Generation of short pulsesGeneration of short pulses

2.7 fs

Ultrashort pulse generation

15 fs pulse

Time [fs] Time [fs]

Wavelength [m]

Wavelength [m]

Single cycle pulse

Raman scattering and attosecond pulses

S. E. Harris and A. V. Sokolov PRL 81, 2894

frequency

Raman processes can cascade many times, yielding a series of equally spaced modes

Input two frequencies nearly resonant with a Raman resonance.

At high intensity, the process cascades many times.

Input pulses

Output pulse as input to a

second process

Output pulse of second process as

input to a third

process

Output pulse of third process as

input to a fourth

process

Etc.

=1+/- n0

1

0

Cascaded Raman generation

ba= 2994 cm-1

A. V. Sokolov et al. PRL 85, 85 562

This can be done with nanosecond laser pulses!

A. V. Sokolov et al. PRL 85, 562

Experimental demonstration of cascaded Raman scattering

- 400MHz

+ 100MHz

+ 700MHz

2994 cm-1

Detuning from 2-photon resonance

75,000 cm-1 (2.3 x 1015 Hz) of bandwidth has been created!

A. V. Sokolov et al. PRL 85, 562

Experimental demonstration of cascaded Raman scattering

The different frequencies are locked

Pulses with 1 fs duration are measured

The spectrum is discrete: the pulses are emitted in a pulse train, separated by the vibrational period.

The main advantage of this process: high efficiency

The main drawback: the carrier frequency is in the visible regime

We cannot produce an isolated pulse.

2001: First observation of an attosecond pulse (650 as)

2006: (130 as)

Breaking the femtosecond limitBreaking the femtosecond limit

M. Hentschel et al., Nature 414, 509-513 (2001)

G. Sansone et al., Science 314, 443 (2006)

Field Intensity: 1014 –1015 W/cm2

2.7 fs

Our main tool: intense laser pulsesOur main tool: intense laser pulses

The force is comparable to the force binding the electrons in the atom or molecule.

Attosecond pulse generation processAttosecond pulse generation process

Acceleration by the electric fieldRe-collision

Tunnel ionization

E>100eV

kp EI

0100~ With I~1014 W/cm2

Fundamental frequency

20

2

43

EI pcutoff

Attosecond pulse generation processAttosecond pulse generation process

Acceleration by the electric field

Tunnel ionization

Optical radiation with attoseconds duration

Attosecond pulse generation processAttosecond pulse generation process

eEmaF

tEtE 0cos

00000000

0

0000

0

sincoscos,

sinsin,

tttttm

eEttx

ttm

eEttv

e

e

20

22

20000

4

sinsin2,

ep

pk

m

EeU

ttUttE

Classical model

Attosecond pulse generation processAttosecond pulse generation process

00000000

0

0000

0

sincoscos,

sinsin,

tttttm

eEttx

ttm

eEttv

e

e

Classical model

Attosecond pulse generation processAttosecond pulse generation process

20000 sinsin2, ttUttE pk

Classical modelThe return times are determined such that x0(t,t0)=0

Short trajectories

Long trajectories

Ek is the instantaneous frequency of the attosecond pulse

Attosecond pulse generation processAttosecond pulse generation process

Quantum model

txxtExVtxi ,cos2

1, 0

2

txxxt cg ,,

cg xtx

The dynamics of the free electron is mapped into the optical field

txFFTI

The electron’s wavefunction

The induced dipole moment

Electron wave packet dynamicElectron wave packet dynamic

Attosecond pulse

Electron wave packet dynamicElectron wave packet dynamicXUV field:

2 2/, t bH t x e xF

Husimi reprsentation

Attosecond pulse generation processAttosecond pulse generation process

Classical model

Elliptically polarized light:

0000

0

0000

0

coscos,

sinsin,

ttm

eEttv

ttm

eEttv

ey

ex

The electron is shifted in the lateral direction: the recollision probability reduces significantly

Isolating a single attosecond pulseIsolating a single attosecond pulse

The multi-cycle regime

n

nn

n n

harmonicseven

harmonicsoddnE

ninEniEEE

nttEtEnttEtEtE

0

exp15.0exp

5.05.0

0

000

0000

H1523.3eV

H2132.6eV

H2741.9eV

H3960.5eV

Isolating a single attosecond pulseIsolating a single attosecond pulse

The multi-cycle regime

Femtosecond pulse

20 fs, 800nm

I~1014 W/cm2

High harmonics

Attosecond pulse generation processAttosecond pulse generation process

M. Hentschel et al., Nature 414, 509-513 (2001)

Attosecond pulse generation processAttosecond pulse generation process

G. Sansone et al., Science 314, 443 (2006)

Time resolved measurements in the Time resolved measurements in the attosecond regimeattosecond regime

Attosecond pulses generation

Measurement

XUV Autocorrelation

focusing NL

NLO effects:2-photon absorption

2-photon ionization

Problems:low XUV fluxsmall abs

Kobayashi et al., Opt. Lett. 23, 64 (1998)

How to measure an attosecond pulse?

t

AtE

teAdttEetp

maF

il

t

li

i

momentum

Attosecond pulse

Laser field

Electron release time

Photo-electrons

Attosecond streak cameraAttosecond streak camera

M. Hentschel et al., Nature 414, 509-513 (2001)

Momentum transfer depends on instant of electron release within the wave cycle

L( ) ( )t

p t e E t dt

Mapping time to momentum

Incident X-rayintensity

Δpi

instant ofelectronrelease

Δp(t7)

Δp(t6)

Δp(t5)

Δp(t3)

Δp(t2)

Δp(t1)

Δp(t4)

Momentumchange along the EL vector

-500 as 0 500 as

800-nm laser electric field

t7t1 t2 t3 t4 t5 t6

Optical-field-driven streak camera J. Itatani et al., Phys. Rev. Lett. 88, 173903 (2002)M. Kitzler et al., Phys. Rev. Lett. 88, 173904 (2002)

Full characterization of a sub-fs, ~100-eV XUV pulse

= 250 attoseconds!!

td = -T0/4

td = +T0/4

Field-freespectrum

Reconstructed temporal intensity profile

and chirp of the xuv excitation pulse:

Time [fs]

Inte

ns

ity [arb

. u.] 0

1In

stan

tane

ou

s

energ

y sh

ift [eV]

-3

-2

-1

0

1

2

-0.4 -0.2 0.0 0.2 -0.4

xuv = 250as

+10 eV

-10 eV

0

ΔW

tD

Energy shift of sub-fs electron wave-packet

dN/dW

As we vary the relative delay between the XUV pulse and the 800-nm field, the direction of the emitted electron packet will vary.

Ph

oto

ele

ctro

n k

ine

tic e

ne

rgy

[eV

]

Delay t [fs]

2 4 8 10 14 18 200 6 12 16 22

50

60

70

80

90

Attosecond streak camera trace

E. Goulielmakis et al., Science 305, 1267 (2004)

RABITT (Reconstruction of Attosecond RABITT (Reconstruction of Attosecond Beating by Interference of Two-photon Beating by Interference of Two-photon

Transition)Transition)

Narrow one photon transition

xuv

Two photon transition

0 xuv

xuv0 xuv

2q

q

2q

The different paths interfere with a relative phase of:

201 2 qqq

RABITT

RABITT (Reconstruction of Attosecond Beating by Interference of

Two-photon Transition)RABBITT takes advantage of the interference of the even-harmonic sidebands created when the XUV pulse interacts with the intense IR laser pulse.

RABITT results for a 250-as pulse

focusing NL

Time resolved measurementsTime resolved measurements

Can we performed an attosecond pump probe measurement?

The main problem is the low photon flax

One solution is to use the strong IR field as either the pump or the probe

Attosecond streaking spectroscopyAttosecond streaking spectroscopy

M. Drescher et al, Nature 419, 803 (2002)

Core level ionizationValence level ionization

Auger Decay

Time resolved atomic inner shell spectroscopy

Time resolved atomic inner shell

spectroscopy

Time resolved atomic inner shell spectroscopy

Oscillating dipoleOscillating dipole

The attosecond pulses contains the spatial information of the ground and the free electron wavefunctions.

The free electron act as a probe - the re-collision step maps the

ground state wave function to the spectrum

Imaging the ground stateImaging the ground state

d(t)= a(k) <g|er|eikx-()t>

c ~1A

Harmonic intensitiesHarmonic intensities

15 20 25 30 35 40 450

1

2

3

4

5

6

7

8

9x 10

5

Harmonic Number

Ha

rmo

nic

In

ten

sit

y

0

22

4567

90

Harmonic intensities from N2 at different molecular angles

EL

Tomographic image reconstructionTomographic image reconstruction

Reconstructed Molecular Reconstructed Molecular Orbital - NOrbital - N22

Reconstructed orbital

Calculated orbital

J. Itatani, et al., Nature 432, 867 (2004).