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Ultrafast opacity in borosilicate glass induced by picosecond bursts of laser-driven ions

Direct investigation of ion-induced dynamics in matter on picosecond (ps, 10-12 s) timescales has been precluded to date by the relatively long nanosecond (ns, 10-9 s) scale ion pulses typically provided by radiofrequency accelerators1. By contrast, laser-driven ion accelerators provide bursts of ps duration2, but have yet to be applied to the study of ultrafast ion-induced transients in matter. We report on the evolution of an electron-hole plasma excited in borosilicate glass by such bursts. This is observed as an onset of opacity to synchronised optical probe radiation and is characterised by the 3.0 +/- 0.8 ps ion pump rise-time . The observed decay-time of 35 +/- 3 ps i.e. is in excellent agreement with modelling and reveals the rapidly evolving electron temperature (>10 3 K) and carrier number density (>10 17cm-3). This result demonstrates that ps laser accelerated ion bursts are directly applicable to investigating the ultrafast response of matter to ion interactions and, in particular, to ultrafast pulsed ion radiolysis of water3-5, the radiolytic decompositions of which underpin biological cell damage and hadrontherapy for cancer treatment6.

with matter is fundamentally different 1 . A significantly higher linear energy transfer (LET, or stopping power � ) for ions results in highly localized energy deposition along their trajectory in matter. The unambiguous characterization of the dynamics of a system immediately following such an interaction is of central importance to multiple fields in science and medicine such as hadrontherapy 6 , the safety of astronauts 6 , electronics for use in space 10 and nuclear engineering 11 . Therefore, the ability to generate sufficiently short pulses of ions is critical to advancing the understanding of ultrafast characteristics of ion interactions by direct experimental investigation.
To date ion-matter interactions have been studied using µs 12 and ns 1,13 ion pulses and have almost exclusively focused on radiolytic yields during pulsed radiolysis of aqueous solutions.
Such studies are typically performed using chemical scavenging techniques 14,15 which themselves have the potential generate significant uncertainty at the concentrations required for high temporal resolution. In recent years, however, laser-driven ion sources have developed rapidly, and ion pulses with initial bunch durations < ps, high particle numbers (>10 13 per bunch) and excellent beam quality have been reported 2 . Such parameters provide an excellent basis for addressing the problem of time-resolved ion-matter interaction dynamics on ultrafast time scales for both aqueous solutions and amorphous/crystalline solids.
Here the excitation of electrons across the optical gap of a borosilicate (BK7) glass sample by a ps laser-driven ion burst is investigated. The resulting electron-hole plasma gives rise to transient opacity (TO) to optical probe radiation 7,8 . This TO is ideally suited to our study since it is expected a) to exhibit a growth time that is essentially instantaneous compared to our ion pulse duration for low doses 8,16 , b) to subsequently relax rapidly on a timescale of 10's of ps 16 and c) does not consist of multiple pathways for species formation and decay, such as are found in the radiolysis of aqueous solutions [3][4][5] . We show how the pump and decay profiles of the TO are in excellent agreement with a semi-empirical Drude-like model (i.e. the charge carriers are assumed to be free and no selection rules are applied due to the lack of a crystalline structure) for our estimated ion pulse characteristics. This allows physical quantities that are otherwise extremely difficult to measure directly, such as the electron temperature and carrier density of the electron-hole plasma, to be estimated.
For this experiment, we used the TARANIS multi-TW laser facility at Queen's University Belfast 17 to accelerate H + ions (protons) that form part of a surface layer on a thin (10µm) gold target foil to an endpoint energy of ~15 MeV via the target normal sheath acceleration (TNSA) mechanism 2 . After spectral filtering in the irradiated sample we obtain an ion pulse of ~3 ps full width half maximum in the region of interest in the sample. The short ion burst duration is made possible by the duration of each energy slice (1 MeV bandwidth) ultimately being set by the initial ps pulse duration of the ion bunch 2 (see Methods).
The H + -glass interaction region was transversely probed using a synchronised ultrafast optical probe (1053 nm, 400 fs, < 10 µJ cm -2 ) from the main laser system to produce spatially resolved snapshots of the TO (Figure 1 a, b). The temporal evolution of the opacity is recorded by varying the relative time delay ∆t between the probe and ion beam. As shown in Figure 1 b), these snapshots reveal the spatial profile of the ion beam and also demonstrate the recovery of the initial state of the subject material as ∆t → ∞, indicating that no permanent macroscopic damage persists after the interaction.
However, obtaining a consistent data set of the temporal evolution of the TO in this manner is limited by shot to shot variation in H + flux (± 12 %) and spectral cut off energy (± 5 %). To permit a more accurate measurement of the TO, the full temporal evolution was instead recorded on a single shot basis. This was achieved by optically streaking 18,19 (Figure 1c delivering an estimated total dose of 60 ± 15 Gy in the region studied. Transmission reduces for the entire duration of the ion pump pulse (~10 ps). After this the medium is observed to rapidly recover with a time constant of 35 ± 3 ps ( 1 � value of maximum opacity at 1mm depth). It is worth noting that due to their higher LET, protons create significantly more electron-hole pairs than a similar energy, dose and pulse duration electron beam in glass 7 . See Methods for pulse duration and dose estimation at 1mm depth.
To investigate the microscopic mechanism underlying the observed TO, we developed a simple Drude-type two-temperature model [20][21][22][23][24][25]  While the model provides a good fit to the ion induced opacity at depths > 850 µm, where the total dose is moderate, this is not true for shallower depths in the target (i.e. < 850 µm where the transmission does not return to the initial value). For the higher doses at those shallower depths (> 100 Gy) initial investigations show that considering a radiative bottleneck to electron relaxation in our model increases the accuracy of the fit, but a study into electron-hole plasma evolution coupled with localised lattice heating and kinetic radiative bottleneck formation is beyond the scope of our study here and will form the basis for future work. In our discussion we are exclusively concerned with interactions where the pulse is sufficiently short and the dose sufficiently low such that lattice heating can be neglected.
In conclusion, we have observed ion-induced dynamics on picosecond timescales during high LET interactions with matter. The intrinsic synchronicity of the laser-driven ion and optical probe beams ensures a high degree of reproducibility in the optical streaking technique. The rise time of the transient opacity is observed to be on the order of the pump pulse duration and rapid recovery to the initial state, with an time constant of 35 ± 3 ps, is consistent with our Drude-like model for electron -hole plasma dynamics. Overall this permits direct estimation of the picosecond time-dependent response of electronic temperature and carrier density in matter to ultrafast pulses of ions. This technique opens the way for ps pulsed ion radiolysis of aqueous solutions, and in particular that of water 3-5 which is of specific relevance to hadrontherapy 6 and neutron radiolysis for nuclear engineering 11 , to be performed at even small scale laboratories.

Ion pulse characteristics and intrinsic pulse shortening:
Substantial stretching of the initial broadband ion bunch as it propagates with a large velocity spread from the target towards the sample results in an ion pulse > 70 ps (since the glass sample is 5 mm behind the target). The ultimate ion pulse duration, however, is a function of depth of propagation into the target. This is due to spectral filtering resulting from continuous energy loss and stopping of lower energy ions in the target, so that by the end of the track (~1 mm into the target) the interaction is essentially a few ps, few MeV ion pulse,   Figure 1a) shows a schematic of the experimental setup. An intense laser pulse (> 10 19 Wcm -2 ) is incident at an angle of 45º on a 10 µm Au foil. An ion pulse produced via the TNSA mechanism 2 in the direction normal to the rear surface of the foil travels a distance of 5 mm to an optical quality BK7 glass slide (1 mm thick in horizontal dimension). The horizontal extent of the ion pulse is apertured to 500 ± 50 µm using a 1mm thick Al collimating slit (CS), centred on the glass sample (Top view inset). Low energy ions, electrons and X-rays were filtered using a 5µm Al foil in front of the CS (not shown). A synchronised probe pulse that can be either ~ 400 fs (compressed) or ~ 210 ps (chirped) is used to transversely image the pumped region (red line) onto an optical Andor CDD. Figure 1 b) shows a series of probe (400 fs) images taken at different time delays ∆t with respect to the arrival of the main laser pulse at the Al foil. The different penetration depths transverse to the beam propagation axis are due to the radially varying peak ion energy typical of such laser-driven accelerators. The temporal evolution of ion induced opacity along the red dashed region in Figure 1b) on a single shot basis is shown in Figure   1c). This region (100 ± 20 µm) was imaged onto the entrance slit of a 1m imaging spectrometer with the pulse duration set to ~ 210 ps. The temporal evolution of TO was then encoded as variation of the signal in the probe spectrum (bandwidth ~ 4nm) with respect to depth in the target. Figure 1c) shows a typical streaked image 18,19 , as detected using an optical Andor CCD.  Here we define the onset of TO for a reduction in transmission > 5% due to fluctuations of ± 3% on the spatial intensity profile probe beam. In Figure 3b) the dark red trace shows the evolution of opacity in the glass at a depth of 1 mm. The horizontal thick translucent red line shows the uncertainty in the transmission of the probe through the glass in the absence of the ion pump beam. The black trace shows the calculated ion pump pulse profile (normalised) taking into account the spectral shape   (Figures 3 a, 3 b inset), the model does not return a good fit to the data, suggesting that a kinetic bottleneck due to increased dose is preventing full electron-hole plasma relaxation on the timescales studied here at these depths. See Supplementary Information for full detail of the Drude-type two temperature model, fitting procedure, and TDDFT 27,28 calculations used to model the experimental data.