PubMed]

1998 (1)

1992 (1)

1986 (1)

B. D. McVey, “3-D simulations of free-electron laser physics,” Nucl. Instrum. Methods Phys. Res. A 250, 449-455 (1986).
[CrossRef]

1965 (1)

L. V. Keldysh, “Ionization in the field of a strong electromagnetic wave,” Sov. Phys. JETP 20, 1307-1314 (1965).

Ako¨zbek, N.

N. Ako¨zbek, C. M. Bowden, and S. L. Chin, “Propagation dynamics of ultra-short high-power laser pulses in air: supercontinuum generation and transverse ring formation,” J. Mod. Opt. 49, 475-486 (2002).
[CrossRef]

Bergé, L.

S. Tzortzakis, L. Bergé, A. Couairon, M. Franco, B. Prade, and A. Mysyrowicz, “Breakup and fusion of self-guided femtosecond light pulses in air,” Phys. Rev. Lett. 86, 5470-5473 (2001).
[CrossRef] [PubMed]

Bowden, C. M.

N. Ako¨zbek, C. M. Bowden, and S. L. Chin, “Propagation dynamics of ultra-short high-power laser pulses in air: supercontinuum generation and transverse ring formation,” J. Mod. Opt. 49, 475-486 (2002).
[CrossRef]

Chin, S. L.

N. Ako¨zbek, C. M. Bowden, and S. L. Chin, “Propagation dynamics of ultra-short high-power laser pulses in air: supercontinuum generation and transverse ring formation,” J. Mod. Opt. 49, 475-486 (2002).
[CrossRef]

Clark, D. S.

D. S. Clark and N. J. Fisch, “Regime for a self-ionizing Raman laser amplifier,” Phys. Plasmas 9, 2772–2780 (2002).
[CrossRef]

Couairon, A.

S. Tzortzakis, L. Bergé, A. Couairon, M. Franco, B. Prade, and A. Mysyrowicz, “Breakup and fusion of self-guided femtosecond light pulses in air,” Phys. Rev. Lett. 86, 5470-5473 (2001).
[CrossRef] [PubMed]

Fisch, N. J.

D. S. Clark and N. J. Fisch, “Regime for a self-ionizing Raman laser amplifier,” Phys. Plasmas 9, 2772–2780 (2002).
[CrossRef]

Franco, M.

S. Tzortzakis, L. Bergé, A. Couairon, M. Franco, B. Prade, and A. Mysyrowicz, “Breakup and fusion of self-guided femtosecond light pulses in air,” Phys. Rev. Lett. 86, 5470-5473 (2001).
[CrossRef] [PubMed]

Keldysh, L. V.

L. V. Keldysh, “Ionization in the field of a strong electromagnetic wave,” Sov. Phys. JETP 20, 1307-1314 (1965).

McVey, B. D.

B. D. McVey, “3-D simulations of free-electron laser physics,” Nucl. Instrum. Methods Phys. Res. A 250, 449-455 (1986).
[CrossRef]

Mlejnek, M.

Moloney, J. V.

Mysyrowicz, A.

S. Tzortzakis, L. Bergé, A. Couairon, M. Franco, B. Prade, and A. Mysyrowicz, “Breakup and fusion of self-guided femtosecond light pulses in air,” Phys. Rev. Lett. 86, 5470-5473 (2001).
[CrossRef] [PubMed]

Prade, B.

S. Tzortzakis, L. Bergé, A. Couairon, M. Franco, B. Prade, and A. Mysyrowicz, “Breakup and fusion of self-guided femtosecond light pulses in air,” Phys. Rev. Lett. 86, 5470-5473 (2001).
[CrossRef] [PubMed]

Schonfeld, J. F.

Tzortzakis, S.

S. Tzortzakis, L. Bergé, A. Couairon, M. Franco, B. Prade, and A. Mysyrowicz, “Breakup and fusion of self-guided femtosecond light pulses in air,” Phys. Rev. Lett. 86, 5470-5473 (2001).
[CrossRef] [PubMed]

Wright, E. M.

J. Mod. Opt. (1)

N. Ako¨zbek, C. M. Bowden, and S. L. Chin, “Propagation dynamics of ultra-short high-power laser pulses in air: supercontinuum generation and transverse ring formation,” J. Mod. Opt. 49, 475-486 (2002).
[CrossRef]

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

Nucl. Instrum. Methods Phys. Res. A (1)

B. D. McVey, “3-D simulations of free-electron laser physics,” Nucl. Instrum. Methods Phys. Res. A 250, 449-455 (1986).
[CrossRef]

Opt. Lett. (1)

Phys. Plasmas (1)

D. S. Clark and N. J. Fisch, “Regime for a self-ionizing Raman laser amplifier,” Phys. Plasmas 9, 2772–2780 (2002).
[CrossRef]

Phys. Rev. Lett. (1)

S. Tzortzakis, L. Bergé, A. Couairon, M. Franco, B. Prade, and A. Mysyrowicz, “Breakup and fusion of self-guided femtosecond light pulses in air,” Phys. Rev. Lett. 86, 5470-5473 (2001).
[CrossRef] [PubMed]

Sov. Phys. JETP (1)

L. V. Keldysh, “Ionization in the field of a strong electromagnetic wave,” Sov. Phys. JETP 20, 1307-1314 (1965).

Other (8)

F. G. Smith, “Atmospheric propagation of radiation,” in The Infrared and Electro-Optical Systems Handbook, Vol. 2, J. S. Accetta and D. L. Shurnaker, eds. (SPIE Press, Bellingham, Wash., 1993), p. 88.

Integrating over the intensity profile of a Gaussian and dividing by the area gives (1 − e−2)/2=1/2.3.

Linearization of Beer’s law I=I0 exp(−αz)∼I0(1−αz).

The thermal diffusivity for air χ can be expressed in term of the thermal conductivity κT as χ=κT/(ρatmCp)∼ 0.2 cm2/s. Since χ/Dbeam≪vwind, one is in the convection dominated regime.

R. W. Boyd, Nonlinear Optics (Academic, San Diego, Calif., 1992), Eq. 4.1.15.

R. L. Sutherland gives n2 = 1 × 10−18 at 1.06 μm; see Handbook of Nonlinear Optics (Marcel Dekker, Monticello, N.Y., 1996).

n0, Cp, and ρatm for air are taken from the CRC Handbook of Chemistry and Physics, 68th ed. (CRC Press, Boca Raton, Fla., 1987).

This extinction value taken from a FASCODE run for mid-latitude summer with 23-km visibility assuming a Beer’s law dependence.

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Figures (3)

Fig. 1
Fig. 1

Initial Gaussian transverse intensity (a) at the center of the pulse, where the transverse grid scale is 20 cm on a side, and (b) after 1.3-km propagation with no self-focusing.

Fig. 2
Fig. 2

Transverse intensity (a) after 1.3-km propagation with self-focusing and Fduty=2.3×10-6 and (b) with Fduty=1.15×10-6.

Fig. 3
Fig. 3

Three-dimensional electric-field magnitude of the self-focused pulse showing four isocontours at equivalent intensities of 0.004, 0.11, 0.6, and 1.1 GW/cm2. The propagation direction is toward the left. The propagation axis has been expanded by a factor of 100 to better depict variations in this direction. Note the hourglass-shaped contour at 0.11 GW/cm2 caused by the intensity-dependent self-focusing effect.

Equations (28)

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Ndry=(n-1)×106=237.2+526.3νa2νa2-ν2+11.69νb2νb2-ν2PdryT,
Δntb=(1-n0) ΔTT0.
E=α I02.3DbeamvwindJcm3,
ΔT=ECpρd=0.4 αI0CpρdDbeamvwind,
Δntb=(1-n0)T0ECpρd=0.4(1-n0) αT0CpρdDbeamvwind I0,
n=n0+ΔnK=n0+n2Ip,
ΔnK=n2Ip=n24PpπDbeam=n2Fduty4P0πDbeam2,
FdutyDbeam=2.5 n2n0-1T0Cpρdvwindα=5.8×10-6(cm),
k=2kω2=-1vg2vgω.
Δt=Lvg1-Lvg2=L vg2-vg1vg1vg2L Δvgvg2,
Δvgvgω Δω=-vg2kΔω=vg2k2πcλ2 Δλ.
Δt=Lk2πcλ2 Δλ,
L=λ2Δt2πckΔλ,
2E(x, t)+2inkvacEz
=-2nkvac2n2IE+nkvack2Et2+1-i vω0ωp2c2 E-iβ(κ)Iκ-1E,
I=c|E|28×107π,
Sretarded1τ-t|E(t)|2exp[-(t-t)/τ]dt
=1k0k=1k0EkEk*exp[-(k0-k)Δt/τ],
ωp2=4πρe2m,
ρt=β(κ)κω Iκ(1-ρ/ρatm)+1n2σAEi ρI,
γ=2Eimc21/2A=231.42λ(cm)Ei(eV)I(W/cm2)1/2
ρt=(ρatm-ρ)w(A)=(ρatm-ρ) ωκ3/2(2γ)2κ=(1-ρ/ρatm)κω β(κ)Iκ,
β(κ)=2hπρatmc2κ5/2(462.84)2κλ2(κ-1)Ei2κ,
I0(x, y)=Fsimzsim0zsimdzIp(x, y, z),
E(x0, y0)=αyminy0dyvwind I0(x0, y)=αFsimzsimvwindyminy0dy0zsimdzIp(x0, y, z),
Ei0,j0=αFsimΔygridvwindΔzgridzsimj=1j0ck=1K|Ei0,j,k|28π×107,
Δntb=(1-n0)T0ECpρatm=(1-n0)T0Cpρatm×αFsimΔygridvwindΔzgridzsimj=1j0ck=1K|Ei0,j,k|28π×107.
(Δφtb)i0,j0=-2πλ ΔntbΔz=cαFsim4×107Δzλ(n0-1)T0CpρatmΔygridvwind×1Kj=1j0k=1K|Ei0,j,k|2.

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