Single-shot visualization of EVOLVING,
light-speed index structures by multiobject phase contrast imaging
Zhengyan Li, Rafal Zgadzaj, Xiaoming Wang, Chih-Hao Pai, Yen-Yu Chang, Michael C. Downer
Department of Physics, University of Texas at Austin, Austin, TX 78712
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Snapshots of Quasi-static Wakes
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N. H. Matlis et al., Nature Phys. 2, 749 (2006)
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Movies of Evolving Wakes Captured in a Single Shot...
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Evolution of index structures is common in different medium and
different applications…
Simulation of spatio-temporal splitting of laser
pulse in silica
Ishikawa, et al., PRE 66, 056608 (2002)
Simulation of evolving wakes for eself-injection in LWFA
S. Kalmykov, et al., PRL 103, 135004 (2009)
Simulation of merging of multi-filament in air
Evolution of
index profile
Δn(ξ,x,z) over
propagation
G Mechain et al., PRL 93, 035003 (2004)
Simulation of evolving electron driving
and witness beam in electron-driven
plasma accelerators
I. Blumenfeld, et al., Nature 445, 741-744 (2007)
Single-shot visualization in laboratory of evolving refractive index structures!
Techniques using transverse probing geometry image spatio-temporal
profile Δn(ξ,x,z) of index structures at specific propagation distance,
and visualize its z-evolution by shifting the probe-pump delay.
In-line holography for plasma filamentation
D. Abdollahpour et al., Phys. Rev. A 84, 053809 (2011)
G. Rodriguez, et al., J. Opt. Soc. Am. B 25, 1988-1997 (2008)
Time-resolved polarimetry and plasma
shadowgraphy for electron diagnosis
A. Buck, et al., Nature Physics 7, 543-548 (2011).
Transverse probing geometry can only visualize z-evolution in multi-shots, and for long interaction
length (~101 cm) large aperture beam and optics are not practical.
Holography/tomography in frequency domain visualized spatiotemporal profiles of index structures Δn(ξ,x,z) and its evolution in
single-shot, however the interaction length is limited to several mm…
Frequency-domain holography
Frequency-domain tomography
N. Matlis et al., Nature Physics 2, 749-753 (2006)
J. K. Wahlstrand, et al., Phys. Rev. Lett. 107, 103901 (2011)
Z. Li et al., in preparation
Multi-object phase contrast imaging with small oblique angle probe maps
~101 cm long z-evolution of index structures’ transverse profiles Δn(ξ,x,z)
onto probe’s transverse profile
Z. Li, et al., Single-shot visualization of evolving, light-speed structures by multi-object
plane phase-contrast imaging, Opt. Lett., in press (2013).
probe
θ
pump
CCD n
The interaction region
CCD 3
lens 2
f2 = 75 cm
CCD 2
1 mm fused
silica plate
CCD 1
lens 1
f2 = 50 cm
ccosθ c
z
X
y
probe
csinθ
index
object
x
z=0
z = L/2
• To optimally resolve z-evolution
• To reduce the object-probe walk-off
z=L
Object planes: 𝑒 𝑖𝜙 ≈ 1 + 𝑖𝜙
Phase
contrast
Image planes:
• Amplitude 𝛼𝑒 𝑖𝜓 + 𝑖𝜙
• Intensity 𝛼 2 1 +
2 sin 𝜓
𝜙
𝛼
To characterize the nonlinear phase shift and absorption in the
thin glass plate, close- and open-aperture z-scan measured
them respectively…
Phase shift at image planes as a function of that at Fourier plane
Simply, if ψ0<<1, ψ~ψ0/3
Measured phase shift in different cameras are iteratively
reconstructed using Gerchberg-Saxton algorithm, no matter the
object at z0 is imaged or not…
Diffracted phase shift profiles captured by
four CCD cameras
Measured
intensity
modulations
Back-projection
to z0 for phase φi
Replace Ai
with
measured
amplitude
modulations
Average
phase
shift
over φi
Forward-projection
to z0 for amplitude Ai
Reconstructed
phase
Reconstructed phase shift along z due to
the plasma channel 1.7 ps after the pulse
In a single shot, the probe overlapping with the index structure
at specific time delay can imaged the transverse profile
evolution over propagation…
T = 0 fs, pump leading edge
• Low plasma density on axis
• Pure self-focusing
T = 66 fs, pump trailing edge
• High plasma density on axis
• Self-focusing and plasma de-focusing
• Side-peaks developed
If the system is stable that multi-shot operation is possible, 4D
visualization with temporal profile characterization of the index
structure is possible. Moreover, it is more sensitive to small
phase by tenuous laser plasma structures.
On-axis index at z = 7.5 cm, y = 0 μm
Off-axis index at z = 7.5 cm, y = 100 μm
• Plasma channel is formed only on-axis, rather off-axis
• Probe with parallel polarization (circle) to the pump has positive rotational index
• Probe with perpendicular polarization (square) showed negative rotational index
MOP-PCI: Tilted pulse compensation for large
angle probe
Optimal compensation condition
•
•
•
No tilted probe compensation
Walk-off angle
𝜙𝑤 = 𝜃/2
Compensation angle
𝑑𝜖
𝜙𝑐 = 𝜆( )
𝑑𝜆
Optimal compensation requires
𝜙𝑤 = 𝜙𝑐
With tilted probe compensation
Visualization of evolving wakefields in laser wakefield accelerators
driven by the Texas Petawatt Laser, at extremely low repetition rate
d = 7 mm
L = 10 cm
x
pump, e-, x-ray
z
f# = 40
probe
Primary results of visualizing laser plasma wakefield acceleration
structures in the Texas Petawatt Laser
Shot 5866 2 GeV electrons with 640 TW laser
in 6.9e17 cm-3 plasma
Shot 5870 1.5 GeV electrons with 640 TW
laser in 6.3e17 cm-3 plasma
Shot 5868 no electrons with 680 TW laser in
5.5e17 cm-3 plasma
•
plasma channel is formed, the maximum
density is reached at z = 3 to 4 cm, channel
width is ~ 1mm and increases with z.
•
After z = 2.5 to 3 cm, a ``streak’’ is formed in
the center of the channel, which is believed to
be contribution from plasma wakefields at the
10th to 20th cycles (time delay 2-3 ps).
•
For shot 5868, plasma channel before z = 2.5
cm is broader than the other two, implying
stronger diffraction effect.
Further improvement of imaging quality includes better design of gas cell, extended
probe beam size, more accurate time delay control…
800 nm, compressed 30 fs(?),
< 1 mJ probe pulse, w0 < 1cm
The vacuum environment
L1 = ?
1 deg.
angle
M1
L0 = ?
35 cm interaction region?
OP1
OP2
OP3
M2
OP4
Optical
quality
window?
What we want to do with index structure n(ζ,x,z)…
1.
2.
3.
4.
Multi-Object-Plane imaging, each object plane (OP) are
imaged to different CCD.
Phase shift imprinted on probe at arbitrary z, not limited to
OPs, is reconstructed.
In single shot, z-depending transverse profile at specific ζ is
obtained.
With multi-shots, full visualization of index object n(ζ,x,z).
Questions:
1.
2.
CCD1
CCD2
CCD4
CCD3
3.
Is the interaction length 35 cm, or longer?
Where is possible for us to couple laser into the chamber?
What are the lengths of L0 and L1? To maintain a good imaging
resolution, we hope L1 is not too large, what is the shortest
length we can get?
Is there anything that potentially blocks or clips the beam
between M1 and M2? Here the angle is 1 deg. = 0.0175 rad, so
the inside diameter of the tube containing the laser has to be
larger than 3 cm, if L0, L1 ~ 50 cm. Is it OK?
Lens f = 75 cm
These are what we expected to observe with 6 cameras
Phase shift reconstructed from probe measurement (right) v.s. direct calculation (left)
1. The object is assumed to be a super-gaussian shape blowed-out bubble, the radius
is 50 um, plasma density is assumed to be 2e16 cm-3.
2. Maximum phase shift is around 0.4 rad.
3. The trend of transverse profile evolution is reconstructed.
4. Some sharp edge or fine structure information is lost due to a confined simulation
box (1.5 cm*1.5 cm), corresponding to hard aperture for actual laser propagation.
For non-evolving bubble, time walk-off or even intentional
“opposite compensation” leads to spatio-temporal profile of
wakefields
Optimal compensation condition
•
•
•
Walk-off angle
𝜙𝑤 = 𝜃/2
Compensation angle
𝑑𝜖
𝜙𝑐 = 𝜆( )
𝑑𝜆
Optimal compensation requires
𝜙𝑤 = 𝜙𝑐
For stable object, intrinsic pump-probe walk-off + tilted probe “opposite compensation”
c cosθ
c sinθ
c
Δζ
z=0
z = L/2
z=L
Specs for MOPPCI in FACET
• The minimum angle for oblique angle geometry
θmin = λ/πσ = 0.146 deg
0.72 deg
•
Temporal walk-off
Δt = Lθ2/2c = 38 fs
152 fs
•
@ σ = 100 um
@ σ = 20 um
@ θ = 0.5 deg
@ θ = 1 deg
z-resolution for evolving bubble
δz = σ/θ = 5.73 mm
11.4 mm
2.29 mm
@ σ = 100 um, θ = 1 deg
@ σ = 100 um, θ = 0.5 deg
@ σ = 20 um, θ = 0.5 deg
• ζ-resolution and range for non-evolving bubble
δζ = max{σ(θ/2+φ)/c, tpr} = max{50, 30} = 50 fs
Δζ = Lθ(θ/2+φ)/c = 1.26 ps
@ σ = 100 um, θ = 0.5 deg, φ = 8 deg
Conclusion
•
Multi-object phase contrast imaging provides evolutional information of the index structure’s
transverse profiles over ~101 cm interaction length, by using a small oblique angle geometry.
•
Nonlinear Kerr effect and absorption improve the sensitivity of detecting small phase shift
induced by tenuous laser plasma structure.
•
In the prototype experiments imaging femtosecond laser filamentation in air, phenomena, like
self-focusing, air ionization, plasma induced laser defocusing, and side peaks due to plasma
refraction, are observed in a SINGLE SHOT.
•
If multi-shot is possible, MOPCI at different time delays can be stacked up for a 4D visualization
of the index structure.
•
For laser wakefield acceleration in Texas Petawatt Lasers with 1 pulse/h, single-shot multiobject imaging imaged the 1016 cm-3 plasma channel and wakefields after 10-20 cycles,
implying dynamics of laser propagation in plasmas for 2 GeV electron accelerations.
This work is supported by DoE grant DE-FG02-07ER54945, DE-FG02-07-96ER40954
and NSF grant PHY-0936283.
Thanks! Questions?