Single-shot visualization of EVOLVING, light-speed index structures by multi-

object phase contrast imagingZhengyan 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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N. H. Matlis et al., Nature Phys. 2, 749 (2006)

Snapshots of Quasi-static Wakes

aim of this work

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Movies of Evolving Wakes Captured in a Single Shot...

Evolution of index structures is common in different medium and different applications…

Simulation of evolving wakes for e- self-injection in LWFA

S. Kalmykov, et al., PRL 103, 135004 (2009)

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!

Evolution of index profile Δn(ξ,x,z) over propagation

Simulation of spatio-temporal splitting of laser pulse in silica

Ishikawa, et al., PRE 66, 056608 (2002)

Simulation of merging of multi-filament in air

G Mechain et al., PRL 93, 035003 (2004)

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 filamentationD. 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 diagnosisA. 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 spatio-temporal 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 holographyN. Matlis et al., Nature Physics 2, 749-753 (2006)J. K. Wahlstrand, et al., Phys. Rev. Lett. 107, 103901 (2011)

Frequency-domain tomographyZ. 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

CCD 1

CCD 2

CCD 3 CCD n

probe

pump 1 mm fused silica plate

lens 2f2 = 75 cm

lens 1f2 = 50 cm

θ

The interaction region

Object planes:

Image planes:• Amplitude • Intensity

Phase contrast

cccosθ

csinθ probe

index object

z = Lz = L/2z = 0

X

z

x

y

• To optimally resolve z-evolution

• To reduce the object-probe walk-off

Z. Li, et al., Single-shot visualization of evolving, light-speed structures by multi-object plane phase-contrast imaging, Opt. Lett., in press (2013).

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

Reconstructed phase shift along z due to the plasma channel 1.7 ps after the pulse

Back-projection to z0 for phase φi

Average phase shift

over φi

Forward-projection to z0 for amplitude Ai

Replace Ai with

measured amplitude

modulations

Measured intensity

modulations

Reconstructed phase

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 T = 66 fs, pump trailing edge

• Low plasma density on axis• Pure self-focusing

• 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

No tilted probe compensation With tilted probe compensation

Optimal compensation condition• Walk-off angle

• Compensation angle

• Optimal compensation requires

Visualization of evolving wakefields in laser wakefield accelerators driven by the Texas Petawatt Laser, at extremely low repetition rate

f# = 40

L = 10 cmd = 7 mm

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pump, e-, x-ray

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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 plasmaShot 5870 1.5 GeV electrons with 640 TW laser in 6.3e17 cm-3 plasmaShot 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…

What we want to do with index structure n(ζ,x,z)…1. Multi-Object-Plane imaging, each object plane (OP) are

imaged to different CCD.2. Phase shift imprinted on probe at arbitrary z, not limited to

OPs, is reconstructed.3. In single shot, z-depending transverse profile at specific ζ is

obtained.4. With multi-shots, full visualization of index object n(ζ,x,z).

Questions:5. Is the interaction length 35 cm, or longer?6. 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?

7. 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?

35 cm interaction region?1 deg. angle

L1 = ?The vacuum environment

Optical quality

window?

CCD1

CCD2

CCD3

CCD4

L0 = ?

800 nm, compressed 30 fs(?), < 1 mJ probe pulse, w0 < 1cm

M1

M2

Lens f = 75 cm

OP1 OP2 OP3 OP4

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

• Compensation angle

• Optimal compensation requires

For stable object, intrinsic pump-probe walk-off + tilted probe “opposite compensation”

c cosθc sinθ

z = 0

c

z = L/2 z = L

Δζ

Specs for MOPPCI in FACET • The minimum angle for oblique angle geometry

θmin = λ/πσ = 0.146 deg @ σ = 100 um 0.72 deg @ σ = 20 um

• Temporal walk-offΔt = Lθ2/2c = 38 fs @ θ = 0.5 deg 152 fs @ θ = 1 deg

• z-resolution for evolving bubbleδz = σ/θ = 5.73 mm @ σ = 100 um, θ = 1 deg 11.4 mm @ σ = 100 um, θ = 0.5 deg 2.29 mm @ σ = 20 um, θ = 0.5 deg

• ζ-resolution and range for non-evolving bubbleδζ = max{σ(θ/2+φ)/c, tpr} = max{50, 30} = 50 fsΔζ = 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 multi-object 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.

Thanks! Questions?

This work is supported by DoE grant DE-FG02-07ER54945, DE-FG02-07-96ER40954 and NSF grant PHY-0936283.