Discussion of measurement methods for femtosecond and attosecond pulses
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Transcript of Discussion of measurement methods for femtosecond and attosecond pulses
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Discussion of measurement methods for femtosecond and attosecond pulses
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Duration & Phase
-10 0 10
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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
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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
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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?
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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
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Laser fields easily push electrons around
Making single attosecond pulses
---
controlling the laser field
1 fs
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Atomic ionization produces a replica photoelectron pulse
V1/2 mV2 =x - IP
Measurement of the photo-electron replica is a measurement of the pulse
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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
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Ele
ctri
c F
ield
(1
0
11
V
/cm
)
time (fs)
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A single sub-cycle X-ray pulse
-1 0 1 2 3 4 5 6 7 8 9 10 11-2
-1
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2
Ele
ctr
ic F
ield
(1
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11
V/c
m )
time (fs)
Vx
Vy
--- photoelectron replica is streaked (attosecond streak camera)
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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
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1.0
0.0
0.6
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1.0
(b)
(a) 70 attosecond
I = 6x1014 W/cm2
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0 20 40 60 80 100
0.0
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1.0
0 100 200 300 400 500
-1.0
-0.5
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-60
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0
0 100 200 300 400 500
-1.0
-0.5
0.0
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1.0
30 Å
g
c=a(k)eikx-it
Attosecond pulses are generated by a pre-existing photoelectron replica
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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
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60 BBO
/2 Wave plate
Supersonic gas jet
Experimental Set-Upcalcite
glass
Ti:sapphire amplifier1mJ , 27 fs @ 50 Hz
grating
MCP
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Harm
onic order
Delay [fs]
What Phase difference moves the interferometer arms optimally?
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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
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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.
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Discussion of Orbital Imaging
What are the meausred quantities?
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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
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Transient alignment of molecules
time
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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
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Angle Dependent High Harmonic Spectrum
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Harmonics from N2 and Ar
2 d()= 2 a(k) greikxdx
Note the relation to Photoelectron spectroscopy
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Normalized Harmonic Intensities
Harmonic intensities from N2 at different molecular angles
EL
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Reconstructed N2 g Orbital
• Reconstructed from 19 angular projections
• wave function, not its square
We see electrons! Amplitude and Phase!
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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?