Single-shot visualization of EVOLVING, light-speed index structures by multi- object 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 µm 0.4 ps ∆  probe (r,  ) N. H. Matlis et al., Nature Phys. 2, 749 (2006) Snapshots of Quasi-static Wakes aim of this work 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, (2009) Simulation of evolving electron driving and witness beam in electron-driven plasma accelerators I. Blumenfeld, et al., Nature 445, (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, (2002) Simulation of merging of multi-filament in air G Mechain et al., PRL 93, (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 filamentation D. Abdollahpour et al., Phys. Rev. A 84, (2011) G. Rodriguez, et al., J. Opt. Soc. Am. B 25, (2008) Time-resolved polarimetry and plasma shadowgraphy for electron diagnosis A. Buck, et al., Nature Physics 7, (2011). Transverse probing geometry can only visualize z-evolution in multi-shots, and for long interaction length (~10 1 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 holography N. Matlis et al., Nature Physics 2, (2006) J. K. Wahlstrand, et al., Phys. Rev. Lett. 107, (2011) Frequency-domain tomography Z. Li et al., in preparation

Multi-object phase contrast imaging with small oblique angle probe maps ~10 1 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 2 f 2 = 75 cm lens 1 f 2 = 50 cm θ The interaction region Phase contrast c ccosθ 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 ψ 0 <<1, ψ~ψ 0 /3

Measured phase shift in different cameras are iteratively reconstructed using Gerchberg-Saxton algorithm, no matter the object at z 0 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 z 0 for phase φ i Average phase shift over φ i Forward-projection to z 0 for amplitude A i Replace A i 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 compensationWith tilted probe compensation

Visualization of evolving wakefields in laser wakefield accelerators driven by the Texas Petawatt Laser, at extremely low repetition rate f# = 40 L = 10 cm d = 7 mm probe pump, e -, x-ray z x

Primary results of visualizing laser plasma wakefield acceleration structures in the Texas Petawatt Laser Shot GeV electrons with 640 TW laser in 6.9e17 cm-3 plasma Shot 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 10 th to 20 th 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: 1.Is the interaction length 35 cm, or longer? 2.Where is possible for us to couple laser into the chamber? What are the lengths of L 0 and L 1 ? To maintain a good imaging resolution, we hope L 1 is not too large, what is the shortest length we can get? 3.Is there anything that potentially blocks or clips the beam between M 1 and M 2 ? Here the angle is 1 deg. = rad, so the inside diameter of the tube containing the laser has to be larger than 3 cm, if L 0, L 1 ~ 50 cm. Is it OK? 35 cm interaction region? 1 deg. angle L 1 = ? The vacuum environment Optical quality window? CCD1 CCD2 CCD3CCD4 L 0 = ? 800 nm, compressed 30 fs(?), < 1 mJ probe pulse, w 0 < 1cm M1M1 M2M2 Lens f = 75 cm OP1OP2OP3 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 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 For stable object, intrinsic pump-probe walk-off + tilted probe “opposite compensation” c cosθ c sinθ z = 0 c z = L/2 z = L Δζ

Specs for MOPPCI in FACET The minimum angle for oblique angle geometry θ min = λ/πσ = σ = 100 um 0.72 σ = 20 um Temporal walk-off Δt = Lθ 2 /2c = 38 θ = 0.5 deg 152 θ = 1 deg z-resolution for evolving bubble δz = σ/θ = 5.73 σ = 100 um, θ = 1 deg 11.4 σ = 100 um, θ = 0.5 deg 2.29 σ = 20 um, θ = 0.5 deg ζ-resolution and range for non-evolving bubble δζ = max{σ(θ/2+φ)/c, t pr } = max{50, 30} = 50 fs Δζ = Lθ(θ/2+φ)/c = 1.26 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 ~10 1 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 cm -3 plasma channel and wakefields after 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-FG ER40954 and NSF grant PHY