We demonstrate a prototype Frequency Domain Streak Camera (FDSC) that can capture the picosecond time evolution of the plasma accelerator structure in a single shot. In our prototype Frequency-Domain Streak Camera, a probe pulse propagates obliquely to a sub-picosecond pump pulse that creates an evolving nonlinear index >bubble> in fused silica glass, supplementing a conventional Frequency Domain Holographic (FDH) probe-reference pair that co-propagates with the >bubble>. Frequency Domain Tomography (FDT) generalizes Frequency-Domain Streak Camera by probing the >bubble> from multiple angles and reconstructing its morphology and evolution using algorithms similar to those used in medical CAT scans. Multiplexing methods (Temporal Multiplexing and Angular Multiplexing) improve data storage and processing capability, demonstrating a compact Frequency Domain Tomography system with a single spectrometer.Physic

Dong, P.

Downer, M. C.

Li, Z. Y.

Reed, S.

Wang, X. M.

Zgadzaj, R.

English

Texas ScholarWorks

Frequency‐Domain Streak Camera and Tomography for Ultrafast Imaging of Evolvingand Channeled Plasma Accelerator StructuresZhengyan Li, Rafal Zgadzaj, Xiaoming Wang, Stephen Reed, Peng Dong, and Michael C. Downer  Citation: AIP Conference Proceedings 1299, 121 (2010); doi: 10.1063/1.3520297 View online: http://dx.doi.org/10.1063/1.3520297 View Table of Contents: http://scitation.aip.org/content/aip/proceeding/aipcp/1299?ver=pdfcov Published by the AIP Publishing  Articles you may be interested in Frequency Domain Tomography Of Evolving Laser‐Plasma Accelerator Structures AIP Conf. Proc. 1086, 131 (2009); 10.1063/1.3080893  Observation of asymmetrically imploded core plasmas with a two-dimensional sampling image x-ray streakcameraa) Rev. Sci. Instrum. 79, 10E920 (2008); 10.1063/1.2981171  Four-channel magnetic resonance imaging receiver using frequency domain multiplexing Rev. Sci. Instrum. 78, 015102 (2007); 10.1063/1.2424426  Ultrafast x-ray imaging with sliced sampling streak cameras Rev. Sci. Instrum. 77, 026105 (2006); 10.1063/1.2173069  Two-dimensional sampling-image x-ray streak camera for ultrafast imaging of inertial confinement fusionplasmas Rev. Sci. Instrum. 70, 620 (1999); 10.1063/1.1149285   This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to  IP:Frequency-Domain Streak Camera and Tomography forUltrafast Imaging of Evolving and Channeled PlasmaAccelerator StructuresZhengyan Li, Rafal Zgadzaj, Xiaoming Wang, Stephen Reed, Peng Dong,Michael C. DownerDepartment of Physics, University of Texas at Austin, Austin, TX, USA, 78712Abstract. We demonstrate a prototype Frequency Domain Streak Camera (FDSC) that can capture the picosecond timeevolution of the plasma accelerator structure in a single shot. In our prototype Frequency-Domain Streak Camera, a probepulse propagates obliquely to a sub-picosecond pump pulse that creates an evolving nonlinear index “bubble” in fused silicaglass, supplementing a conventional Frequency Domain Holographic (FDH) probe-reference pair that co-propagates with the“bubble”. Frequency Domain Tomography (FDT) generalizes Frequency-Domain Streak Camera by probing the “bubble”from multiple angles and reconstructing its morphology and evolution using algorithms similar to those used in medicalCAT scans. Multiplexing methods (Temporal Multiplexing and Angular Multiplexing) improve data storage and processingcapability, demonstrating a compact Frequency Domain Tomography system with a single spectrometer.Keywords: Laser plasma acceleration, Frequency Domain Holography (FDH), Frequency Domain Streak Camera (FDSC), FrequencyDomain Tomography (FDT), pulse multiplexingPACS: 42.40.Kw, 42.30.Wb, 52.38.KdINTRODUCTIONIntense laser pulses or particle bunches propagating through plasma create complex micrometer-scale, luminal-velocity wakefields that are challenging to image in the laboratory, and thus are often known in detail only throughintensive computer simulations. Accurate single-shot visualization can improve fundamental understanding of the gen-eration and evolution of laser plasma wakefield structures, and improve the functioning of plasma-based accelerators.In 2006 Matlis et al. [1] captured “snapshots” of quasi-static linear laser plasma accelerator structures using Fre-quency Domain Holography (FDH) [2]. Frequency Domain Holography use a temporally stretched probe-reference(P–R) pulse pair that co-propagates with an intense pulse and the plasma structures it creates (see Fig.1a). The probepulse (wavelength λpr) covers the whole “object”, accumulating phase shift∆φpr(r,ζ ,z) = 2piλpr∫ L0[1−η(r,ζ ,z)]dz (1)because of the pump-induced refractive index structure η(r,ζ ,z) over distance L. Here r denotes transverse distancefrom the pump propagation axis, ζ longitudinal distance behind the pump. ∆φpr is reconstructed by interfering theprobe with a temporally advanced “reference” pulse in a spectrometer, and Fourier analyzing the resulting frequency-domain hologram [1, 2, 3]. In the strongly nonlinear “bubble” regime [4], however, which is important for producingnearly monoenergetic, low-emittance electron beams, the “bubble” structure evolves significantly [5], elongating atthe beginning to trap electrons and contracting in the end to yield mono-energetic e-beam. The evolution history ofthe wakefield structure is critical to laser plasma accelerator functions and to the quality of electron beams. However,as shown in Eq. (1), ∆φpr in Frequency Domain Holography averages the evolving, z-depending η(r,ζ ,z). To recoverlost information, it is necessary to generalize Frequency Domain Holography to a new visualization technique, whichyields a movie of the “bubble” evolution history.121 This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to  IP:FIGURE 1. Schematic probe-reference (P–R) pulse configurations for a. Frequency Domain Holography (FDH) and b. Fre-quency Domain Streak Camera (FDSC) after pump has just entered (z ≈ 0), is about to exit (z ≈ L), and has exited (z > L) themedium. Arrows denote propagation directions of pump-induced index perturbation η(r,ζ ,z) and chirped probe-reference pulses.The latter are imaged from z = L to the entrance slit of a spectrometer.FREQUENCY DOMAIN STREAK CAMERAWe generalize Frequency Domain Holography by including a Frequency Domain Streak Camera (FDSC), whichuses a probe-reference pair that propagates at angle θ to the pump (see Fig. 1b). In the probe pulse frame, the evolving“bubble” sweeps across the probe profile with velocity~v =vp cosθ − vpr1− vpvpr cosθ/c2 eˆ||+vp sinθ√1− v2pr/c21− vpvpr cosθ/c2 eˆ⊥, (2)imprinting a phase shift “streak” that records information about the bubble’s evolution. Here eˆ|| and eˆ⊥ are parallel andperpendicular, respectively, to the probe propagation direction, while vp and vpr denote lab frame group velocities ofpump and probe pulses, respectively, in the medium. The phase streak is reconstructed using conventional FrequencyDomain Holography methods. A transverse line-out at a specific time of the streak perpendicular to its axis vˆaccumulates phase shift as the bubble sweeps through. If the time interval taken by the bubble to sweep through theline-out is short enough compared to the whole propagation time that the bubble shape does not experience significantchanges, the transverse line-out yields a projection of the bubble structure at the θ dependent projection angleφ(θ) = arctan(sinθcosθ − vpr/vp)−θ , (3)with time resolution d||/v, where d|| is the bubble’s dimension along vˆ. The Frequency Domain Streak Cameraconsisting of transverse line-outs at different time yields a time sequence of projections at the projection angle φ(θ),revealing information about the bubble’s evolution.As a proof of concept, we performed a prototype experiment by creating an evolving bubble-like object by focusinga 600fs pump pulse (wavelength λpu = 800 nm, bandwidth ∆ν = 30 nm FWHM) inside a fused silica plate of thicknessL = 3 mm. The pump induced refractive index η(r,ζ ,z) = n2I(r,ζ ,z), where n2 ≈ 3×10−16 cm2/W is the nonlinearindex of glass and I(r,ζ ,z) is the pump intensity profile. Thus η(r,ζ ,z) evolves as the pump pulse diffracts, self-focuses, etc. Initial peak intensity I of the pump (focused here to spot radius w0 ∼ 20 µm at z= 0) varied between 0.04122 This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to  IP:I = 0.04 TW/cm2Radial         position (µm)500−50T (ps)Radial       position (mm)−1 0 110.50I = 0.47 TW/cm2T (ps)−1 0 1I = 0.93 TW/cm2T (ps)−1 0 1I = 1.47 TW/cm2T (ps)−1 0 1700 800 900λ (nm)700 800 900λ (nm)700 800 900λ (nm)700 800 900050010001500λ (nm)Intensity (a.u.)−1.5−1−0.5−0.25−0.2−0.15−0.1−0.05(rad)(rad)Z=010µmFIGURE 2. Phase shifts on 0◦ (top row) and 14◦ (middle row) probes, and transmitted pump spectrum (bottom row) and spatialprofile (inset), for initial pump intensity (left to right) I = 0.04, 0.47, 0.93, and 1.47 TW/cm2.and 1.5 (right) TW/cm2 on different shots. In the upper end of this intensity range, n2IL > λpu, so pump propagationbecomes nonlinear. Two linearly chirped, 1 ps, second harmonic (λpr = 400 nm) pulse pairs P1-R1 and P2-R2 probedη(r,ζ ,z) simultaneously at θ = 0◦ (FDH) and 14◦ (FDSC), respectively. At 14◦, the streak sweeps nearly transverselyacross the probe profile. The two pairs, each with probe and reference separated by ∆tPR = 3.3 ps, were imaged fromthe sample exit plane (z = L) of the silica plate to spatially offset locations at the spectrometer entrance slit so FDHand FDSC data were analyzed by a single spectrometer.Figure 2 shows reconstructed images from the spatially multiplexed Frequency Domain Holography (top row) andFrequency Domain Streak Camera (2nd row) probes, and the spectrum (3rd row) and spatial profile (3rd row inset)of the pump at z = L for four different I (indicated at top). The Frequency Domain Holography images show thelongitudinally–averaged η(r,ζ ,L). There are two complications in interpreting the Frequency Domain Holographyimages by themselves: (i) there is a discrepancy between the measured index “bubble” longitudinal extent (∼1 ps)and the pump pulse duration (∼600 fs) measured from a transverse line-out of the FDSC streak, which is caused by450 fs group velocity walk-off between 800 nm pump and 400 nm probe; and (ii) phase wrapping artifacts created by∆φpr exceeding 2pi near r = 0 appear at large I. These complications underscore the importance of Frequency DomainStreak Camera.The Frequency Domain Streak Camera images (Fig.2, middle row) show a distinct phase streak that increases inamplitude with I. Line-outs along the streak axis, plotted in Fig.3(a), reveal intensity-dependent evolution of the axialphase shift. To help interpret this evolution, we modeled propagation of Gaussian pump pulses using the nonlinearSchrödinger equation, including multi-photon absorption and plasma formation [6]. Fig.3(b) shows the calculatedpeak pump intensity I(z) for various initial I. For I = 0.04 TW/cm2, nonlinearities are negligible, I(z) decreasesmonotonically by linear diffraction over Rayleigh range zR = pin0w20/λpu ≈ L, and the transmitted pump spectrum isbarely perturbed from the incident spectrum (Fig.2, 3rd row, left). For I = 0.47 TW/cm2, peak pump power (3 MW)reaches critical power Pcr = pi(0.61)2λ 2pu/8n0n2 = 2.15 MW, and the pump propagates with nearly constant intensity,indicating a balance between self-focusing and diffraction with multi-photon absorption still weak. Simultaneously,we begin to observe pump frequency broadening to ∆ν ∼ 50 nm (Fig. 2, 3rd row, 2nd panel), a signature of self-phase modulation. As pump intensity increases further (I = 0.70 to 1.47 TW/cm2), nonlinear Schrödinger equationcalculations show: (i) the pump self-focuses closer and closer to the glass entrance, initially increasing its intensity,123 This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to  IP:128.83.205.78 On: Thu, 19 Mar 2015 18:14:59FIGURE 3. a. Measured line-outs along streak axis. b. Calculated line-outs along streak axis based on the generalized nonlinearSchrödinger equation.followed by a monotonic decrease in intensity (see Fig. 3(b)); (ii) direct multi-photon absorption is the primary cause ofthe monotonic intensity decrease; (iii) the pump converges to a nearly intensity-independent transverse Townes profile[7] with FWHM 16 µm, in good agreement with the exit profiles shown in the insets of the last two panels, 3rd row ofFig. 2. Meanwhile the transmitted pump spectrum further broadens (Fig. 2, 3rd row, last 2 panels), indicating strongerself-phase-modulation. The transverse FWHM of the FDH phase profiles (Fig.2, top row) agree well the exit pumpprofiles and nonlinear Schrödinger equation calculations (their apparent broadening with increasing I results fromincreased visibility of the wings as total ∆φpr increases). The initial self-focusing accounts for the large ∆φpr near thecenter of the Frequency Domain Holography images at high I. The example illustrates how combining informationfrom Frequency Domain Holography and Frequency Domain Steak Camera improves accuracy of interpretation.PROBE MULTIPLEXING FOR FREQUENCY DOMAIN TOMOGRAPHYFrequency Domain Tomography (FDT) with streak cameras at different θ corresponds to time sequences ofprojections at multiple projection angles φ . Projections at a specific time from each streak can be processed usingtomographic algorithms [8] to reconstruct an instantaneous “frame” of the bubble’s structure at that time. Repeatingthe procedure for different times yields a multi-frame “movie”, all from single-shot data. If we assume that the pumplaser pulse or particle beam is cylindrically symmetric so the bubble is symmetric as well, the projection angle φ(θ)ranging from 0◦ to 90◦ can provide enough information to reconstruct bubble evolution without “streak artifacts” [9].However, if the bubble is not perfectly cylindrically symmetric in reality and the required projection angle range isφ ∈ [0◦,180◦], two color probe sets with wavelength larger and smaller than pump respectively are needed, in order toavoid too small phase shift on probes that counterpropagate with the pump (θ > 90◦). 873 nm Stokes line generatedby pumping Ti:Sapphire crystal with 800 nm laser pulse in chirped Raman pulse amplification (CRPA) [10] would beused as the other color of probes beside the already used frequency doubled 400 nm probes.FIGURE 4. Probe pulses multiplexing. a. Temporal multiplexing pulse arrangement and Fourier transform of raw frequencydomain hologram line-out; b. Angular multiplexing pulse arrangement and raw frequency domain hologram data.124 This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to  IP:Compact and cost-effective Frequency Domain Tomography is achieved by temporal multiplexing and angularmultiplexing methods to collect probes at different θ with a single spectrometer in a single shot. In temporalmultiplexing, one reference pulse and several probes are combined into a single pulse train as shown in Fig.4(a).The raw frequency-domain hologram shows multiple frequency domain modulations as a result of different timedelays between pulses. A 1-D Fourier transform in frequency isolates peaks corresponding to interference between thereference and each probe. We have demonstrated 3-probe temporal multiplexing experimentally with probes separatedby ∼ 400 fs to avoid overlap between neighboring peaks in the Fourier transform data, and thus to avoid cross-talkbetween different probes.In angular multiplexing, several reference-probes sequences like the one in Fig.4(a) propagate into the spectrometerslit at slightly different angles, as shown in Fig.4(b), creating interference fringes along the transverse dimension of thehologram in addition to the conventional longitudinal frequency-domain fringes. The result is a 2-D grid-like map ofinterference fringes. A 2-D Fourier transform isolates peaks corresponding to probes at specific time delays behind thereference and specific angles of incidence into the spectrometer. We have experimentally demonstrated 3 probes at 0◦,0.6◦, and 3◦ angles angularly multiplexed and 3.3 ps separated from the reference without cross-talk in reconstruction.These results demonstrate the feasibility of multiplexing tens of probes to a single spectrometer for compact, low-costFrequency Domain Tomography.CONCLUSIONWe implemented Frequency Domain Holography with Frequency Domain Streak Camera to observe the evolutionof a microscopic light-speed object, demonstrating the possibility of visualizing evolving wakefields in the nonlinear“bubble” regime. Moreover, Frequency Domain Streak Camera with probes at multiple angles yields FrequencyDomain Tomography, which can reconstruct a time sequence of a quasi–static snapshots, like frames of movie, ofevolving laser wakefields. By using temporal and angular multiplexing methods, we demonstrated a compact setupwhich is able to process data from multiple probes with a single spectrometer.Oblique angle Frequency Domain Streak Camera and Frequency Domain Tomography can also find their applicationin situations where a collinear probe is not available. For example, in the generation of high quality electron beamabove 1 GeV [11] and future Berkeley Lab Laser Accelerator (BELLA) experiments, a gas-filled capillary dischargedplasma waveguide [12] is used, scrambling any wakefields structure encoded in the phase shift imprinted on acopropagating probe. However, the problems with conventional Frequency Domain Holography can be solved byhaving oblique angle Frequency Domain Tomography probes cross the waveguide area from windows on both sides.Thus Frequency Domain Tomography should enable laboratory visualization of channeled laser plasma acceleratorstructures for the first time. With Frequency Domain Streak Camera or Frequency Domain Tomography, we canexpect a movie of “bubble” evolution for better understanding of laser–plasma interactions, and a compact instrumentdiagnosing laser plasma accelerator structures for 10 GeV electron generation in various applications.ACKNOWLEDGMENTSThis work was supported by U.S. DoE grants DE-FG02-07ER54945 and DE-FG02-96ER40954 and NSF grantPHY-0936283.REFERENCES1. N. Matlis, S. Reed, S. S. Bulanov, V. Chvykov, G. Kalintchenko, T. Matsuoka, P. Rousseau, V. Yanovsky, A. Maksimchuk,S. Kalmykov, G. Shvets and M. C. Downer, Nature Phys. 2, 749–753 (2006).2. S. P. Le Blanc, E. W. Gaul, N. H. Matlis, A. Rundquist and M. C. Downer, Opt. Lett. 25, 764–766 (2000).3. J. P. Geindre, P. Audebert, A. Rousse, F. Falliès, J. C. Gauthier, A. Mysyrowicz, A. Dos Santos, G. Hamoniaux and A. Antonetti,Opt. Lett. 19, 1997–1999 (1994).4. A. Pukhov and J. Meyer-ter-Vehn, Appl. Phys. B 74, 355 (2002).5. S. Kalmykov, S. A. Yi, V. Khudik, G. Shvets, Phys. Rev. Lett. 109, 135004 (2009).6. A. L. Gaeta, Phys. Rev. Lett. 84, 3582–3585 (2000).7. K. D. Moll, A. L. Gaeta and G. Fibich, Phys. Rev. Lett. 90, 203902 (2003).8. A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging, IEEE Press, New York, 1987.125 This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to  IP:9. H. Stark, Image Recovery: Theory and Application, Academic Press, New York, 1987, pp. 325.10. F. Grigsby, P. Dong and M. C. Downer, J. Opt. Soc. Am. B 25, 346–350 (2008).11. W. P. Leemans, B. Nagler, A. J. Gonsalves, Cs. Tóth, K. Nakamura, C. G. R. Geddes, E. Esarey, C. B. Schroeder, and S. M.Hooker, Nature Phys. 2, 696–699 (2006).12. A. Butler, D. J. Spence, and S.M. Hooker, Phys. Rev. Lett. 89, 185003 (2002).126 This article is copyrighted as indicated in the article. 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Frequency-Domain Streak Camera And Tomography For Ultrafast Imaging Of Evolving And Channeled Plasma Accelerator Structures

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Frequency-Domain Streak Camera And Tomography For Ultrafast Imaging Of Evolving And Channeled Plasma Accelerator Structures

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