Transcript 4.83 Mb - ELI-NP

Modeling propagation of femtosecond laser
pulses in ionized gas media
Valer TOSA
National Intitute for R&D of Isotopic and Molecular Technology,
Cluj-Napoca, ROMANIA
ELI-NP: The Way Ahead, Bucharest, 10-12 March 2011
High order harmonics generation (HHG)
High-order harmonics
Intense fs laser
X-ray filter
electron
X-ray CCD
Soft X-ray spectrometer
Gas jet
Laser
atom X-ray
Signal process
H95
80
85
H85
90
95
H75
100
105
H65
110 115 120 125 130
High-order harmonics (Å)
ELI-NP: The Way Ahead, Bucharest, 10-12 March 2011
Modeling laser field propagation:
2
2
1

E
(
r
,
z
,
t
)

2 ) E (r, z, t )
1
2 E1(r, z,t )  2
 2 (1eff
1
2
c
t
c
 p2 (ne , r , z , t )
 eff (na , ne , r , z , t )   0 (na )   2 (n0 ) I (r , z , t ) 
2 2
Method to solve
1. Write wave equation in the moving frame
2. Perform the Fourier transform and paraxial approximation
3. Advance solution by a Cranck-Nicolson scheme
4. Inverse Fourier transform
V. Tosa, et al, Phys. Rev. A 67, (2003) 063817
ELI-NP: The Way Ahead, Bucharest, 10-12 March 2011
Model capabilities
• uses experimentally measured parameters
(focusing conditions, pulse energy, duration)
• includes different focusing configurations
(gaussian, supergaussian, truncated gaussian, bessel-gauss)
• may account for frequency chirp of the pulse
• CEP can be an input parameter
Recent developments
• additional time-frequency
analysis (post-processing)
• simultaneous propagation of two (three) fields
•including double (multiple) ionization to account for high intensity cases
ELI-NP: The Way Ahead, Bucharest, 10-12 March 2011
Example results (1)
ELI-NP: The Way Ahead, Bucharest, 10-12 March 2011
Example results (2)
ELI-NP: The Way Ahead, Bucharest, 10-12 March 2011
Example results (3)
ELI-NP: The Way Ahead, Bucharest, 10-12 March 2011
ELI-NP: The Way Ahead, Bucharest, 10-12 March 2011
Propagation effect in time domain
0.3
gas propagation
vacuum propagation
Ar
65 Torr
9 mm
15
2
3x10 W/cm
Electric field (atomic units)
0.2
0.1
0.0
-0.1
-0.2
-0.3
-60
-40
-20
0
20
Time (optical cycles)
ELI-NP: The Way Ahead, Bucharest, 10-12 March 2011
40
60
V. Tosa et al.
PRA 71, 063807
PRA 71, 063808
Propagation effect in frequency domain
100000
gas propagation
vacuum propagation
10000
1000
Ar
65 Torr
9 mm
15
2
3x10 W/cm
100
10
1
0.1
0.6
0.8
1.0
1.2
1.4
1.6

ELI-NP: The Way Ahead, Bucharest, 10-12 March 2011
1.8
2.0
Formation of
far field
from
constructive
interference
of
near fields
Harmonic intensity (arb units)
Coherent superposition of harmonic fields (1)
60
r=45 m
50
r=30 m
40
r=15 m
30
r=0
20
near field
10
far field
0
-6
-4
-2
0
t/T0
ELI-NP: The Way Ahead, Bucharest, 10-12 March 2011
2
4
6
V. Tosa et al, PRA 79, 043828 (2009)
Coherent superposition of harmonic fields (2)
V. Tosa et al, PRA 79, 043828 (2009)
(a) Harmonic near fields contributing to the attosecond pulse at t=−2T0 and different r
distances from the axis.
(b) The normalized envelopes of the corresponding field intensities.
ELI-NP: The Way Ahead, Bucharest, 10-12 March 2011
Conclusions:
- Propagation of laser pulses in gaseous ionizing media
can be characterized by a numerical model
- Two or more pulses can be described in simultaneous propagation
- Measured quantities can be used as input
- Methods to describe coherent field superposition are available
- The above instruments could be used to model the process of
coherent beam combining in ELI-NP Project (?)
ELI-NP: The Way Ahead, Bucharest, 10-12 March 2011