High Eciency Laser-Driven Proton Sources Using 3D-Printed Micro-Structure

We applied 3D-printed microwire-array (MWA) structure to boost the energy conversion eciency of laser proton acceleration. The advanced nano-printing technique allows precise control on the spacing and geometrical size of 3D structures at 100-500 nm resolution. Under irradiation of high contrast laser pulse (15J, 35fs), the MWA target generates over 1.2×1012 protons (> 1MeV) with cut-off energies extending to 25MeV, corresponding to top-end of 8.7% energy conversion eciency from femtosecond lasers. When comparing to at foils the eciency is enhanced by three times, while the cut-off energy is increased by 30-70% depending on their thicknesses. By precisely controlling the array period via 3D nano-printing, we found the dependence of proton energy/conversion-eciency on the spacing of the MWA. The experimental trend is well reproduced by hydrodynamic and Particle-In-Cell simulations, which reveal for the rst time the modulation of pre-plasma prole induced by laser diffraction within the ne structures. Optimal geometry for laser-proton acceleration is therefore strongly modied. Our work validates the use of 3D-printed micro-structures to produce high eciency laser-driven particle sources and pointed out the new effect in optimizing the experimental conditions.


Background
In the past two decades, laser-driven proton acceleration has been widely studied for its signi cance in applications such as probing high energy density states 1 , treating cancer therapy 2 , fast ignition fusion 3 , laboratory astrophysics 4 and so on. These applications impose certain requirements for the energy and current intensity of proton beams. By optimizing the laser conditions and thickness of planar targets, protons could be accelerated up to 85 MeV via the robust target normal sheath acceleration (TNSA) mechanism [5][6][7] . A higher cutoff energy of 94 MeV has been reported via radiation pressure-sheath acceleration in an ultrathin planar foil 8 . These sub-100MeV protons are obtained by relatively long laser pulses of 100's J energies. For femtosecond lasers, typical cutoff energy of protons lies in 30-70 MeV using planar targets [9][10][11] , since the pulse energy is usually much less than picosecond lasers.
Realizing the above-mentioned applications of laser-driven proton sources strongly relies on maximizing the laser-proton energy conversion e ciency. In laser-foil interaction, reducing target thickness 12 is usually adopted to improve laser-to-proton energy conversion e ciency. In general, plasma targets irradiated by picosecond lasers behave differently from a femtosecond laser because the instability of the plasma and self-generated electromagnetic elds expand over time 13,14 . Consequently, high laser-toproton energy conversion e ciency up to 10%-15% 5,15 tends to appear in TNSA when using large energy picosecond laser pulses. The e ciency of 3%-4% 11,16 is achieved on femtosecond lasers of much lower pulse energy, which is still below the theoretical value ~8% predicted by Sentoku et al 17 .
For ultra-short laser pulses, optimizing the target condition to enhance the laser absorption e ciency has become a promising solution. Employing carbon nanotube foam (CNF) on a planar diamondlike carbon (DLC) foil has realized triple energy gain for protons 18,19 . An alternative method is to introduce periodic/aperiodic nano/micro-structures in front of planar targets [20][21][22][23][24][25][26][27][28] . Experimental data indicate that microstructure can greatly raise the temperature of hot electrons beyond that of the ponderomotive acceleration 29,30 . In the case of picosecond relativistic lasers irradiating microstructure targets at large angles, the yield of electron and x-ray could be increased 31,32 , but the proton energy from TNSA remains unchanged 27 or even becomes less 33 . The main reason is that the rising edge of picosecond lasers is long enough to ionize the surface structure so that the plasma in ll could shutter the laser from further interaction. Considerable energy enhancement for protons has been observed by using defocused picosecond lasers with normal incidence (10 17~1 0 18 W/cm 2 ) 25 . The effect of pre-plasma in ll is suppressed when employing ultrashort femtosecond relativistic lasers 28 . Judging from the reported results, when using ne surface structures to improve proton acceleration in TNSA, high contrast femtosecond lasers with an incidence angle as small as possible is more favorable.
We notice that the fast development of three-dimensional (3D) nano-printing technique allows for wellcontrolled fabrication of ne solid structures. The two-photon polymerization (TPP) method can readily achieve lateral resolution ~100 nm and vertical resolution ~500 nm 34 . Compared to other approaches such as Si semiconductor-based technique 33 and electrochemical deposition method 28 , 3D nano-printing can accurately print various complex structures as desired in experiments at micro or sub-micro scale. It is therefore timely to apply this advanced technique to laser-plasma physics such as to manipulate ultrafast laser-plasma interaction 22 , generation of high bright x/gamma-ray 35 , high power coherent Terahertz 36 and positrons 37 .
In this paper, we use the TPP Nanoscribe 3D printer 38 to fabricate microwire array (MWA) onto SiN at foils and investigate laser-driven proton acceleration at various spacing conditions of the array. The MWA structure boosts the laser-to-proton energy conversion e ciency to 8.7% (total number 1.2×10 12 for proton energies more than 1 MeV), about three times more than that of at foils of optimal thickness. After implementing the MWA structure the cut-off energy of protons is increased by 70% compared to at foils of similar thickness (4 µm-thickness). It reaches 25 MeV (MWA targets) at on-target laser intensity of about 2.2×10 20 W/cm 2 , which is 30% more than that of the optimized at foil (1 µm-thickness). We change the spacing of MWA precisely via 3D nano-printing and nd out how it in uences the proton acceleration process. Our 2D hydrodynamic simulations point out that the pre-plasma condition of MWA targets induced by the pre-pulse is signi cantly different from the at target case where the density length scale is almost uniform in the latter. The micro-structures can induce strong diffraction of the incident pre-pulse, resulting in featured pre-plasma distributions depending on the surface pro le. After bringing the pre-expansion plasma conditions into 2D particle-in-cell (PIC) simulations, we reproduce the experimental results and nd the optimal MWA parameters for proton acceleration.

Methods
MWA fabrication. The 3D printing machine we employed is based on two-photon polymerization technique 34 . A brief schematic diagram is shown in Fig. 1(b). A femto-ber laser system delivers pulses at a center wavelength of 780 fs with a repetition rate of 80 MHz. The light pulses typically exhibit a duration of 100 fs with an average power of more than 350 mW. The laser is guided into the objective lens with a magni cation of 63×(NA1.4) and focused on the sample surface. The photo-resin is partial exposed following the designed structure model. To remove unexposed photo-resist, the structures are developed in the developer liquid followed by careful rinsing with isopropanol (IPA). After UV treatment 42 and natural drying in air, solid structures are obtained. The structure is a polymer C 14 H 18 O 7 with a mass density of ~1.17 g/cm 3 . We use the commercial 3D printer of Nanoscribe Photonic Professional GT1 38 to fabricate MWAs onto the 1-μm SiN substrates within an area of 400 μm × 400 μm. The diameter and height of microwires were xed at d=0.4 μm and h=2.5 μm, while their period varied from p=1.3 μm to p =3.3 μm.
Simulations. The hydrodynamics simulations were performed using the 2D FLASH code 48 in Cartesian coordinate system. A at-top laser with a steep rising edge irradiated the Al MWA at an incident angle of 5.5°. The material initial temperature was set to 290 K. The laser intensity is 5×10 9 W/cm 2 and ablation time was 500 ps for Figs. 3(a) and (b). The PIC simulation was performed using the 2D EPOCH code 49 . The simulation box was 65 μm × 30 μm with mesh cell size equal to 4 nm × 8 nm. The incoming laser pulse temporal and spatial pro les were both Gaussian, with FWHM equal to 35 fs and 10 μm, respectively. The peak intensity was 2.2×10 20 W/cm 2 . Open boundary condition was used in all simulations. The at targets were initialized as a uniform mixture of Si 14+ and N 7+ , both at 12 n c . The ats coupled with CH contaminant layers at the rear of the lm with thickness of 20 nm and electron density of 45 n c . For MWA targets, the wires were de ned as fully ionized CH and the electron density were 210 n c (mass density ~ 1.17 g/cm 3 ). Each pillar is surrounded with modulated pre-plasma of two components. Around the tip the pre-plasma forms a semicircular with n pre1 = n e1 exp(-△r/l h ), where n e1 , △r, and l h are the pillar electron density, the distance to the tip center and the corresponding density scale length, respectively. The pre-plasma density in the rest area takes the form n pre2 = n e1 exp[-(△y/l h +△x/l x )]+n e2 exp(-△ /l f ), where n e2 ,△(x ,y), l x,f ,is the foil electron density, the distance to initial target boundary and the related scale lengths, respectively. The substrate was the same as the at situation.

Experimental Results
Experimental set-up. The experiments were carried out in a petawatt-class Ti:sapphire laser system with central wavelength λ = 800 nm, which delivers around 15±2 J on-target energy within 35 fs duration (full width at half maximum, FWHM) in the current run. About 40% of the laser energy is enclosed in a focal spot of 10 μm diameter (FWHM), yielding a peak intensity of about (2.2±0.3)×10 20 W/cm 2 . The laser contrast of ampli ed spontaneous emission (ASE) pedestal is ~10 11 (10 10 ) at 30 (6) ps prior to the main pulse 39 , which could induce pre-plasmas with typical scale length of several hundreds of nanometers 40 .
Our micro-structures of MWA targets used here survived the above pre-pulse condition. The sketch of the experimental setup is shown in Fig. 1(a). The p-polarized laser pulse is focused by a f / 4 off-axis parabolic mirror onto the target at an incident angle of 5.5°, which is the smallest angle one can set to avoid light backscattering to the laser chain. A stack of radiochromic lms (RCFs) with a 3-mm-diameter hole in the center are enwrapped with 15 μm-thickness Al foil to shield the stack from debris. It is located at L 1 = 5.3 cm to measure the proton energy spectrum and pro le. Several EBT3-type RCFs of high sensitivity are placed behind the HD-V2s in stack to guarantee the accuracy near the spectral cut-off. The ion transport code SRIM 41 was used to model the range of proton energies stopped in each layer.
Following that a Thomson parabola (TP) spectrometer equipped with a BAS-TR image plate is set at L 2 = 46 cm. Both of RCF stacks and TP are aiming at the target normal direction. We x the diameter and height of the micro-wires of MWA targets at d=0.4 μm and h=2.5 μm and vary the period, i.e., p = 1.3 μm, 1.8 μm, 2.3 μm and 3.3 μm. The diagram of laser direct writing (see Methods) employed in our experiment is sketched in Figure 1 The printed material is polymer with a mass density of 1.17 g/cm 3 . In addition, ultra violet (UV) treatment is employed before they are dried to maintain the stability of the structures 42 .
Enhancing proton acceleration. At certain pre-pulse condition there exists an optimal thickness of planar targets for TNSA 43 . To identify the enhancement brought by the micro-structure, it is very important to exclude the effect of target thickening due to the additional structure. Therefore, before doing comparison we rst nd out the optimal foil thickness that gives highest proton energy. This was omitted in previous reports [26][27][28] , where the structure target is compared to the planar target with the same thickness of only the substrate, or the structure (substrate thickness is ignored). We scan over the thickness of planar SiN layers from 0.2 μm to 4.0 μm and summarize the measured results in Fig. 2(a) (black square). It can be clearly seen that with the target thickness increasing, the cut-off energy of protons increases rst and then declines. For 1 μm-thickness at foils, the proton energy reaches maximum of 18~19 MeV.
For the case of MWA targets, the substrate thickness remains unchanged at 1 μm. Figure 2(a) also shows the measured cutoff energy of protons as a function of the microwire period of MWA targets (red circle). It should be noted that the cut-off energy for all period conditions of MWA targets are above the highest obtained with at foils. As the array period increases from 1.3 μm to 3.3 μm, the cut-off energy of protons rises from 20 MeV to 25 MeV. The maximum energy gain of protons is experimentally observed for MWA targets of 3.3 μm period, which is 30% more than that with 1 μm SiN-foil. The combined substrate and structure correspond to an effective thickness of about 4 μm for at SiN-foil. When comparing to the latter, the MWA energy enhancement is close to 70%.
Representative proton spectra obtained from RCF stacks over the whole proton beam and TP spectrometer for 1 μm SiN foils, and MWA targets with three periods of 1.3 μm, 2.3 μm, and 3.3 μm are shown in Fig. 2(c). The absolute response of the RCF dosimeter was calibrated following the method introduced previously 44,45 . The experimental results of proton spectra from RCF stacks are consistent with that of TP spectrometer. The total number of protons for MWA targets of 3.3 μm period with energy more than 1MeV is about 1.2×10 12 according to RCF spectrum integral, approximately 2.5 times more than that of 1 μm SiN foils of 4.8×10 11 . Here, the Al layer with thickness of 15 μm could minimize possible dose contribution from other heavy ion species. The presence of this foil limited the minimum detectable proton energy to around 1 MeV.
Further, the laser-to-proton energy conversion e ciency (η) is summarized in Fig. 2(b). As the foil thickness decreases from 4 μm to 200 nm, a clear increase in conversion e ciency is observed. The number of 4.5% obtained with 200 nm at can be interpreted as the appearance of piston-like acceleration due to the initial density gradient of rear pre-plasma 46,47 . To exclude this complication, we limit our discussion in the TNSA dominated regime (thickness ). In this case, the maximum η of planar SiN is about 2.9±0.2% for 1 μm SiN foils. When equipping MWA on 1 μm SiN foils, the η is signi cantly enhanced. The e ciency exhibits similar variation tendency as the cutoff energy such that the η increases with larger array spacing. The maximum η of MWA target reaches to 8.7% for one shot at p=3.3 μm, corresponding to a total of 1.1 J for protons with energy > 1 MeV. This is three times that of the average value for the 1 μm SiN foil thickness. This high conversion e ciency is at the top end of report values for TNSA driven by Ti:sapphire based 10's J laser systems 11,16 , which exceeds the maximum conversion e ciency predicted in the Ref. [30]. It should be noted that even though the cut-off energy for 1.3 μm MWA targets is almost the same as that of the 1 μm SiN, the energy conversion e ciency is almost doubled for the former. Both the cut-off energy and conversion e ciency increase with larger spatial period, indicating that the acceleration does not reach maximum for the MWA periods chosen in the current run. We therefore perform further simulations to interpret the experimental observation and more importantly, to nd out the optimal condition for laser-proton acceleration.

Simulation And Discussion
To better understand the experimental results, we carry out hydrodynamic and PIC simulations. The preplasma distribution is determined by 2D hydrodynamic simulations in Cartesian coordinate system using the FLASH 48 code. Limited by the available material in the code, the Al material data is used in numerical simulation. The 3D-printed-MWA parameters are inputted into FLASH. After the pre-pulse ablating MWA targets, it can be seen from Fig. 3(b) that the heads of the pillars expand more obviously than their roots. The plasma forms large clouds around the tips, which narrows the gap between the wires. This type of plasma expansion is more severe for denser pillar arrays. It may even shutter the laser from further interaction as shown in Fig. 3(a). Figs. 3 (c) and (d) show the mass density distribution along three ypositions y= 17 μm, 18 μm and 19 μm from Figs. 3 (a) and (b), corresponding to the inside, edge and outside of the array respectively. Obvious blocking inside the array can be seen in Fig. 3(c), while the structure remains open for arrays with larger gaps (p=3.3 μm) in Fig. 3 (d).
We further show the laser eld distribution when incident onto the MWA structure. As seen in Fig. 3(e), the laser eld is diffracted by the periodic structure such that it is locally intensi ed around the tips of the pillars. Modulated laser intensity produces pre-plasma of larger scale length in the light-intensi ed vicinity, leading to the featured plasma pro le in Figs.

3(a) and (b)
Based on the results of FLASH simulations, we set the density distribution of pre-expanding MWA targets in Fig. 3(f). Each pillar is surrounded with modulated pre-plasma of two components. Around the tip the pre-plasma forms a semicircular with n pre1 = n e1 exp(-△r/l h ), where n e1 , △r, and l h are the pillar electron density, the distance to the tip center and the corresponding density scale length, respectively. The preplasma density in the rest area takes the form n pre2 = n e1 exp[-(△y/l h + △x/l x )]+n e2 exp(-△ /l f ), where n e2 , △(x ,y), l x,f , is the foil electron density, the distance to initial target boundary and the related scale lengths, respectively.
We take the above modulated pre-plasma distribution in the following 2D PIC simulations using the code EPOCH 49 . The simulation box size was W x × W y = 65 μm × 30 μm with the cell size of dx = 4 and dy = 8 nm. Particle-per-cell is set to 9. The p-polarized Gaussian laser pulse is incident at 5.5° from the left side with a central wavelength of 800 nm of pulse duration of 35fs (FWHM). Its peak intensity reaches 2.2 × 10 20 W/cm 2 after being focused to 10 μm spot size. There parameters are the same as experimental conditions. The targets are fully ionized as cold plasma and keep electrically neutral. The at targets consist of Si 14+ and N 7+ with the same density of 12 n c (total electron density is n e = 252n c , n c = m e ω 2 /4 e 2 is the critical density). A thin CH contaminant layer of 20 nm and electron density 45 n c is attached to the rear side of the foil. The front surface of at target is located at x=0, with preplasma of scale length l f = 100 nm. We vary the foil thickness between 0.2 μm, 1 μm, 2 μm and 4 μm. In particular, for the ultrathin 0.2 μm foil a rear pre-plasma with the same scale length is also added 46 . The related simulation results of cut-off energy and spectra of protons are summarized in Figs. 2(a) and (d), which are in reasonable agreement with the experimental results.
The pre-plasma parameters for MWA targets employed in 2D PIC simulations are based on the hydrodynamic results as shown in Fig. 3(f). For spatial period of 2.3 and 3.3 μm, we set l h = 350 nm and l x = 1 μm while the one of the at foil is l f = 100 nm, according to the modulated pre-pulse intensity by the periodic structure. At small period of 1.3 μm, l h is set to 100 nm according to the distribution in Fig. 3(a).
Here the wires are de ned as fully ionized CH and the electron density is 210 n c (mass density ~ 1.17 g/cm 3 ).
From the electron energy spectra in Fig. 4(a) it is seen that the MWA generates much higher temperature due to the DLA mechanism 50 . Here the highest temperature appears at p=5.3 μm, which was not tested in the current experimental run. The corresponding temporal evolution of the longitudinal electric eld E x are plotted in Fig. 4(b). We see that the peak eld strength is largely enhanced due to the MWA. For the spatial period shown here (3.3 μm), one nds higher peak value for the situation without pre-plasma while a slow decrease with pre-plasma, indicating stronger proton acceleration for the former. As pointed out in previous studies 27,29,30,51 , enhancement of the sheath eld results from the higher population of energetic electrons generated in micro-structures.
The scale lengths of l h and l x have different in uence on the proton maximum energy, as illustrated in Fig.   4(c), where l f is xed to 100 nm. When changing l x from 0.5 μm to 5 μm with l h = 350 nm, the proton cutoff energy remains at 27-28 MeV. The scale length of l f has similar effects when changing within several hundred nanometers range (not shown here). However, the maximum energies drop from 35 MeV to 22 MeV when slightly increasing l h from 250 nm to 450 nm with l f = 1 μm. It suggests that proton cut-off energy is more sensitive to the scale length of the wire tip l h , which is closely related to the modulated plasma expansion resulting from pulse diffraction.
In other words, the laser contrast has a signi cant impact on proton acceleration when using MWA targets. Figure. 4(d) shows proton maximum energy as a function of the wire period with and without preplasma. When the pre-plasma is absent, proton energy is maximized to 42 MeV at optimal period around 2.3 μm. However, when introducing the modulated pre-plasma, the energy distribution shows slightly lower peak value of 37 MeV at much larger spatial period 5.3-6.3 μm. This trend agrees well with the electron temperature in Fig. 4(b) and more importantly, with the experimental observation. Because of the modulated pre-plasma in MWA, the optimal period for proton acceleration is modi ed such that one should increase the spatial period as compared to the case when no pre-plasma is considered. However, there is also tradeoff of using MWA with larger spacing. For nite laser spot size, decrease of wire number covered by the laser beam may lead to energy drop for protons 28 . In our case, optimized laserproton acceleration is achieved when the laser spot size covers 0.7~1.5 unit. In the current experimental run, we had best results at p=3.3 μm.
In addition, the energy conversion e ciency from simulations is plotted in Fig. 4(d) after including the pre-plasma condition. Since the simulations are 2D, we calibrate the e ciency with the average value of 6.9 % measured in experiment for p=3.3 μm, which gives a xed ratio for all simulation data. The e ciency shows similar trend as the cut-off proton energy. The highest e ciency appears for p=5.3 μm. When using the maximum calibration factor (8.7% for p=3.3 μm measured in experiment), the η could boost to 10.7% with p=5.3 μm (not shown here).
Snapshots of longitudinal electric eld E x at t=100 fs from simulations are shown in Figs. 5(a-c) respectively in three cases. According to comparison, it is observed that the eld strength and length scale are both evidently larger for MWA targets. When introducing pre-expanding plasma, much of the main laser pulse is re ected while only part of the laser pulse could propagate into structure, as shown in Fig. 5(b). In this case, direct laser acceleration (DLA) of electrons becomes less effective. The latter is usually expected in micro-wires/tubes to greatly improve electron temperature 29,30,51 . Comparing to the case without pre-plasma (Fig. 5(c)), the peak acceleration eld is notably smaller in Fig. 5(b). These distributions agree with the comparison in Fig. 4(d) for p=3.3 μm. We notice the periodic structure induces diffraction for the main laser pulse in both cases. The re ected laser eld is diffracted along large divergence angles while the sheath eld is also modulated with signi cant periodic and divergent patterns. The difference between each case is also imprinted onto the proton acceleration process, as shown in Figs. 5(d-f), where the one without pre-plasma generates several streams of protons following each unit of micro-wire. We did not see the streamed pro le in the current experimental run due to the prepulse condition here. This feature could be further measured as an identi cation of the clean microstructures during interaction, with higher beam contrasts enabled by plasma mirrors.

Conclusion
In conclusion, using a 3D-nano printer to fabricate MWA structures onto the front surface of at foils, we have experimentally demonstrated simultaneous increase of the proton maximum energy and laserproton energy conversion e ciency. We identi ed the effect of pre-plasma modulation caused by the diffraction of laser pre-pulse in MWA structure, which successfully interprets the experimental results. This is the rst time to reveal the role of the scale length l h of the tip of wire structures, which depends on the wire gap and laser pre-pulse. Adjusting the wire number in the laser focal spot and the wire gap could further improve proton cutoff energy.

Data availability
All relevant data are available from the corresponding authors upon reasonable request.   Cut-off proton energy (a) and energy conversion e ciency (b) as a function of the thickness of planar SiN foils (black) and the spatial period of MWA targets (red), from experiments (solid dots) and simulations (solid lines). The error bars are de ned by the level of uncertainty in different shots. The conversion e ciency from laser to protons (kinetic energy >1 MeV) is obtained from the RCFs. Here the high conversion e ciency for 0.2 μm results from more complicated mechanisms thus is excluded from comparison. (c) Proton spectra obtained from RCF stacks (scattered points) and TP spectrometer (dashed lines) for 1 μm SiN foils, and MWA targets with three periods of 1.3 μm, 2.3 μm, and 3.3 μm, respectively. The horizontal error bar marked for p=3.3 μm as the last sheet of RCF stack changed color in this shot. (d) The simulated proton spectra corresponding to the conditions from (c).