Femtosecond laser produced periodic plasma in a colloidal crystal probed by XFEL radiation
Nastasia Mukharamova, Sergey Lazarev, Janne-Mieke Meijer, Oleg Yu. Gorobtsov, Andrej Singer, Matthieu Chollet, Michael Bussmann, Dmitry Dzhigaev, Yiping Feng, Marco Garten, Axel Huebl, Thomas Kluge, Ruslan P. Kurta, Vladimir Lipp, Robin Santra, Marcin Sikorski, Sanghoon Song, Garth Williams, Diling Zhu, Beata Ziaja-Motyka, Thomas Cowan, Andrei V. Petukhov, Ivan A. Vartanyants
FFemtosecond laser produced periodic plasma in a colloidal crystalprobed by XFEL radiation
Nastasia Mukharamova, Sergey Lazarev,
1, 2
Janne-Mieke Meijer, ∗ Oleg Yu.Gorobtsov, † Andrej Singer, † Matthieu Chollet, Michael Bussmann,
6, 7
DmitryDzhigaev, ‡ Yiping Feng, Marco Garten,
6, 8
Axel Huebl,
6, 8, § Thomas Kluge, Ruslan P. Kurta, ¶ Vladimir Lipp, Robin Santra,
9, 10
Marcin Sikorski, ¶ Sanghoon Song, Garth Williams, ∗∗ Diling Zhu, Beata Ziaja-Motyka,
9, 11
Thomas Cowan, Andrei V. Petukhov,
3, 12 and Ivan A. Vartanyants
1, 13, †† Deutsches Elektronen-Synchrotron DESY,Notkestraße 85, D-22607 Hamburg, Germany National Research Tomsk Polytechnic University (TPU),pr. Lenina 30, 634050 Tomsk, Russia Debye Institute for Nanomaterials Science,University of Utrecht, Padualaan 8,3508 TB Utrecht, The Netherlands University of California, 9500 Gilman Dr.,La Jolla, San Diego, CA 92093, USA SLAC National Accelerator Laboratory,2575 Sand Hill Rd, Menlo Park, CA 94025, USA Institute of Radiation Physics, Helmholtz ZentrumDresden-Rossendorf, 01328 Dresden, Germany Center for Advanced Systems Understanding (CASUS), G¨orlitz, Germany Technische Universit¨at Dresden, 01069 Dresden, Germany Center for Free-Electron Laser Science,DESY, D-22607 Hamburg, Germany Department of Physics, Universit¨at Hamburg, 20355 Hamburg, Germany Institute of Nuclear Physics, PAS,Radzikowskiego 152, 31-342 Krakow, Poland Laboratory of Physical Chemistry,Department of Chemical Engineering and Chemistry, a r X i v : . [ c ond - m a t . s o f t ] N ov indhoven University of Technology P.O. Box 513, 5600 MB Eindhoven, Netherlands National Research Nuclear University MEPhI (Moscow Engineering Physics Institute),Kashirskoe shosse 31, 115409 Moscow, Russia (Dated: November 12, 2019)
Abstract
With the rapid development of short-pulse intense laser sources, studies of matter under extremeirradiation conditions enter further unexplored regimes. In addition, an application of X-ray Free-Electron Lasers (XFELs), delivering intense femtosecond X-ray pulses allows to investigate sampleevolution in IR pump - X-ray probe experiments with an unprecedented time resolution. Here wepresent the detailed study of periodic plasma created from the colloidal crystal. Both experimentaldata and theory modeling show that the periodicity in the sample survives to a large extent theextreme excitation and shock wave propagation inside the colloidal crystal. This feature enablesprobing the excited crystal, using the powerful Bragg peak analysis, in contrast to the conventionalstudies of dense plasma created from bulk samples for which probing with Bragg diffraction tech-nique is not possible. X-ray diffraction measurements of excited colloidal crystals may then leadtowards a better understanding of matter phase transitions under extreme irradiation conditions. ∗ Present address: Universiteit van Amsterdam, Science Park 904, 1090 GL Amsterdam, The Netherlands † Present address: Cornell University, Ithaca, NY 14850, USA ‡ Present address: Division of Synchrotron Radiation Research, Department of Physics, Lund University,S-22100 Lund, Sweden § Present address: Lawrence Berkeley National Laboratory, 1 Cyclotron Rd, Berkeley, CA 94720, USA ¶ Present address: European XFEL, Holzkoppel 4, D-22869 Schenefeld, Germany ∗∗ Present address: NSLS-II, Brookhaven National Laboratory, Upton, NY 11973-5000, USA †† Corresponding author email: [email protected] . INTRODUCTION Studies of materials at high-pressure conditions above Mbar are highly relevant to thephysics of shock compressed matter [1–5], planetary formation [6–8], warm dense mat-ter [3, 5, 9], and different types of plasma-matter interactions [10, 11]. The thermodynamicand transport properties of the high energy density material dictate its dynamics. The gen-eral understanding of processes in materials under high pressure and temperature such asphase transitions [3] or phase separations [12] are of a great scientific interest. Theoreticalinvestigations of the dynamics of materials under high pressure are widespread, however,due to the limited diagnostic capabilities, experimental studies are still quite challenging.There are currently two major methods of generating extreme high pressure, that are thestatic compression with diamond anvil cells and dynamic (shock wave) compression. Thelatter can be done for example by the powerful short-pulse lasers which offer the possibility ofcreating ultra-high pressure, much higher than achievable in static compression experiments.The fundamental property of such high-power lasers is the creation of plasma at extremepressure and temperature, which is causing a shock compression of the material. Dynamicshock compression of aluminum [9], copper [13], carbons [3] and hydrocarbons [12], as wellas other materials driven by high-power lasers is a subject of recent extensive studies. Theshock wave speed is in the range of several kilometers per second, therefore, a facility pro-viding picosecond resolution is required for the in situ measurements of the shock-induceddynamics.Newly developed X-ray Free-Electron Lasers (XFELs) [14–17] are especially well suited fortime-resolved measurements of the ultrafast structural dynamics of laser-created plasma [12,18]. XFELs provide extremely intense coherent femtosecond X-ray pulses, which are neces-sary to perform experiments with a time resolution that outperforms synchrotron sourcesby orders of magnitude [9, 19]. X-ray scattering at XFEL is a powerful tool for successfulstudies of the rapid changes in the material caused by a high-power infrared (IR) laser inboth space and time [20]. Although the scattering signal from the uniform plasma is not veryhigh, sufficient response can be achieved if the plasma is periodically modulated in spacethus allowing the use of much stronger X-ray Bragg scattering [21] and imaging [22–26]techniques.Such a unique form of matter as periodic plasma [27] can be created, for example, by the3igh-power laser interaction with the periodically ordered dielectric material. Recently, theproperties of periodic plasma have been studied theoretically [28, 29] and experimentally [30–33]. One of the fascinating properties of laser-produced periodic plasma is the enhancementof the generated intensity in the cases of low order harmonic generation in comparison toa uniform plasma [34]. Therefore, investigation of dynamics and properties of a periodicplasma is beneficial for the development of laser-based radiation sources. In the presentstudy a periodic plasma was formed by the IR laser interaction with colloidal crystals madeof polystyrene.Polystyrene, consisting of carbon and hydrogen, is an ideal model system for creating aplasma by the IR laser sources because these atoms have a relatively low ionisation threshold,accessible by high-power IR laser. This material is also of high relevance to the biologicalcommunity, since most of the biological samples consist of light atoms such as carbon, nitro-gen, oxygen, and hydrogen [35, 36]. In addition, hydrocarbons are one of the most commonchemical species throughout the Universe [37]. A considerable amount of hydrocarbons com-pressed to 150 GPa exists inside giant planets, especially icy giants such as Neptune andUranus [38]. Also, some extrasolar planets [39] and white dwarf stars [40], are built fromhigh-pressure carbon which was recently extensively studied [41].Here, we present in situ
IR pump–X-ray probe diffraction experiment performed at XFELon a periodic polystyrene colloidal crystals. The periodicity of the sample allowed us toapply the Bragg peaks analysis and to observe dramatic ultrafast changes in the colloidalcrystal sample. The experiment was performed with the IR laser intensity on the order of10 W/cm . With such high intensities a confined hot periodic plasma was created andgenerated a shock wave that compressed the surrounding pristine material. This shock wavereached pressures on the order of 100 GPa, triggering fast changes in the colloidal crystalstructure. We found a good correspondence between the characteristic times determinedin the experiment and in simulations. Below we discuss the details of the pump-probeexperiment and theoretical modeling of the processes involved in our studies.4 I. RESULTSA. Pump-probe experiment
The pump-probe experiment was performed at the Linac Coherent Light Source (LCLS) [15]X-ray Pump Probe (XPP) beamline [42] (see [43] and Methods for experimental details).The colloidal crystal films were prepared from polystyrene spheres with a diameter of163 ± τ from -10 ps to 1000 ps with 25.25 ps time increment. Additionally, for two higher IRlaser intensities ( I and I ) we also accomplished measurements from -10 ps to 48.5 ps withthe 6.5 ps time increment. Due to a sample degradation, measurements for each time delaywere performed at a new position of the sample.Typical single-shot diffraction patterns for three different time delays are shown in theinsets in Fig. 1. Bragg peak parameters corresponding to the most intense 110 reflectionssuch as integrated intensity ( I ) and the peaks Full Width at Half Maximum (FWHM) inthe radial ( w q ) and azimuthal ( w ϕ ) directions were analyzed. For three IR laser intensitiesvariation of the Bragg peak intensity ∆ I ( τ ) /I , radial ∆ w q ( τ ) /w q , and azimuthal ∆ w ϕ ( τ ) /w ϕ broadening of the Bragg peaks are shown in Fig. 2 as a function of time delay (see Methodsfor the details of the diffraction data analysis).The experimental measurements in Fig. 2 are depicted by black dots for 25.25 ps timeincrement and by blue dots for 6.5 ps time increment. The decay of the relative Bragg peakintensity accompanied by the growth of the peaks size (FWHM) for all three measured IRlaser intensities is well visible. For two higher IR laser intensities, an additional fast drop ofthe relative intensity during the first picoseconds was also observed. From Fig. 2 this dropof intensity can be estimated to be about 10% of the initial intensity during the first 6.5picoseconds. This intensity drop was not accompanied by significant changes in the radialor azimuthal peaks size.In order to obtain the characteristic timescales, results of our measurements were fitted5ith exponential functions. For the lower IR laser intensity, the Bragg peak integratedintensity was fitted with one exponential function. For the two higher IR laser intensities, theBragg peak intensity decay could not be fitted with a single exponential function due to thefast drop during first picoseconds. Therefore, these data were fitted with the two exponentialfunctions which took into account both short and long characteristic timescales. For theradial and azimuthal peaks sizes (FWHM) fitting was performed by a single exponentialfunction for all IR intensities. The results of the fits are shown in Fig. 2 by red lines andthey provide a good agreement with the experimental data. For all three IR laser intensitiesthe exponential fit of Bragg peak parameters such as intensity and peaks size (FWHM)provided about 300-400 ps characteristic timescales (see Fig. 2 and Table S1). For twohigher IR laser intensities the short timescale on the order of 5 ps was also revealed by theanalysis of the Bragg peak intensities. B. Physics of high-power laser interaction with matter
To further analyze the obtained scattering results, we propose the following model of theIR laser-matter interaction. At the first stage the incoming high-power IR laser pulse ionizesthe top layer of colloidal particles, creating a confined plasma on the top of the colloidalcrystal. The processes of plasma creation and expansion are modeled taking into accountthe periodicity of the colloidal crystal sample and the polystyrene properties and will bediscussed below in this section.Polystyrene is a dielectric material and has no free electrons in the ground state. It isalso known to be transparent for the incoming IR pulses with 1.55 eV energy at low laserintensities. However, the situation changes dramatically at high IR laser intensities. Thetight focusing of a 50 fs IR laser pulse with the energy about millijoules produces an IR laserintensity on the order of hundreds of terawatts per cm . At such high IR laser intensitiesthe so-called field ionisation is important. It causes the plasma formation in the top layerof the colloidal crystal which may be described by the Keldysh theory [45]. An importantparameter of the theory is the so-called Keldysh parameter γ , γ = ω IR √ m e E i E = > → multi-photon regime ,< → quasi-static regime , (1)6here ω IR is the frequency of the laser field, m e is the electron mass, E i is the zero-fieldionisation energy of an atom, and E is the electric field generated by the laser. For low fieldsand high frequencies ( γ >
1) the multi-photon ionisation occurs, while for strong fields andlow frequencies ( γ <
1) tunneling ionisation prevails. Dependence of the Keldysh parameteron the IR laser intensity is shown in the Appendix Fig. S3. For all three IR laser intensitiesand low ionisation states of carbon and hydrogen the Keldysh parameter is lower than unity(see Fig. S3), so the quasi-static ionisation regime prevails [46, 47]. The high-intensity IRlaser field ionizes atoms in the polystyrene colloidal crystal up to H + and C + for the lowerIR intensity and up to C for the two higher IR laser intensities (see Appendix). As aresult during first femtoseconds of the IR laser pulse propagation plasma is created on topof the colloidal crystal.Due to the plasma creation, the incoming IR radiation is not penetrating any more intothe colloidal crystal sample, due to the well-known plasma skin effect [48, 49]. The depthof the skin layer l skin depends on the frequency of the IR laser ω IR and plasma frequency ω p = (cid:112) n e e /m e ε , where n e is the number density of electrons, e is the electric charge,and ε is the permittivity of free space. In our case, assuming single ionisation of eachatom, the skin depth l skin = c/ (cid:113) ( ω p − ω IR ) is about 10-20 nm. Free electrons formedin the skin layer by the strong laser-matter ionisation process are further accelerated bythe inverse bremsstrahlung [50] and resonance absorption [51] mechanisms. As such, high-energetic electrons are propagating inside the first layer of the colloidal particles of thecrystal. Accelerated electrons collide inelastically with the atomic ions inside the colloidalparticle which causes additional collisional ionisation of the C atoms up to C (see Appendixfor further details). Ionisation and IR laser energy absorption processes described aboveoccur within the colloidal crystal which has a periodic structure. As a result, created plasmaalso has the same periodicity as the colloidal crystal during the first picoseconds after theIR laser pulse interaction with a colloidal crystal.In order to simulate the first stages of creation and dynamics of the periodic plasmawe used the Particle-In-Cell on Graphic Processor Units (PIConGPU) code version 0.4.0-dev developed at Helmholtz-Zentrum Dresden-Rossendorf (HZDR) [52, 53]. PIConGPUsimulations were performed in the time interval from 0 to 1 ps for all three IR laser intensitiesmeasured in our pump-probe experiment. Two different types of ionisation processes aredominating in the colloidal crystal, namely field ionisation and collisional ionisation, and7hey were included in the simulations. The ionisation rate of the field ionisation process wascalculated according to the Ammosov-Delone-Krainov (ADK) model [54] and the collisionalionisation was simulated using the Thomas-Fermi ionisation model [55] (see Appendix fordetails).The electron energy density distribution as a function of depth and transverse spatialcoordinate at 80 fs and 1 ps after the start of the IR laser pulse propagation are shown inFig. 3. As one can see from Fig. 3(a-c), at 80 fs only the first layer of the colloidal particlesis strongly ionized by the IR laser pulse. As a result, the periodic plasma is formed on top ofthe colloidal crystal. Our simulations show that the maximum electron energy density wasreached in the center of colloidal particles of the first layer 80 fs after the start of the IR laserpulse propagation (see Fig. 3(a-c)). The maximum electron energy density is summarizedin Table S1 for three measured IR laser intensities. The pressure reaches its maximum inthe first layer in the center of each colloidal particle, thus forming a periodic plasma state.At 1 ps after the beginning of the interaction of the IR laser with the colloidal crystalsample, accelerated electrons move deep inside the colloidal crystal and collisionally ionizethe inner part of the crystal (see Fig. 3(d-f) and Appendix for further details). The electronenergy density at 1 ps has its maximum still in the first layer of the colloidal crystal but itsmagnitude is much lower than at 80 fs (see Table S1). Even after 1 ps the electron energydensity distribution resembles a periodic structure of the colloidal crystal.To determine the evolution of the electron energy density distribution, we averaged simu-lated values over the transverse x- and y-coordinates. The time dependence of the maximumelectron energy density is shown in Fig. 4(a). As shown in this figure the electron energydensity reaches its maximum value at 80 fs for all IR laser intensities values, and after 0.6 psremains practically constant. The z-dependence at 1 ps is shown in Fig. 4(b). It is clearlyseen that the electron energy density is decaying along the z-direction but periodic modu-lations due to the colloidal crystal structure are well visible. This periodicity is less visiblefor the lower IR laser intensity because of the low ionisation level of the inner part of thecolloidal crystal. 8 . Ablation and shock wave propagation After the plasma formation, the electron-ion thermalisation occurs and further dynamicsin the colloidal crystal is governed by the hydrodynamics. These processes are ablation ofthe material and shock wave propagation inside the cold material. This last hydrodynamicstage of our model, which was also observed in our experiment, will be discussed in thissection.As can be seen from Fig. 4(a) the ionisation of the colloidal crystal was practically finishedat 1 ps. Around these times the high-pressure dense plasma in the top layers of the colloidalcrystal induced ablation and shock wave propagation inside the sample. As a result, thetop layers of the sample were ablated and a strong shock wave compressed the solid anddestroyed the periodicity of the inner part of the colloidal crystal. We relate experimentallyobserved fast drop of the scattered intensity to the ablation process of the top layers of thecolloidal crystal. The shock wave propagation manifests itself as an exponential drop ofintensity with the typical time scales on the order of hundreds of picoseconds (see Fig. 2) inthe IR pump–X-ray probe diffraction experiment.In order to model structural changes in the colloidal crystal, hydrodynamic simulationsusing the HELIOS code were performed [56] (see Methods for simulation details). The HE-LIOS code is widely used to simulate the dynamics of plasma evolution created in high-energydensity physics experiments [3, 12, 37]. The hydrodynamic simulation was one-dimensional,therefore the 3D structure of the colloidal crystal was modeled as layers with the periodicvariation of a mass density. The simulations were performed using two-temperature model,which takes into account the fact that the energy of hot electrons is not instantaneouslytransferred to cold ions, but is governed by the electron-phonon coupling. The pressure andmass density evolution obtained from the hydrodynamic simulations are shown in Fig. 5 (seealso Appendix).The first process that was determined in the hydrodynamic simulations is the ablationof the material on the top of the colloidal crystal. The ablation threshold of polystyrenefor 800 nm laser wavelength with 40 fs pulse duration as reported in [57] is on the orderof 10 mJ/cm . The laser fluences used in our pump-probe experiment were three ordersof magnitude higher than the polystyrene ablation threshold (see Table S1). During thefirst picoseconds the top layers of the colloidal crystal were already damaged by the ablation9rocess, and we observe a steep gradient of the mass density in our hydrodynamic simulations(see in Fig. 5(d-f), and Appendix for details). After the first picoseconds the ablation processcontinues and results in a zero mass density on the top of the sample. Due to the ablationprocess of the top layers of the colloidal crystal we observed a fast initial drop of the scatteredintensity in Fig. 2(b,c). The ablation process stops at about 180 nm – 450 nm depth whichcorresponds to about 1-3 layers (see Table S1).The next process that occurs is the shock wave propagation inside the periodic colloidalcrystal. As one can see from Fig. 5(a-c), the shock pressure is propagating along the z-direction and destroys the periodicity of the significant part of the sample. During the firstpicoseconds the maximum shock wave pressure is located in the top layer of the colloidalcrystal (see Fig. 4, 5(a-c)). The shock wave speed is proportional to the square root ofpressure, and it was about 6 km/s on the top of the sample and about 4 km/s on theborder of the shock wave front with the cold material. Therefore, around 100 ps at thedepth of about one micrometer (that corresponds to about 8 layers) the high pressure frontreaches the low pressure front (see Fig. 5 and Appendix). After 100 ps the high pressurefront propagates further inside the sample and destroys the sample periodicity. The averageshock wave propagation speed obtained from our simulations is on the order of 5 km/s andmaximum mass velocity is on the order of 2 km/s which is in a good agreement with previousstudies [58].While propagating inside the colloidal crystal, the shock wave is losing its speed due todissipation of energy and consequently the pressure of the shock wave front is decreasinggradually. At the distance where the shock wave pressure is not sufficient to compress thecolloidal crystal, the shock wave effectively stops. For three IR laser intensities used in thisexperiment, the shock wave stopped after approximately 400 ps – 900 ps propagation timeat a depth of 2 µ m – 5 µ m and the exact values are provided in Table S1. The sampleperiodicity was not further destroyed beyond this point, because the shock wave convertsinto a sound wave, which does not induce any structural transformation of the colloidalcrystal sample [59].In order to study the influence of the sample periodicity on the shock wave propagation,we performed hydrodynamic simulations for the non-periodic polystyrene sample. The re-sults were obtained for all three IR laser intensities used in our XFEL experiment and aresummarized in Appendix. From the comparison of these two sets of simulations we can10onclude that for the non-periodic sample the shock wave stops earlier and the depth ofthe shock wave propagation is about 30% smaller than for the periodic one. The ablationdepth is also about twice shorter for the non-periodic sample (see Appendix Fig. S15-S17and Table SIV). Such difference can be explained by the higher average mass density inthe case of the non-periodic sample. A comparison of two simulation sets shows that thepressure modulations observed in Fig. 5(a-c) are caused by the periodic structure of thecolloidal crystal sample. III. DISCUSSION
In the present work we studied experimentally and by theoretical modelling the dynamicsof the periodic plasma induced by high-power IR laser in the polystyrene colloidal crystals.We performed a pump-probe diffraction experiment at LCLS on a periodic plasma createdfrom a colloidal crystal sample. The periodic structure of the colloidal crystal allowedus to measure Bragg peaks from the sample. We observed a fast decay of the Bragg peakintensity and the growth of the radial and azimuthal peaks width. Such changes of scatteringparameters indicate ultrafast dynamics of the colloidal crystal periodic structure, which isproducing the scattering signal. From the analysis of the Bragg peak parameters we obtained5 ps short and 300 ps long characteristic timescales.We have proposed a three-stage model of interaction between the high-power IR laserpulse and the periodic colloidal crystal to explain the ultrafast changes in the colloidalsample (see Fig. 1). First, all colloidal particles are in the initial condition, unaffected bythe laser pulse. The incoming IR laser pulse generates a plasma in the top layer of thecolloidal crystal within the first few femtoseconds (see Fig. 1(a,b)). Due to the plasma skineffect the IR laser pulse is partially reflected (see Fig. 1(b)). This hot confined periodicplasma then propagates inside the colloidal crystal up to about 0.6 ps time (see Fig. 1(b)).The second stage is the ablation of a few layers on the top of the colloidal crystal. Thetop layers of the sample are damaged during the first few picoseconds and are completelydestroyed afterwards (see Fig. 1(d)). During the third and last stage the shock wave isformed and propagates inside the colloidal crystal sample. This shock wave destroys theperiodicity of the sample by compressing the structure in its deeper parts (see Fig. 1(d)).The three-stage model of the laser-matter interaction allowed us to attribute the short11 ps time scale determined in our diffraction pump-probe experiment to the ablation of thematerial. The long 300 ps time scale is related to the shock wave propagation. Simulationswere performed for all three stages of the laser-matter interaction: plasma formation andexpansion were simulated with the 3D PIConGPU code, ablation and shock wave propaga-tion were simulated with the HELIOS code. From the results of plasma and hydrodynamicsimulations the time dependence of the structural changes in the colloidal crystal was ob-tained. The results of simulations are in a good agreement with the analysis of the Braggpeaks, extracted from the diffraction patterns measured in our pump-probe experiment (seeFig. 2 and Table S1)).In the hydrodynamic simulations, the shock wave stops at different depth of the colloidalcrystal depending on the incoming IR laser intensity (see Fig. 5 and Table S1). As a result,the amount of colloidal crystal affected by the shock wave is higher for higher IR laserintensity and this is consistent with the experimental data.Finally, we demonstrated that shock wave propagation inside the periodic colloidal crystalcan be visualized in situ with a high temporal resolution by an IR pump – X-ray probeexperiment at an XFEL facility. The periodic structure of the colloidal crystal allowed usto reveal the picosecond dynamics of the propagating shock wave by Bragg peak analysis.We obtained short and long characteristic timescales corresponding to the ablation of thematerial and shock wave propagation, respectively. At the same time our simulations predictmuch shorter times of evolution of plasma and ablation processes in polystyrene colloidalsamples. This is still an open and intriguing question of investigation of the plasma dynamicsand ablation process with sub-picosecond time resolution and will need special attention infuture experiments.By performing IR-pump and X-ray probe experiments on the periodic samples we foreseethat formation and development of the periodic plasma may be studied in detail in fu-ture. The application of these ideas and methodology based on scattering from the periodicsamples may lead towards new ways of investigating of phase transitions in matter underextreme conditions. 12
V. METHODSA. Experiment
The pump-probe experiment was performed at the Linac Coherent Light Source (LCLS) [15]in Stanford, USA at the X-ray Pump Probe (XPP) beamline [42] (see also for the details ofexperiment [43]). LCLS was operated in the Self Amplified Spontaneous Emission (SASE)mode. We used LCLS in the monochromatic regime with the photon energy of a singleXFEL pulse of 8 keV (1.5498 ˚ A ), energy bandwidth ∆ E/E of 4 . · − , and pulse durationof about 50 fs at a repetition rate of 120 Hz.The X-ray beam was focused using the Compound Refractive Lenses (CRL) on the sampledown to 50 µ m Full Width at Half Maximum (FWHM) The experimental setup is shownin Fig. 1 and the detailed description is given in [43]. Series of X-ray diffraction imageswere recorded using the Cornell-SLAC Pixel Array Detector (CSPAD) megapixel X-raydetector [60] with a pixel size of 110 × µ m positioned at the distance of 10 m andcovering an area approximately 17 ×
17 cm . Our experimental arrangement provided aresolution of 0.5 µ m − per pixel in reciprocal space.The Ti:sapphire IR laser was used to pump the colloidal crystals. The pump pulses weregenerated at the wavelength λ = 800 nm (1.55 eV) and duration about 50 fs (FWHM). TheIR laser pulses were propagating collinear with XFEL pulses and were synchronized withthe XFEL pulses with less than 0.5 ps jitter. The size of the laser footprint on the samplewas 100 µ m (FWHM) and hence twice the size of the X-ray beam.In order to obtain sufficient statistics of the measured data, for each time delay 100 diffrac-tion patterns without IR laser and one diffraction pattern with IR laser were measured. Fortwo lower IR laser intensities 5 diffraction patterns were measured for each time delay. Forhigher IR laser intensity measurements were repeated 9 times for 6.5 ps time delay and10 times for 25.25 ps time delay. B. Data analysis
Due to the varying intensity of each incoming X-ray pulse, normalization of the diffrac-tion patterns by the incoming beam intensity was necessary. In order to obtain more carefulcharacterization of FWHM of the Bragg peaks, projections on azimuthal and radial direc-13ions were performed. These data were fitted with the one-dimensional Gaussian functionsand the integrated intensity as well as broadening in radial and azimuthal directions weredetermined.In order to compare the dynamics of the collected data as a function of the time delay τ the following dimensionless parameters were used:∆ I ( τ ) I = (cid:104) I on ( τ ) − I off ( τ ) (cid:105) I off ( τ ) , (2)∆ w ( τ ) w = (cid:104) w on ( τ ) − w off ( τ ) (cid:105) w off ( τ ) . (3)Subscript letters ’on’ and ’off’ define measurements with and without IR laser, respectively.The ’off’ pulses were averaged over 100 incoming pulses for each time delay. Brackets (cid:104) . . . (cid:105) correspond to averaging of the chosen Bragg peak parameter over the different positions atthe sample. C. PIConGPU simulations
To simulate plasma formation in the colloidal crystal during the first 1 ps of the IRlaser pulse propagation we used PIConGPU code [52, 53] developed in Helmholtz-ZentrumDresden-Rossendorf. PIConGPU is a fully-relativistic, open-source Particle-in-Cell (PIC)code running on graphics processing units (GPUs). The PIC algorithm solves the so-calledMaxwell-Vlasov equation describing the time evolution of the distribution function of aplasma consisting of charged particles (electrons and ions) with long-range interaction. Thesimulated volume of the colloidal crystal was considered according to the colloidal particlesize ( d = 163 nm). The simulation box was 284 × × in the x × y × z directionswith 2.2 nm cell size in the x and z directions and 2.5 nm cell size in the y direction (seeFig. S1 in Appendix). On the top and bottom of the simulation box additional absorbinglayers were introduced. In the PIConGPU simulations the IR laser wavelength was set to800 nm. Simulations were performed with 4.25 attosecond time increment in order to resolvethe plasma frequency oscillations. 14 . Shock wave and ablation simulations Shock wave and ablation simulations were performed using 1D HELIOS code solving one-dimensional Lagrangian hydrodynamics equations. We used two-temperature model optionfor the hydrodynamic simulations. The PROPACEOS tables were used as an equation ofstate for polystyrene. The hydrodynamic simulations were coupled to the plasma PIConGPUsimulations in the following way. The 1D projection of the electron energy density profileat 1 ps obtained from the PIConGPU simulations was calculated (see Fig. 4). The electronenergy density for the initial condition was converted to electron temperature accordingto PROPACEOS equation of state (see Appendix for details). The electron temperaturewas extended up to 6 µ m according to the room temperature conditions. The ions wereassumed to have room temperature. Calculated electron temperature and 1D projection ofthe density of the hexagonal-close-packed colloidal crystal structure were used as an initialcondition of the hydrodynamic simulation.Hydrodynamic simulations were performed from 1 to 1000 ps with 1 ps time incrementfor the 6 µ m thick polystyrene colloidal crystals. The boundaries of the plasma were allowedto expand freely. The quiet start temperature was set to 0.044 eV which is equal to thepolystyrene melting temperature. The time increment in the HELIOS simulations waschosen according to Courant condition, and other criteria which constrain the fractionalchange of various physical quantities used in the simulation. The simulation results weresaved each 1 ps due to a huge amount of the output data. Acknowledgements
We acknowledge support of the project and discussions with E. Weckert. We acknowl-edge the help and discussions with T. Gurieva, Z. Jurek , A. Rode, A. G. Shabalin, E. A.Sulyanova, O. M. Yefanov, and L. Gelisio for the careful reading of the manuscript. Theexperimental work was carried out at the Linac Coherent Light Source, a National UserFacility operated by Stanford University on behalf of the U.S. Department of Energy, Officeof Basic Energy Sciences. A. Huebl and M. Garten acknowledge support from the EuropeanCluster of Advanced Laser Light Sources (EUCALL) project which has received fundingfrom the European Unions Horizon 2020 research and innovation programme under grant15greement No. 654220. This work was supported by the Helmholtz Associations Initiativeand Networking Fund and the Russian Science Foundation, grant No. HRSF-0002.16
ABLE I. IR laser parameters and results of the plasma and shock wave simulations. The cor-responding plasma pressure was calculated from the PIConGPU simulations. Ablation depth andshock wave time and depth were calculated from the hydrodynamic HELIOS simulations. Theexperimental shock wave times were obtained from exponential fits of the measured data.Intensity, 10 W/cm
16 25.5 33.6Short times of intensity decay, ps - 3 ±
10 7.9 ± ±
33 300 ±
28 275 ± ±
32 279 ±
50 425 ± ±
235 353 ±
86 410 ± J/m
49 98 149Maximum electron energy density at 1 ps, 10 J/m
12 20 25Ablation depth, nm 180 280 450Shock wave depth, µ m 2.36 4.15 5.00Maximum mass velocity, km/s 2.3 2.7 2.8Simulated shock wave stop times, ps 437 756 931 IG. 1. Scheme of the pump-probe experiment. XFEL pulses generated by the undulatorare monochromatized by the diamond crystals and focused by the compound refractive lenses (notshown) to the size of 50 µ m at the sample position. CSPAD detector is positioned 10 m downstreamfrom the colloidal sample. Evolution of diffraction patterns as a function of time delay betweenthe IR pump laser and X-ray Probe laser is shown on the right. Insets (a-d). Three-stage modelof the IR laser-matter interaction. The colloidal particles are shown as circles. The color of theparticles corresponds to the temperature of the colloidal crystal - red is plasma and blue is thecold material. The incoming IR laser pulse is pointing in the direction of the pulse propagation.Initially, the IR laser pulse is propagating towards the colloidal crystal sample and after interactionwith the sample it is reflected by the created plasma on the top layer of the colloidal crystal. Thetop surface level of the initial colloidal crystal is marked by the black dashed line in (d). IG. 2. Time dependence of the relative change of the integrated intensity of the Bragg peaks∆ I ( τ ) /I (a-c) and their widths in the radial ∆ w q ( τ ) /w q (d-f) and azimuthal ∆ w ϕ ( τ ) /w ϕ (g-i)directions at three measured IR laser intensities. Black (blue) dots are experimental data corre-sponding to 25.25 ps (6.5 ps) time delay increment and solid red lines are exponential fits. IG. 3. Electron energy density distribution in the colloidal crystal at 80 fs (a-c) and 1 ps (d-f)after the start of the IR laser pulse for three different IR laser intensities. The IR laser pulse iscoming from the top along the z direction. Here we show a projection of the electron energy densityalong the y-direction. IG. 4. Time (a) and depth (b) dependencies of the electron energy density for three measuredintensities I = 3 . · W/cm , I = 4 . · W/cm and I = 6 . · W/cm . Timedependencies of the electron pressure are shown at 75 nm distance from the top of the sample thatcorrespond to the center of colloidal particles in the first surface layer. Electron energy density-depth dependence is shown at 1 ps after start of the interaction with the IR laser pulse. IG. 5. Hydrodynamic simulations of the shock wave propagation. Color plots show simula-tion results for the pressure (a-c) and mass density (d-f) for three different IR laser intensities:(a,d) I =3 . · W/cm , (b,e) I =4 . · W/cm , (c,f) I =6 . · W/cm . ppendix I. INFRARED LASER CALIBRATION
FIG. S1. The infrared (IR) laser energy calibration curve. The measured data is shown bythe black dots and the sine fit is shown by the solid red line. The IR laser energy used in theexperiments for three samples is marked with blue circles.
In our pump-probe experiment the Ti:sapphire IR laser was used to pump the colloidalcrystal film. The IR laser energy was controlled by the rotation of the optical axis of awaveplate, and was calibrated by power sensor at the position of the sample. The calibrationcurve showing the dependence of the laser pulse energy from the waveplate angle is presentedin Fig. S1. The corresponding IR laser intensity is shown on the right vertical axis. The IRlaser intensity was calculated from the IR laser energy assuming Gaussian shape of the pulsewith 50 fs FWHM in the temporal domain and 100 µ m FWHM in the spatial domain. Zerodegrees of waveplate angle corresponds to the minimum and 15 degrees correspond to themaximum calibrated energy and intensity of the IR laser. The calibration curve was fitted23ith a sine function shown by the solid red line in Fig. S1. The three IR laser intensities( I = 3 . · W/cm , I = 4 . · W/cm and I = 6 . · W/cm ) used in the currentexperiment are marked by the blue circles. At energies lower than 1 mJ, no ultrafast meltingwas observed and different dynamics of the colloidal crystal was investigated in a separatework [43]. II. PLASMA FORMATION SIMULATIONSA. Simulation cell
To simulate plasma formation in the colloidal crystal during the first 1 ps of the IRlaser pulse propagation we used PIConGPU code version 0.4.0–dev developed at Helmholtz-Zentrum Dresden-Rossendorf [52, 53]. In the PIConGPU simulation a rectangular shape ofthe simulation box is considered. The simulated volume of the colloidal crystal was chosenaccording to the colloidal particle size (d= 163 nm). The simulation box is shown in Fig. S2and was 284 × × in x × y × z directions ( d × d √ x × y direction). The top viewon the simulation box is shown in Fig. S2(a) and two layers of the hexagonal-close-packedcolloidal crystal are shown by red and blue color. From Fig. S2(a) it is clear that such asimulation box is periodic in x and y direction. Therefore, such a size of the simulation boxwas chosen to apply periodic boundary conditions on the sides (x=0 nm, x = 284 nm andy=0 nm, y=163 nm planes) of the simulation box. On the top and bottom of the simulationbox additional absorbing layers were introduced. To optimize the simulation process thesimulation box consisted of 128 × ×
512 cells in x × y × z directions. From that condition,the size of one cell was chosen to be 2.2 nm in x and 2.5 nm in y and z directions. On thetop of the simulation box 128 cells or 320 nm were not filled with any colloidal particles.This empty space was introduced in the simulation box to initialize the incoming IR laser.In order to satisfy Courant Friedrichs Lewy condition [61] the simulations were performedwith 4.25 as time increment. Such a time increment allows to resolve the plasma frequencyoscillations in the 2 . × . × . × nm cell size in x × y × z directions. The output of thesimulation was saved each 5 fs during the first 100 fs and each 20 fs up to 1 ps due to ahuge amount of the output data. We used a standard Yee solver scheme [62] and the HDF5openPMD output [63] implemented in the PIConGPU code.24 IG. S2. Simulation cell used in PIConGPU simulations. a) The top view on the simulation box.Different layers of the hexagonal-close-packed colloidal particles are shown in blue and red color.b) 3D view on the simulation box.
B. ADK ionisation of the colloidal crystal
Field ionisation process can be described according to Keldysh theory [45]. For low fieldsand high frequencies the Keldysh parameter γ > γ < E generated by the laser in the quasi-static regime, ioni-sation can be described as tunneling or above-barrier ionisation (ABI). If laser field energy ishigher than the threshold E ABI = E i / Z , where ( Z −
1) is ion charge, the ionisation is above25
IG. S3. a) Keldysh parameter for 4 carbon ionisation energies ( E − E ) and hydrogen ionisationenergy E H . Measured intensities I = 3 . · W/cm , I = 4 . · W/cm and I =6 . · W/cm are shown by green vertical lines. For C +, C + and H + Keldysh parameteris lower than one for all three intensities. Temporal b) and spatial c) Gaussian profile of the IRlaser. ionisation thresholds for C and H are indicated by horizontal dashed lines. Beginning of thesimulation is indicated as vertical red arrow. barrier and if it is lower the tunneling ionisation is prevailing [50]. ionisation thresholds forABI are shown at the temporal and spatial profiles of the IR laser intensity in Fig. S3(b,c)by horizontal dashed lines. Beginning of the simulation time is indicated in Fig. S3(b) bythe vertical red arrow 50 fs before the IR laser pulse reaches it’s maximum. It is well seenthat at the beginning of the simulation the IR laser intensity is below ionisation thresholds26or C and H.From Fig. S3(b,c) it is well seen that for lower laser intensity of 3 · W/cm onlyC and H are expected to be fully ionized. For two higher laser intensities we also haveionisation of C . It is interesting to look also at the spatial distribution of the IR laserpulse (see Fig. S3(c)). In the area of about 150 µ m the sample is ionized to C and H forlower laser intensity, and to C for two higher IR laser intensities. Therefore in the 50 µ mfocused x-ray beam the plasma was considered to be ionized.The ionisation rate Γ implemented in PIConGPU code was calculated according toAmmosov-Delone-Krainov (ADK) model [54] in the case of a linearly polarized field (ans-state is taken for simplicity) asΓ ADK = (cid:114) n ∗ EπZ E πZ (cid:18) eZ En ∗ (cid:19) n ∗ exp (cid:18) − Z n ∗ E (cid:19) , (4)where n ∗ = Z/ √ E i is the effective principal quantum number. The ionisation equations areonly in this form if you use the atomic unit system. The ionisation probability is calculatedfrom the ionisation rate as P = 1 − e − Γ ADK ∆ t .The version of the ADK model that was used in the PIConGPU code is simplified due tothe fact that our particles are carbon and hydrogen and do not have much inner structure.This model was applied for both the tunneling regime E < E
ABI and above-barrier regime E ≈ E ABI . For strong fields
E > E
ABI where the potential barrier binding an electron iscompletely suppressed the so-called barrier-suppression ionisation (BSI) regime is reached.Therefore, the ADK model was combined with a check for the BSI threshold. Also the ADKmodel used in this work is based on the assumption that the material investigated consistsof independent atoms and it did not consider the molecular-orbital structure of covalentlybonded materials.In Fig. S4 ionisation rates calculated according to ADK ionisation model for H, C andC are shown. The intensities of the IR laser used in our experiment are marked by thevertical dashed lines. As can be seen from Fig. S4 the ionisation rate is growing with thefield strength up to 10 s − for the C . From this figure one can conclude that each carbonand hydrogen atoms are ionized up to C and H for all three IR laser intensities and fortwo higher IR laser intensities significant amount of C is created.27 IG. S4. ADK ionisation rates for three different IR laser intensities. The ionisation rates areshown for H, C and C by solid lines. IR laser intensities I = 3 . · W/cm , I = 4 . · W/cm , I = 6 . · W/cm are marked by the vertical dashed lines. C. Thomas-Fermi ionisation of the colloidal crystal
The second ionisation mechanism is collisional ionisation. Accelerated electrons collideinelastically with the atomic ions inside the colloidal particle which causes ionisation ofthe atom. Due to the collisional ionisation mechanism, the atoms in the inner part of thecolloidal particle are ionized to C for the highest IR laser intensity. The ionisation rate ofthis process was calculated according to the Thomas-Fermi ionisation model [55]. Thomas-Fermi ionisation model uses the self-consistent method, where atom is represented as a pointnucleus embedded in a spherical cavity in a continuous background positive charge. Thecavity radius R , is determined by the plasma density ( ρ = 3 M p / πR , where M p is the28 IG. S5. Thomas-Fermi ionisation for H and C for 0 eV, 10 eV and 100 eV electron temperatures.For 10 eV and 100 eV charge state predictions are marked by solid lines and for 0 eV the chargestate predictions are marked by dashed lines because they show unphysical behavior and wereexcluded from the simulations. atomic mass). The ionisation state was calculated using an approximate fit to the definitionof the ionisation state Z ∗ ( ρ, T ) = 4 / πR n ( R ) , (5)where the ionisation state Z ∗ ( ρ, T ) is defined from the boundary density n ( R ). The pa-rameters of the fit which were used in PIConGPU can be found in Table 4 in Ref. [55]. Theion proton number, ion species mass density, and electron temperature are used as an inputfor the Thomas-Fermi ionisation model in the PIConGPU simulation.The charge state estimates for carbon and hydrogen obtained from this model are shownin Fig. S5. As can be seen from this figure the Thomas-Fermi model displays unphysical29ehavior in several cases, thus the cutoff values were introduced, to exclude some particlesfrom the calculation. For carbon and hydrogen it predicts non-zero charge states at zerotemperature, therefore the lower electron-temperature cutoff value should be defined, andin our model it was 1 eV. For low ion densities Thomas-Fermi model predicts an increasingcharge state for decreasing ion densities (see Fig. S5). This occurs already for electrontemperatures of 10 eV and the effect increases as the temperature increases. Low ion-densitycutoff value was 1 . · ions/cm in our case. Also, super-thermal electron cutoff valuewas introduced to exclude electrons with kinetic energy above 50 keV. That is motivated bya lower interaction cross-section of particles with high relative velocities. D. Ionisation simulations
PIConGPU simulations were performed for all three IR laser intensities measured in ourpump-probe experiment. PIConGPU simulations intrinsically included field and collisionalionisation discussed in the previous section and thus the averaged charge state of the colloidalcrystal was obtained. The average charge state projections along the y-axis after 80 fs andafter 1 ps of the IR laser pulse propagation are shown in Fig. S6. The IR laser pulse is comingfrom the top along the z-direction, and it starts the ionisation of the colloidal crystal sample.As one can see from Fig. S6(a-c), after 80 fs only the first layer of the colloidal particlesis ionized by the IR laser pulse. The highly ionized skin layer of the thickness about 10 nmon top of the first layer of colloidal crystals is also well visible. The average charge state inthe skin layer can reach up to 2.9 and is summarized in Table S1. Also, high charge stateis reached in the center of the colloidal particles for all three IR laser intensities, and theirvalues are summarized in Table S1.At 600 fs after the beginning of the simulation accelerated electrons collisionally ionizedthe inner part of the colloidal crystal and until 1 ps the ionisation state of the colloidalcrystal remained practically constant (see Fig. S6(d-f) and Supplementary movie). FromFig. S6(d-f) it can be observed that the ionisation depth varies a lot with the IR laserintensity. The ionisation depth is different for three IR laser intensities and is summarizedin Table S1. Even at 1 ps after the start of the PIConGPU simulation the highest ionisationstate remains at the center of the top layer of the colloidal particles.30
IG. S6. The average charge state distribution in the colloidal crystal at 80 fs (a-c) and at 1 ps(d-f) after the beginning of the IR laser pulse for three different IR laser intensities. Here we showthe projection of the average charge state along the y-direction. II. HYDRODYNAMIC SIMULATIONSA. PIConGPU simulations coupled to HELIOS simulations
The HELIOS hydrodynamic simulations were performed to model structural changes inthe colloidal crystal due to the shock wave propagation. The hydrodynamic simulationswere coupled to the plasma PIConGPU simulations in the following way. The 1D projectionof the electron energy density profile at 1 ps was obtained from the PIConGPU simulations.The electron energy density distribution was further converted to the electron temperatureusing PROPACEOS (PRism OPACity and Equation Of State code) data tables. The hori-zontal axis is the electron internal energy and the vertical axis is the electron temperature.The PROPACEOS data for polystyrene with typical polystyrene density of 1.05 g/cm isshown by the black dots. This data was fitted with 7th order polynomial function and thepolynomial fit is shown by the red line in Fig. S7. Further this polynomial function wasused to convert the electron energy density to electron temperature.The temperature distribution used as an input for hydrodynamic simulations is shownin Fig. S8 for three IR laser intensities. The oscillations of the electron temperature dueto the periodic colloidal crystal structure are clearly visible. The PIConGPU simulationswere performed for the first 882.5 nm of the colloidal crystal, below this depth up to 6 µ mthe temperature distribution was set to a room temperature value of 0.025 eV (see Fig. S8).By that we got a drop of the temperature distribution at 882.5 nm depth, which was notsmoothed for deeper parts of the colloidal crystal due to the following reasons. The ionisation TABLE S1. IR laser parameters and results of plasma simulations used in our experiment. Thecorresponding average ionisation state and ionisation depth were calculated from the PIConGPUsimulations.Intensity, 10 W/cm IG. S7. Polystyrene equation of state obtained from PROPACEOS data tables (black dots) andpolynomial fit (solid red line). rate in the PIConGPU code does not take into account the recombination process, due tothat the temperature distribution on the top of the sample should be lower in reality. Ourapproach was later confirmed by the hydrodynamic simulations performed only by HELIOScode (see section IIIc in Appendix).These PIConGPU and HELIOS combined set of simulations is further referred to as asimulation Set 1.
B. Results of the simulation Set 1
The 1D pressure and mass density distribution obtained from the hydrodynamic sim-ulations are shown in Fig. S9, S10, respectively, for all three IR laser intensities. The33
IG. S8. Electron temperature distribution in the colloidal crystal for three measured intensities I = 3 . · W/cm , I = 4 . · W/cm and I = 6 . · W/cm at 1 ps after the IR laserpulse. initial density distribution used as an input for the hydrodynamic simulations is shown inFig. S10(a-c). These density profiles were obtained as a projection on the hexagonal-close-packed colloidal crystal along x- and y-direction. The periodicity of the mass density dueto colloidal crystal structure is well resolved with the chosen step size of 2.5 nm. The initialpressure distributions are shown in Fig. S9(a-c) as snapshots at 1 ps after the beginning ofthe IR laser pulse. As one can see at 1 ps the pressure is decaying along the z-direction,and the maximum pressure is in the center of the top layer of the colloidal particles. In thedeeper part of the sample the pressure distribution is periodic due to the periodicity of thecolloidal crystal. The negative pressures in the simulation are zeroth-order approximation tomaterial strength used in the PROPACEOS and other, for example SESAME EOS tables.34uring the first picoseconds of the shock wave propagation the mass density of the ap-proximately 1 µ m region on the top of the sample is affected. The snapshot of the massdensity at 20 ps is shown in Fig. S10(d-f) where the ablation of the material is clearly visible.The modulations of the mass density become less pronounced and the steep gradient of themass density going down to zero value is well visible. That is a clear sign of the ablation ofthe top layer of the colloidal crystal. At 20 ps after the beginning of the HELIOS simulationthe high pressure from the top of the colloidal crystal is propagating inside the sample (seeFig. S9(d-f)). At the top 100 nm of the sample pressure is equal to zero due to ablation ofthe first layer of the colloidal crystal. At about 100 ps the highest pressure is reaching theshock wavefront and the shock wave propagates inside the sample with increased speed.The shock wave propagating inside the colloidal crystal compresses the surrounding ma-terial and from Fig. S10 it is clearly visible that density at the shock wavefront is higherthan density after the shock wavefront. When the energy of the shock wave is not sufficientto compress the sample the shock wave stops. The shock wave stops at different times forthree IR laser intensities. The pressure distribution at the moment when the shock wavestops is shown in Fig. S9(j-l). The shock wave depth is marked by the blue dashed line. Theshock wave stops at different time and depth for all three IR laser intensities (see Table 1in the main text). The mass density deeper the shock wavefront remains unperturbed whilebefore the shock wavefront is undergoing some small changes even after the shock wave stops(see Fig. S10(j-o)).The last time point of the hydrodynamic simulation was at 1000 ps and the mass densityand pressure snapshots are shown in Fig. S10(m-o) and Fig. S9(m-o). The shock wave did notpropagate any deeper inside the colloidal crystal but the mass density on the shock wavefrontis smaller than in Fig. S10(j-l) and the pressure front changed its shape significantly. Theablation of the material has also practically finished at that time. From Fig. S10(m-o) it iswell seen that the amount of ablated material is higher for higher IR laser intensity, and thevalues are summarized in the Table 1 in the main text. The ablation threshold is markedby the blue dashed line in Fig. S10(d-f).The fluid velocity evolution is shown in Fig. S11 for all three IR laser intensities. The fluidvelocity of the unperturbed material is equal to zero and the velocity of perturbed materialcan be positive (moving down along the z-direction) or negative (moving in the oppositedirection). On the top of the colloidal crystal the fluid velocity is negative which is a sign35 IG. S9. Pressure in the colloidal crystal from the hydrodynamic simulation. In this case thecombination of PIConGPU and HELIOS code was used. Results are shown at 1 ps (a-c), 20 ps(d-f), 100 ps (g-i) after the stop of the shock wave (j-l) and at 1000 ps, the end of the simulation(m-o). The blue dashed line shows the shock wave stop depth (j-l). IG. S10. Mass density of the periodic colloidal crystal from the hydrodynamic simulation. Inthis case the combination of PIConGPU and HELIOS code was used. Results are shown at 1 ps(a-c), 20 ps (d-f), 100 ps (g-i) after the stop of the shock wave (j-l) and at 1000 ps, the end of thesimulation (m-o). The blue dashed line shows the shock wave stop depth (j-l) and the ablationthreshold (d-f).
37f ablation. On the shock wavefront the velocity is positive, and the liquid polystyrene ismoving inside the colloidal crystal. When the shock wave stops the fluid velocity becomesnegative due to the reflection of the shock wave. The maximum fluid velocity is observedduring the first 100 ps of the shock wave propagation (see Fig. S11). The maximum fluidvelocity is on the order of 2 km/s and is summarized in Table 1 in the main text.
FIG. S11. Hydrodynamic simulations of the shock wave propagation. Color plots show simulationresults for the fluid velocity (a-c) for three different IR laser intensities: (a) I =3 . · W/cm ,(b) I =4 . · W/cm , (c) I =6 . · W/cm . C. Simulations using HELIOS code only
We performed another set of the hydrodynamic simulations for three IR laser intensityusing only HELIOS program (Set 2). The simulation Set 2 was performed in order tocompare PIConGPU coupled to HELIOS simulations and pure HELIOS simulations.In the simulation Set 2 the experimental laser parameters were used. The simulationswere performed for three experimental laser intensities ( I =3 . · W/cm , (b) I =4 . · W/cm , (c) I =6 . · W/cm ) with 800 nm wavelength. The FWHM of the laserpulse was 50 fs and the peak laser power was set at 50 fs after the beginning of the simulation.Percentage of power reflected at the critical surface was obtained from the PIConGPUsimulations. The energy emitted by IR laser and the energy absorbed by electrons for threeIR laser intensities is summarized in Table S2 and the absorption coefficient was around10% for all three IR laser intensities. Therefore the reflection coefficient in the HELIOS38imulations was set to 90%. This value of the reflection coefficient is also confirmed bysimple estimations. In case of dense plasma the absorption coefficient derived from theFresnel formulas can be written in the form A = 4 πl s /λ , where A is the absorption coefficient, l s is the skin depth and λ is the IR laser wavelength [64]. For the estimated skin depth of10 nm the absorption coefficient is about 15 %.In the simulation Set 2, the two-temperature model was used, similar to the previouscase. In the two-temperature model both electrons and ions were assumed to have a roomtemperature in the initial state. All other parameters of the simulation, except the laserparameters were the same as in the previous case (simulation Set 1 summarized in theMethods section in the main text). The initial mass density of the colloidal crystal wassimilar to the previous simulation and had the same periodicity. The quiet start temperaturewas set to 0.044 eV which is equal to the polystyrene melting temperature.The pressure and mass density obtained from these set of simulations are shown inFigs. S12,S13,S14. Two processes occur in the simulated colloidal crystal sample - ablationand shock propagation (the same processes were observed in simulation Set 1). Ablation iswell seen in Fig. S12(d-e) as the zero mass density on the top of the sample. The top 1-2layers are ablated during the first picoseconds and the ablation depth is summarized in Ta-ble S3. In the simulation Set 2 the ablation depth is slightly smaller than in the simulationSet 1 (see Fig. 5 in the main text and Fig. S10). Such a difference may be caused by thedifferent IR laser absorption mechanisms implemented in these programs.The maximum shock wave pressure achieved at the first picosecond of the simulation ison the order of 150-200 GPa (see Table S3 and Fig. S13(a-c)). At 20 ps the shock wavefrontpropagated through 0.5 µ m of the colloidal crystal and destroyed the periodic structure of thesample. In the simulation Set 1 the periodicity of the first 1 µ m was damaged 20 picosecondsafter the beginning of the laser pulse. Therefore the simulation Set 2 is not explaining thefast drop of the diffracted intensity in the experimental results, while the simulation Set 1the changes in the colloidal crystal structure can be attributed to the reduced diffractedintensity.Further the shock wave is propagating through the colloidal crystal sample. The shockwave stops at the different time and depth summarized in Table S3. It is worth to noticethat compare to simulation Set 1, here the shock wave stops earlier and destroys less of thematerial. The difference in the shock wave depth is on the order of 25% for two higher IR39aser intensities and approximately 1% for the lower IR laser intensity. Such a differencein the shock induced dynamics might be due to the different geometries (1D in HELIOSor 3D in PIConGPU). In the 3D PIConGPU simulations the colloidal crystal structure wasproperly set, while in the HELIOS simulation only a 1D projection of the mass density wasused. TABLE S2. The IR laser emitted and absorbed energy, and absorption coefficient estimated fromPIConGPU simulations.Intensity, 10 W/cm eV 3.5 5.5 7.2Absorbed energy, 10 eV 3.5 5.7 7.0Absorption coefficient, % 10.0 9.6 9.7TABLE S3. Results of the simulation Set 2 (performed only with HELIOS code on the periodiccolloidal crystal sample). The results are shown for three IR laser intensities. Ablation depth andshock wave time and depth were calculated from the results of the hydrodynamic simulations.Intensity, 10 W/cm µ m 2.24 3.30 4.10Simulated shock wave stop times, ps 377 589 751 D. HELIOS simulations for the bulk polystyrene sample
The last set of the hydrodynamics simulations was performed using only HELIOS codewith the bulk polystyrene sample (Set 3). In this case all the simulations parameters weresimilar to the Set 2, except the initial polystyrene mass density. The polystyrene massdensity was set to be constant along z - direction (1.05 g/cm ) considering bulk polystyrene.The results of the simulation Set 3 are present in Fig. S15, S16, S17. The two main processesin the simulation Set 3 are ablation and the shock wave propagation, similar to simulationSet 1 and Set 2. 40 IG. S12. Hydrodynamic simulations of the shock wave propagation inside the periodic colloidalcrystal. The simulations were performed using only the HELIOS code. Color plots show simu-lation results for the pressure (a-c) and mass density (d-f) for three different IR laser intensities:(a,d) I =3 . · W/cm , (b,e) I =4 . · W/cm , (c-f) I =6 . · W/cm . The snapshot of the simulation at 1 ps is shown in Fig. S15(a-c) and S16(a-c), and theinitial constant pressure and density of the sample is visible. The ablation of the materialis already visible at 20 ps and it continues up to 100 ps (see Fig. S15, S17. The ablationdepth is on the order of 100-200 nm and is summarized in Table. S4. In the simulationSet 3 the ablation depth was approximately twice smaller than for simulation Set 2. Thedifference in the ablation depth can be explained by smaller average mass density in case ofthe simulation Set 2.The maximum pressure is reached at the first picosecond of the simulation on the very toplayer of the polystyrene sample (see Fig. S16 and Table. S4). The pressure–depth dependence41ad a periodic structure in the simulation Set 1 and Set 2 but in the simulation Set 3 itdoes not show any periodicity. Therefore we can conclude that such pressure modulationswere caused by the periodic structure of the colloidal crystal sample.The peak pressure is decaying while the shock wave is propagating inside the sample (seeFig. S16), but the shape of the shock wavefront remains stable. When the shock pressure isnot sufficient to compress the material the shock wave stops and the shock wave stop timeand depth are summarized in Table. S4. For the simulation Set 3 the shock wave stop timeare much smaller than in case of simulation Set 2. The difference can be explained by thehigher average mass density of the simulated sample.
TABLE S4. Results of the simulation Set 3 (performed only with HELIOS code on the periodiccolloidal crystal sample). The results are shown for three IR laser intensities. Ablation depth andshock wave time and depth were calculated from the results of the hydrodynamic simulations.Intensity, 10 W/cm µ m 1.53 2.16 2.69Simulated shock wave stop times, ps 301 454 581 IG. S13. Pressure in the colloidal crystal from the hydrodynamic simulation. The simulationswere performed using only the HELIOS code. Results are shown at 1 ps (a-c), 20 ps (d-f), 100 ps(g-i) after the stop of the shock wave (j-l) and at 1000 ps, the end of the simulation (m-o). Theblue dashed line shows the shock wave stop depth (j-l). IG. S14. Mass density of the periodic colloidal crystal from the hydrodynamic simulation. Inthis case only the HELIOS code was used. Results are shown at 1 ps (a-c), 20 ps (d-f), 100 ps (g-i)after the stop of the shock wave (j-l) and at 1000 ps, the end of the simulation (m-o). The bluedashed line shows the shock wave stop depth (j-l) and the ablation threshold (d-f). IG. S15. Hydrodynamic simulations of the shock wave propagation inside the bulk polystyrenesample. In this case only the HELIOS code was used. Color plots show simulation results for thepressure (a-c) and mass density (d-f) for three different IR laser intensities: (a,d) I =3 . · W/cm , (b,e) I =4 . · W/cm , (c-f) I =6 . · W/cm . IG. S16. Pressure inside the of the bulk polystyrene from the hydrodynamic simulation. In thiscase only the HELIOS code was used. Results are shown at 1 ps (a-c), 20 ps (d-f), 100 ps (g-i)after the stop of the shock wave (j-l) and at 1000 ps, the end of the simulation (m-o). The bluedashed line shows the shock wave stop depth (j-l). IG. S17. Mass density of the bulk polystyrene from the hydrodynamic simulation. In this caseonly the HELIOS code was used. Results are shown at 1 ps (a-c), 20 ps (d-f), 100 ps (g-i) afterthe stop of the shock wave (j-l) and at 1000 ps, the end of the simulation (m-o). The blue dashedline shows the shock wave stop depth (j-l) and the ablation threshold (d-f).
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