ponderomotive force cause turbulent state in the pre-formed plasma, and there is
another type of dominant interaction physics between laser and the plasmas, being
rather independent of the laser polarization. In [3], it is concluded that the laser
energy is transferred to the hot electron energy via stochastic heating process [4].
For a given laser intensity, higher plasma density of solid implies a higher
restoring force by charge separation due to electron oscillations. This may deduce
the oscillation amplitude of the surface and degrade the HHG according to the ROM
model. In contrast, if the plasma density is too low, large amplitude surface
oscillation becomes unstable, resulting the non-synchronized oscillation to cause
broadening of generated higher harmonic spectrum. It is also noted that if the density
is lower than the relativistic critical density defined in (6.2.3), the plasma becomes
relativistic transparent and no reflection is expected. The optimized density is also a
function of laser intensity.
The generation of HH also depends on the scale length of pre-formed plasma as
shown in Fig. 7.3b. It is noted that with 1D PIC code, HHG is more efficient for the
case with pre-formed plasma with an appropriate length, being equal to L/λ ¼ 0.2
(figure c) in Fig. 7.6 [5]. The target is 5 μm thickness with solid density of 49n c (n c :
critical density), and the laser is irradiated with p-polarized oblique incidence at the
intensity 10
18 W/cm
2 (a 0 ¼ 0.3). For three different L/λ cases, the HHG is seen also
at L/λ ¼ 0.02 (case b), while the Fourier components of the transverse currents
generating HH are seen in the higher density positions whose plasma frequencies
resonate with the HH frequencies in the case (b). The transverse currents are shown
in the middle of figure b with the black lines along with the density profile (red).
Such HHG is also driven by the nonlinearity of plasma oscillations as seen in Sect.
6.2. The HHG in case b is due to such resonance in the over-dense region and as a
result HHG is limited by the plasma frequency (ω p ) of the solid density. For λ/
L ¼ 0.2 (case c), the higher harmonic currents are seen to be localized at the same
position of the critical density x cr , and the amplitude in the bottom well explains the
PIC result when the amplitude of ROM is assumed to be X 0 ¼ 0.06λ in (6.8.5) as
plotted with red circles.
As clear from comparison between the results in Figs. 7.3 and 7.6, the optimum
density scale length is different. It is obvious that the optimum condition of HHG is
depends on the laser intensity, density scale length, 1D PIC or 2D PIC simulation,
ion-electron mass ratio, the number density of solid, etc. It is not valuable to compare
the difference but to keep in mind the physics of HHG is important to analyze
computational and experimental data, since it is not always the case that we are able
to measure the energy fraction carried out as higher harmonics lights.
7.2 Laser Absorption at Solid Targets
Laser absorption of ultra-intense laser is very sensitive to the laser and target
conditions. Especially, the laser-matter interaction physics strongly depends on the
property of the pre-formed plasma. Roughly saying, the physics of laser absorption
244
7 Relativistic Laser and Solid Target Interactions
another type of dominant interaction physics between laser and the plasmas, being
rather independent of the laser polarization. In [3], it is concluded that the laser
energy is transferred to the hot electron energy via stochastic heating process [4].
For a given laser intensity, higher plasma density of solid implies a higher
restoring force by charge separation due to electron oscillations. This may deduce
the oscillation amplitude of the surface and degrade the HHG according to the ROM
model. In contrast, if the plasma density is too low, large amplitude surface
oscillation becomes unstable, resulting the non-synchronized oscillation to cause
broadening of generated higher harmonic spectrum. It is also noted that if the density
is lower than the relativistic critical density defined in (6.2.3), the plasma becomes
relativistic transparent and no reflection is expected. The optimized density is also a
function of laser intensity.
The generation of HH also depends on the scale length of pre-formed plasma as
shown in Fig. 7.3b. It is noted that with 1D PIC code, HHG is more efficient for the
case with pre-formed plasma with an appropriate length, being equal to L/λ ¼ 0.2
(figure c) in Fig. 7.6 [5]. The target is 5 μm thickness with solid density of 49n c (n c :
critical density), and the laser is irradiated with p-polarized oblique incidence at the
intensity 10
18 W/cm
2 (a 0 ¼ 0.3). For three different L/λ cases, the HHG is seen also
at L/λ ¼ 0.02 (case b), while the Fourier components of the transverse currents
generating HH are seen in the higher density positions whose plasma frequencies
resonate with the HH frequencies in the case (b). The transverse currents are shown
in the middle of figure b with the black lines along with the density profile (red).
Such HHG is also driven by the nonlinearity of plasma oscillations as seen in Sect.
6.2. The HHG in case b is due to such resonance in the over-dense region and as a
result HHG is limited by the plasma frequency (ω p ) of the solid density. For λ/
L ¼ 0.2 (case c), the higher harmonic currents are seen to be localized at the same
position of the critical density x cr , and the amplitude in the bottom well explains the
PIC result when the amplitude of ROM is assumed to be X 0 ¼ 0.06λ in (6.8.5) as
plotted with red circles.
As clear from comparison between the results in Figs. 7.3 and 7.6, the optimum
density scale length is different. It is obvious that the optimum condition of HHG is
depends on the laser intensity, density scale length, 1D PIC or 2D PIC simulation,
ion-electron mass ratio, the number density of solid, etc. It is not valuable to compare
the difference but to keep in mind the physics of HHG is important to analyze
computational and experimental data, since it is not always the case that we are able
to measure the energy fraction carried out as higher harmonics lights.
7.2 Laser Absorption at Solid Targets
Laser absorption of ultra-intense laser is very sensitive to the laser and target
conditions. Especially, the laser-matter interaction physics strongly depends on the
property of the pre-formed plasma. Roughly saying, the physics of laser absorption
244
7 Relativistic Laser and Solid Target Interactions