high-power laser pulse propagation in silica
DESCRIPTION
Diffraction. Higher-order dispersion. Group velocity dispersion. Multi-photon absorption. Kerr response. Plasma defocusing. correction beyond the slowly varying envelope approximation (SVEA). Evolution of the electron density r in the conduction band. from the Keldysh theory. - PowerPoint PPT PresentationTRANSCRIPT
ナノデザイン特論１（石川顕一）学内向け講義資料
High-power laser pulse propagation in High-power laser pulse propagation in silica silica
Extended Nonlinear Schrödinger EquationExtended Nonlinear Schrödinger Equation
Group velocity dispersionGroup velocity dispersionHigher-order dispersionHigher-order dispersion
Kerr responseKerr response
DiffractionDiffraction
Plasma defocusingPlasma defocusing
Multi-photon absorptionMulti-photon absorption
in a reference frame moving at the group velocityin a reference frame moving at the group velocity
correction beyond the slowly varying envelope approximation (SVEA)correction beyond the slowly varying envelope approximation (SVEA)
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∂E∂z
+i2β2
∂2E∂t2
−i6β3
∂3E∂t3
−i
2n0k0
∂2
∂r2 +1r∂∂r
⎛
⎝ ⎜ ⎞
⎠ ⎟ 1−
iω0
∂∂t
⎛
⎝ ⎜ ⎞
⎠ ⎟ E
=in2k0 1+iω0
∂∂t
⎛
⎝ ⎜ ⎞
⎠ ⎟ E
2E( )−
ik0
21−
iω0
∂∂t
⎛
⎝ ⎜ ⎞
⎠ ⎟ ρρcr
E⎛
⎝ ⎜ ⎞
⎠ ⎟ −3σ 6 ρ0 −ρ( )
E2
hω0
⎛
⎝ ⎜
⎞
⎠ ⎟
5
E
Evolution of the electron density Evolution of the electron density in the conduction band in the conduction band
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∂ρ∂t
=σ 6
E2
hω0
⎛
⎝ ⎜
⎞
⎠ ⎟
6
ρ0 −ρ( )
€
ρ0 =2.23×1022 cm-3
€
σ6 =2.6×10−180 cm12s5 from the Keldysh theory
(1)
(2)
ナノデザイン特論１（石川顕一）学内向け講義資料
Change of the spatio-temporal Change of the spatio-temporal intensity profile with propagationintensity profile with propagation
Intensity (1012 W/cm2)
0 5 10 15
0 3 6 9 0 105
zz = 3200 = 3200 mm
200 100 0 -100 -200
0
25
50
75
100
Time (fs)
Rad
ius
r (
m)
3300 3300 mm 3400 3400 mm 3500 3500 mm 3600 3600 mm
3700 3700 mm 3800 3800 mm 4000 4000 mm 4500 4500 mm 5000 5000 mm
Self-focusingSelf-steepening
Self-focusingSelf-steepening Plasma defocusingPlasma defocusing
More than 10 conesMore than 10 cones
1st cone1st cone2nd cone2nd cone 3rd cone3rd cone
input energy = 135mJinput energy = 135mJpropagation distance
(a) (b) (c) (d) (e)
(f) (g) (h) (i) (j)
ナノデザイン特論１（石川顕一）学内向け講義資料
Mechanism of the multiple-cone Mechanism of the multiple-cone formation formation
At At zz = 3340 = 3340 m, the intensity decreases with increasing m, the intensity decreases with increasing rr in the range in the range rr = 9 - 12 = 9 - 12 m, while m, while nn is nearly flat there. is nearly flat there.
Due to self-focusing, the first peak takes up much energy from its vicinity.Due to self-focusing, the first peak takes up much energy from its vicinity. At At zz = 3360 = 3360 m, the second local maximum in m, the second local maximum in nn is formed around is formed around rr = 11.3 = 11.3
m. → The local self-focusing leads to the grow-up or the second cone.m. → The local self-focusing leads to the grow-up or the second cone.
3300 3300 mm 3400 3400 mm
1st cone 2nd cone
Fig. Radial distribution of intensity and refractive index change Fig. Radial distribution of intensity and refractive index change nn at at tt = 44 fs. = 44 fs.
ナノデザイン特論１（石川顕一）学内向け講義資料
0 100 200 300 400
0
5000
Radius (micron)
Propagation distance (micron)
0.0e+00 2.0e+14 4.0e+14 6.0e+14Fluence (1e-15J/cm2)
Fluence vs. Propagation distanceFluence vs. Propagation distance
Self-focusingSelf-focusing
Propagation
Propagation
Propagation
Propagation
distance
distance
((m)m)
Fluence (10Fluence (10-15-15 J/cm J/cm22))
Radius
(m)
Fluence (10-15 J/cm2)
Plasma defocusingPlasma defocusing
Propagation distance (micron)
ナノデザイン特論１（石川顕一）学内向け講義資料
Dependence on the input energyDependence on the input energy
With decreasing input pulse energy,With decreasing input pulse energy, the number of cones decreases.the number of cones decreases. the cones are more parallel to the beam axis.the cones are more parallel to the beam axis.The multiple-cone formation ceases when we further decrease the input energy.The multiple-cone formation ceases when we further decrease the input energy.
Intensity (1012 W/cm2)
0 5 10 15
135 135 JJ, z, z = 4500 = 4500 mm 45 45 JJ, z, z = 5500 = 5500 mm 15 15 JJ, z, z = 7000 = 7000 mm
200 100 0 -100 -200
0
25
50
75
100
Time (fs)200 100 0 -100 -200
0
25
50
75
100
Time (fs)200 100 0 -100 -200
0
25
50
75
100
Time (fs)
Input energyR
adiu
s r
(m
)
Rad
ius
r (
m)
Rad
ius
r (
m)
ナノデザイン特論１（石川顕一）学内向け講義資料
ConclusionConclusion
When the input power is several hundred When the input power is several hundred times higher than times higher than PPcrcr, the pulse is split , the pulse is split many times both temporally and spatially.many times both temporally and spatially.
As a result, the intensity distribution As a result, the intensity distribution contains contains multiple conesmultiple cones. . This is a new This is a new feature that emerges only in thefeature that emerges only in the high-power high-power regimeregime
This structure is formed by the interplay This structure is formed by the interplay of Kerr self-focusing and plasma of Kerr self-focusing and plasma defocusing.defocusing.