1. Single-Shot Tomographic Imaging of Evolving, Light Speed Object Zhengyan Li, Rafal Zgadzaj, Xiaoming Wang, Yen-Yu Chang, Michael C. Downer Department of Physics and Institute of Fusion Studies The University of Texas at Austin, Austin, TX 78712 Advanced Accelerator Concepts, Austin, TX, June 15, 2012

2. 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! Simulation of evolving pulse intensity during nonlinear propagation in fused silica A. Couairon, et al., Phys. Rev. B 71, 125435 (2005)

3. Single-shot Frequency-Domain Holography (FDH) took snapshots of quasi-static laser wakefields… N. Matlis et al., “Snapshots of laser wakefields,” Nature Physics 2, 749-753 (2006) Phase accumulated in the collinear probe averages the z-dependence of the wakefields, i.e. index structure η(r, ζ, z). Thus FDH can only take snapshots of quasi-static objects.

4. As a generalization FDH, Frequency-Domain Streak Camera (FDSC) is a time sequence of the object’s tomographic projections… Z. Li, et al., “Frequency-domain streak camera for ultrafast imaging of evolving, light-speed objects,” Opt. Lett. 35, 4087-4089 (2010) FDSC is a time sequence of the object’s projections along projection angle ϕ

5. Frequency-domain tomography (FDT) incorporate multiple probes to get FDSC covering projection angles from -70 to 70 degree in a single shot…

6. Compact probe array generation are based on nonlinear optical effects for tomographic application… Large n 2 glass HZF4 for cascaded FWM BBO Go to another HZF4 for chirp Incident beam pair 800 nm cascade FWM: 8 in total polarization 400 nm probes through SHG & SFG: 15 in total Frequency domain streak cameras (FDSC) coded in selected 5 probes  No movable parts for tomographic angle scanning  Self-synchronized by imaging the “sandwich” to interaction region  Up to 15 probes generated with comparable energy  Minimized phase mismatch in BBO by using correct polarization  Compact and inexpensive

7. Angular or temporal multiplexing of probes enables cost-efficient data collection with a single spectrometer in a single shot… FDH raw data2D Fourier transform RefProbe 1 RefProbe 1 Probe 2 RefProbe 1 Probe 2 Probe 3

8. Single-shot tomographic movies reveal dynamics of nonlinear pulse propagation, i.e. self-focusing, laser filamentation, plasma generation…

9. Simulation of femtosecond pulse nonlinear propagation is consistent with measured movie, including effects of diffraction, dispersion, self-focusing, plasma effect, and multi-photon processes… 400 nJ 500 nJ 600 nJ 700 nJ

10. What interesting physics can we learn from movies for glass experiments? It is not only a prototype experiment for future application in plasma based wake field accelerators, but also important to understanding femtosecond filamentation. White-light LIDAR J. Kasparian et al., Science 301,61-64 (2003) Lightening control Nature Photonics 3, 120 - 121 (2009) Triggering rain in air P. Rohwetter et al., Nature Photonics 4, 451 - 456 (2010) What is the mechanism of filamentation? Established theory: the balance between positive nonlinear refractive index n 2 I and negative index by plasma New theory: negative contribution of high order nonlinearity (e.g. n 4, n 8 ) leads to saturation of nonlinear refractive index V. S. P. Bejot, et al., PRL 104, 103902 (2010) P. Bejot, et al., PRL 106, 243902 (2011) C. Bree, et al., PRL 106, 183902 (2011) A. Couairona, et al., Phys. Rep. 441, 47-189 (2007) P. Polynkin, et al., PRL 106, 153902 (2011) J. M. Brown, et al., Opt. Lett. 37, 1604-1606 (2012)

11. Different mechanisms yield different behaviors of refractive index profiles… Established theoryNew theory For peak plasma density, i.e. steady state Movie frame at z = 2.5 mm for 700 nJ pump In simulation, plasma effect starts to balance nonlinear Kerr effect at z = 2.5 mm, with laser peak intensity of 26 TW, and plasma density of ~10 18 cm -3 Our “movie” supported the established theory about plasma effect for glass in our parameter regime.

12. Single-shot tomographic technique, i.e. frequency-domain tomography (FDT), yields a movie of wake-field evolution or electron bunch interactions for both high and low density LWFA/PWFA… Index structure evolution in laser- filamentation in glass medium A broadening of probe band- width to ~100 nm for temporal resolution of ~10 fs For high density LWFA, modified FDT system with broader bandwidth can make a movie of wake-field “bubble” evolution For low density LWFA/PWFA, small oblique angle probing reveals temporal profile evolution For LWFA @ Texas Petawatt, temporal profile of wake field and its elongation and contraction would be visualized, which is critical for electron injection.

13. Summary Frequency-domain tomography (FDT) applies multiple probes at different angles in a single shot, yielding a movie of evolving index structures. FDT is compact and inexpensive by generating multi-probe array through standard nonlinear optical effects, and by detecting probes through angular/temporal multiplexing methods. The application of FDT to laser-dielectrics interactions reveals the mechanism of femtosecond filamentation. FDT will be applied to wake field diagnosis in future. This work is supported by U.S. Department of Energy (DoE) grants DE-FG02-07ER54945 and DE-FG02-96ER40 954 and National Science Foundation (NSF) grant PHY-0936283