Macroscopic Effects in Single
Attosecond Pulse Generation
Valer Tosa
National Institute R&D Isotopic Molecular Technologies, Cluj-Napoca, Romania
Carlo Altucci, Raffaele Velotta
Dipartimento di Scienze Fisiche, Università “Federico II”, Napoli, Italy
UDIM09, Ischia island,
Naples, Italy
1
UDIM09, Ischia island,
Naples, Italy
2
Layout
1. Tools for numerical modeling of SAP
2. A proposed sheme to obtain a single attosecond pulse (SAP)
3. The mechanism of SAP formation
4. Analysis of scheme feasibility
5. Conclusions
UDIM09, Ischia island,
Naples, Italy
3
Tools
2
2

E
(
r
,
z
,
t
)
1

x
,
y
2 ) E (r, z, t )
2 Ex, y (r, z,t)  2
 2 (1eff
x, y
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
A
3/ 2
t




 * 


d (t )  2 Re i  dt ' 
 d pst (t ' , t )  A(t )
nl


i
(
t

t
'
)
/
2


  
 


 t'




exp[ iS st ( pst , t ' , t )] d pst (t ' , t )  A(t ' ) E (t ' ) exp    w(t" )dt '  
 



B
C
UDIM09, Ischia island,
Naples, Italy



2
2  2 E h (r, z,t )

Px, y (r, z,t)

x
,
y
2 Exh, y (r, z,t)  2


0
2
2
c
t
t
4
Scheme of Principle
[for details see C. Altucci et al, Opt. Lett. 33, 2943 (2008) ]
M
G
PA
M
BS
OUTPUT
HWP
INPUT
2

 t  
E x t , r, z   E0 x exp  1.39   sin  0t   r, z   CEPx 
  

 p 


 t  Td
E y t , r, z   E0 y exp  1.39
 

 p

UDIM09, Ischia island,
Naples, Italy




2

2L

 sin  0 t  Td  




n
I
(
t
)
t

T


r
,
z

CEP
2
d
y


 

5
1D mechanism of SAP formation (1)
-8
-6
-4
-2
0
2
1
6
electron fraction

4
0
Ix, Iy
2
0
-8
-6
-4
-2
0
2
Time (optical cycles)
UDIM09, Ischia island,
Naples, Italy
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1D mechanism of SAP formation
10
8
8
6
6
4
4
2
2
0
-3.5
-3.0
-2.5
t/T0
single dipole during propagation
10
single dipole response
z=0.0 mm
z=0.5 mm
z=1.0 mm
0
-3.5
-2.0
-3.0
-2.5
-2.0
t/T0
4
Final harmonic field
on-axis
3
2
1
UDIM09, Ischia island,
Naples, Italy
0
-3.5
-3.0
-2.5
Time (optical cycles)
-2.0
7
Trajectory phase (radians)
Time (optical cycles)
Trajectory analysis (on-axis)
-2.7
-2.8
-2.9
short trajectories
long trajectories
-3.0
-3.1
1.6
1.8
2.0
2.2
2.4
z (mm)
Trajectory
phase:
UDIM09, Ischia island,
Naples, Italy
2.6
2.8
3.0
80
60
40
20
0
-20
tr=-2.6T0
tr=-3.1T0
-40
1.6
1.8
2.0
2.2
2.4
2.6
2.8
3.0
z (mm)
V. Tosa et al.
PRA 79, 043828 (2009)
8
3D SAP formation
40
Emitted near field
4
3
2
1
0
-4.0
-3.5
-3.0
-2.5
3.0 3.5 4.0 4.5 5.0
Time (optical cycles)
UDIM09, Ischia island,
Naples, Italy
Radial coordinate
5
30
20
10
-5
-4
-3
-2
-1
0
1
2
3
4
5
Time (optical cycles)
9
SAP selection
Intensity (arb. un.)
6
nearfield
farfield (iris 1.5 mm @ 500 mm)
5
4
3
2
1
-4
-3
3
4
5
Time (optical cycles)
UDIM09, Ischia island,
Naples, Italy
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Explore the limits of the method
6
6
20 fs
CEP=-/4
CEP=0
CEP=/4
4
Intensity (arb. un.)
Intensity (arb. un.)
15 fs
2
0
-3.0
-2.5
-2.0
CEP=0
CEP=2/5
CEP=3/4
4
2
0
-4.0
-1.5
-3.5
-3.0
-2.5
-2.0
Time (o. c.)
Time (o. c.)
6
Power Spectrum
Intensity (arb. un.)
25 fs
CEP=2/3
CEP=0.7
CEP=3/4
4
2
0
-5.0
-4.5
-4.0
Time (o. c.)
UDIM09, Ischia island,
Naples, Italy
-3.5
-3.0
5
10
4
10
CEP=0
CEP=0.40
CEP=0.75
21
31

41
11
Explore the limits of the method (2)
Intensity variation
7
6
0.7 I0
I0
5
1.3 I0
4
3
2
1
0
-4
-3
-2
3
4
Time (optical cycles)
UDIM09, Ischia island,
Naples, Italy
12
Explore the limits of the method (4)
12
constant chirp
along radial direction
10
8
6
4
2
0
-4
-2
0
2
Time (optical cycles)
12
5% radial variation of chirp
(but not optimized in CEP)
10
4
12
10% radial variation of chirp
(but not optimized in CEP)
10
8
8
6
6
4
4
2
2
0
0
-5
0
Time (optical cycles)
UDIM09, Ischia island,
Naples, Italy
5
-4
-2
0
2
4
Time (optical cycles)
13
Explore the limits of the method (3)
Using a truncated gaussian
Near field power emission
15
CEP = 0.5
CEP = 0.4
CEP = 0.35
12
9
6
3
0
-4
-3
-2
3
4
5
Time (optical cycles)
UDIM09, Ischia island,
Naples, Italy
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Method efficiency
Harmonic emission
12
x6
10
Case calculated using the
polarization gate and
conditions specified in
L. J. Sola, et al.
Nat. Phys. 2, 319 (2006)
8
6
352 as
367 as
4
2
0
-4
-2
0
2
Time (optical cycles)
UDIM09, Ischia island,
Naples, Italy
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Conclusions
• Polarization gate does not always insure a
SAP at single dipole level
• High brightness SAP can be generated if
the interplay among polarization, ionization,
and spatial filtering is properly applied
• The proposed scheme could produce single
attosecond pulse from multicycle lasers
UDIM09, Ischia island,
Naples, Italy
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