Discussion of measurement methods for femtosecond and attosecond pulses

Duration & Phase

-10 0 10

-1

0

1

Long pulse = one color

Short pulse = many colors; perfectly synchronized.

-10 0 10

0

10

0.7 1.3

This is mathematical.

It cannot be avoided

What is fast enough for measurement?

Streak Camera (currently ~500 fs)

½ ns

Produce photoelectron replica

Rapidly changing field

Space charge, operating over many nanoseconds is a problem

photocathode

Measuring femtosecond pulses

Why not ask the pulse to measure itself!

c

c

x or ct

Transmission, Fluorescence, Ions, Electrons, Diffraction

question: What can be used for mirrors and beam splitters? What can be the nonlinear medium for attosecond pulses?

Attosecond pulses were generated using laser fields and electrons(Why not use the streak

camera?)

1. Photoionization

2. Use the pre-existing re-collision electron replica

Laser fields easily push electrons around

Making single attosecond pulses

---

controlling the laser field

1 fs

Atomic ionization produces a replica photoelectron pulse

V1/2 mV2 =x - IP

Measurement of the photo-electron replica is a measurement of the pulse

F=ma once again

•linear polarization

•initial velocity (V0x, V0y, V0Z)

Vdrift, x = V0x- {Vd= qE0(t)/m Sin ( tI + )}

Vdrift, y = V0y

Vdrift, z = V0z

,d xv

,d yv

0v

( )dv t

Drift velocity distribution

Polarization

-1 0 1 2 3 4 5 6 7 8 9 10 11-2

-1

0

1

2

Ele

ctri

c F

ield

(1

0

11

V

/cm

)

time (fs)

A single sub-cycle X-ray pulse

-1 0 1 2 3 4 5 6 7 8 9 10 11-2

-1

0

1

2

Ele

ctr

ic F

ield

(1

0

11

V/c

m )

time (fs)

Vx

Vy

--- photoelectron replica is streaked (attosecond streak camera)

Streaked photoelectron of 100 eV pulse -- parallel observation

Ph

oto

ele

ctro

n s

pe

ctra

(arb

. u

nits

)

12010080604020

Electron energy (eV)

0.0

0.6

0.2

0.4

0.8

1.0

0.0

0.6

0.2

0.4

0.8

1.0

(b)

(a) 70 attosecond

I = 6x1014 W/cm2

0 20 40 60 80 100

0.0

0.2

0.4

0.6

0.8

1.0

0 100 200 300 400 500

-1.0

-0.5

0.0

0.5

1.0

0 20 40 60 80 100

-100

-80

-60

-40

-20

0

0 100 200 300 400 500

-1.0

-0.5

0.0

0.5

1.0

30 Å

g

c=a(k)eikx-it

Attosecond pulses are generated by a pre-existing photoelectron replica

We need to do a similar thing to the pre-existing replica

A (weak)2 2 field breaks symmetry, generating even harmonics

Each moment of birth (re-collision) has an optimum phase difference () between and 2

60 BBO

/2 Wave plate

Supersonic gas jet

Experimental Set-Upcalcite

glass

Ti:sapphire amplifier1mJ , 27 fs @ 50 Hz

grating

MCP

16

18

20

22

24

26

Harm

onic order

Delay [fs]

What Phase difference moves the interferometer arms optimally?

Re-collision time [rad]

(t)

Harmonic number

(N)

Attosecond Temporal Phase Gate

d,2(t) ~ d(t) e i(t) SFA

: two color delay which maximizes the even harmonic signal

Electron Wave-Packet Reconstruction

Re-collision time [rad]

Short trajectoriesLong trajectoriesH

armon

ic order

SFA

Electron wave packet measurement is equivalent to a xuv pulse measurement up to the transition dipole.

Discussion of Orbital Imaging

What are the meausred quantities?

High Harmonics/Attoseconds pulses

d(t)={ra(k)eikx d3r}ei{(IP+KE)t +}

d(t) is essentially the Fourier transform of the wave function

Transient alignment of molecules

time

The Experiment

““Pump”Pump”AlignmentAlignment pulse pulse

““Probe”Probe”HHG pulseHHG pulse

(60(60fs, 5fs, 5xx101013 13 W/cmW/cm22)) (30(30fs, 1.5fs, 1.5xx101014 14 W/cmW/cm22))

H1523.3eV

H2132.6eV

H2741.9eV

H3351.2eV

H3960.5eV

Space

Ti:sapphire CPA1 TW, 27 fs @ 50 Hz

Angle Dependent High Harmonic Spectrum

Harmonics from N2 and Ar

2 d()= 2 a(k) greikxdx

Note the relation to Photoelectron spectroscopy

Normalized Harmonic Intensities

Harmonic intensities from N2 at different molecular angles

EL

Reconstructed N2 g Orbital

• Reconstructed from 19 angular projections

• wave function, not its square

We see electrons! Amplitude and Phase!

Final comment:

Another perspective on the re-collision electron

The probability of the electron being driven back is 50%

The area of the electron wave packet when it returns is ~(10 Angstroms)2

The time window is about 1 femtosecond

Charge per unit area per unit time is current density. J~1011Wcm2. This is a truly phenomenal number--- the electron can hardly miss. Why not allow it to diffraction from the molecule?