Discussion of measurement methods for femtosecond and attosecond pulses.
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Transcript of 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)
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1.0
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1.0
(b)
(a) 70 attosecond
I = 6x1014 W/cm2
0 20 40 60 80 100
0.0
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1.0
0 100 200 300 400 500
-1.0
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1.0
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0 100 200 300 400 500
-1.0
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1.0
30 Å
g
c=a(k)eikx-it
Attosecond pulses are generated by a pre-existing photoelectron replica
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.
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
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
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?