UDIM09, Ischia island, Naples, Italy

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Valer TosaValer TosaNational Institute R&D Isotopic Molecular Technologies, Cluj-Napoca, RomaniaNational Institute R&D Isotopic Molecular Technologies, Cluj-Napoca, Romania

Macroscopic Effects in Single Macroscopic Effects in Single Attosecond Pulse GenerationAttosecond Pulse Generation

Carlo Altucci, Raffaele VelottaCarlo Altucci, Raffaele VelottaDipartimento di Scienze Fisiche, Università “Federico II”, Napoli, ItalyDipartimento di Scienze Fisiche, Università “Federico II”, Napoli, Italy

UDIM09, Ischia island, Naples, Italy

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UDIM09, Ischia island, Naples, Italy

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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

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),,()1(),,(1),,(

,2

2

2

2,

2

2,2 tzrE

ct

tzrE

ctzrE

yxeffyx

yx

2

2

020 2

),,,(),,()()(),,,,(

tzrn

tzrInntzrnn epaeaeff

A

'

*

2/3

')"(exp)'()'(),'()],',(exp[

)(),'(2/)'(

'Re2)(

t

ststst

t

st

dttwtEtAttpdttpiS

tAttpdtti

dtitnld

B

2,

2

02,

2

2

2

,2 ),,(),,(

),,(t

tzrP

t

tzrE

ctzrE yx

hyxh

yx

C

Tools

UDIM09, Ischia island, Naples, Italy

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Scheme of Principle

BS

MG

M

HWP

INPUT

OUTPUT

PA

yddp

dyy

xp

xx

CEPzrTttInL

TtTt

EzrtE

CEPzrtt

EzrtE

,)(2

sin39.1exp,,

,sin39.1exp,,

20

2

0

0

2

0

[for details see C. Altucci et al, Opt. Lett. 33, 2943 (2008) ]

UDIM09, Ischia island, Naples, Italy

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1D mechanism of SAP formation (1)

-8 -6 -4 -2 0 2

0

1

-8 -6 -4 -2 0 2-8 -6 -4 -2 0 2

0

2

4

6

Time (optical cycles)

Ix, I

y

electron fraction

UDIM09, Ischia island, Naples, Italy

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1D mechanism of SAP formation

-3.5 -3.0 -2.5 -2.00

2

4

6

8

10

t/T0

single dipole response

-3.5 -3.0 -2.5 -2.00

2

4

6

8

10 single dipole during propagation

t/T0

z=0.0 mm z=0.5 mm z=1.0 mm

-3.5 -3.0 -2.5 -2.00

1

2

3

4

Time (optical cycles)

Final harmonic fieldon-axis

UDIM09, Ischia island, Naples, Italy

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1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0-40

-20

0

20

40

60

80

Tra

ject

ory

ph

ase

(ra

dia

ns)

z (mm)

tr=-2.6T

0

tr=-3.1T

0

Trajectory analysis (on-axis)

Trajectoryphase:

V. Tosa et al.PRA 79, 043828 (2009)

1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0

-3.1

-3.0

-2.9

-2.8

-2.7

Tim

e (

op

tica

l cyc

les)

z (mm)

short trajectories long trajectories

UDIM09, Ischia island, Naples, Italy

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-4.0 -3.5 -3.0 -2.5 3.0 3.5 4.0 4.5 5.00

1

2

3

4

5

Time (optical cycles)

Emitted near field

3D SAP formation

-5 -4 -3 -2 -1 0 1 2 3 4 5

10

20

30

40

Time (optical cycles)R

ad

ial co

ord

ina

te

UDIM09, Ischia island, Naples, Italy

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SAP selection

-4 -3 3 4 5

1

2

3

4

5

6

Inte

nsi

ty (

arb

. u

n.)

Time (optical cycles)

nearfield farfield (iris 1.5 mm @ 500 mm)

UDIM09, Ischia island, Naples, Italy

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-3.0 -2.5 -2.0 -1.50

2

4

6

In

tens

ity (

arb.

un.

)

Time (o. c.)

15 fs CEP=-/4 CEP=0 CEP=/4

-4.0 -3.5 -3.0 -2.5 -2.00

2

4

6

Inte

nsity

(ar

b. u

n.)

Time (o. c.)

20 fs CEP=0 CEP=2/5 CEP=3/4

-5.0 -4.5 -4.0 -3.5 -3.00

2

4

6

Inte

nsity

(ar

b. u

n.)

Time (o. c.)

25 fs CEP=2/3 CEP=0.7 CEP=3/4

21 31 41

104

105

Po

we

r S

pe

ctru

m

CEP=0 CEP=0.40 CEP=0.75

Explore the limits of the method

UDIM09, Ischia island, Naples, Italy

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Explore the limits of the method (2)

-4 -3 -2 3 40

1

2

3

4

5

6

7

Time (optical cycles)

0.7 I0

I0

1.3 I0

Intensity variation

UDIM09, Ischia island, Naples, Italy

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Explore the limits of the method (4)

-4 -2 0 2 40

2

4

6

8

10

12

Time (optical cycles)

constant chirp along radial direction

-5 0 50

2

4

6

8

10

12

Time (optical cycles)

5% radial variation of chirp(but not optimized in CEP)

-4 -2 0 2 4

0

2

4

6

8

10

12

10% radial variation of chirp(but not optimized in CEP)

Time (optical cycles)

UDIM09, Ischia island, Naples, Italy

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Explore the limits of the method (3)

-4 -3 -2 3 4 5

0

3

6

9

12

15

Ne

ar

field

po

we

r e

mis

sion

Time (optical cycles)

CEP = 0.5 CEP = 0.4 CEP = 0.35

Using a truncated gaussian

UDIM09, Ischia island, Naples, Italy

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Method efficiency

Case calculated using the polarization gate and conditions specified in

L. J. Sola, et al. Nat. Phys. 2, 319 (2006)

-4 -2 0 20

2

4

6

8

10

12

Har

mon

ic e

mis

sion

Time (optical cycles)

x 6

367 as 352 as

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