Alignment of solid targets under extreme tight focus conditions generated by an ellipsoidal plasma mirror

The design of ellipsoidal plasma mirrors (EPM) for the PEARL laser facility is presented. The EPM achieved a magnification of 0.32 in the focal spot size and the corresponding increase in focused intensity is expected to be ∼ 8. Designing and implementing such focusing optics for short pulse (< 100 fs) systems paves the way for their use in future high power facilities where they can be used to achieve intensities beyond 10 W/cm. A retro-imaging based target alignment system is also described, which is used to align solid targets at the output of the ellispoidal mirrors (numerical aperture of 0.75 in this case). Email address: Deepak.Kumar@eli-beams.eu (Deepak Kumar) Current affiliation: Helmholtz-Zentrum Dresden-Rossendorf, Bautzner Landstrasse 400, 01328 Dresden, Germany. Current affiliation: Space Micro Inc., San Diego, California, USA. Preprint submitted to Journal of Matter and Radiation at Extremes October 14, 2018


Introduction
The consistent technological development of high intensity short pulse lasers and the corresponding improvement in focused intensity over the last few decades have led to the exploration of new frontiers of basic science and applications [1].
Current generation of petawatt (PW) class lasers provide focused intensities 5 around ∼ 10 21−22 W/cm 2 with traditional focusing optics of about f/3. In upcoming facilities like Apollon [2], ELI pillars [3,4,5], etc. the corresponding focused intensities will increase to about ∼ 10 22−23 W/cm 2 . However, the ability to achieve higher intensities of the order of 10 23−24 W/cm 2 will enable the possibility of exploring novel phenomena like radia-10 tion reaction [6] and ion acceleration to relativistic energies [7]. Laser plasma interaction in the radiation reaction dominated regime is qualitatively different from the currently achievable regimes of focused intensities 10 22 W/cm 2 because the energy radiated by the oscillating electrons at the focus is comparable to the energy the electrons gain 15 from the laser field. Consequently, a significant fraction of the laser energy is expected to be emitted in multi-MeV X-rays [8,9]. Thus it will be highly beneficial to increase the achievable intensities, for e.g., by tightly focusing the laser beam to a spot size of the order of the laser wavelength. To achieve this, scientists have either used a small f-number parabola [10] or an 20 ellipsoidal plasma mirror (EPM) [11,12,13,14]. Because of debris damage to the parabola and the associated financial implications, using a small f-number parabola is not a viable option for upcoming facilities like ELI Beamlines [3].
Thus the performance of the EPMs on currently available PW class short pulse lasers is being studied to gain valuable experience in pursuing this technology 25 on future high intensity laser facilities.
2 An EPM is a small mirror designed to be placed after the focus of the main focusing element. It images the first focus into the second one with a significantly smaller f-number in order to reduce the focal spot. The EPM acts in the plasma mirror regime with very high irradiance on the surface and so is a 30 single-use optic. Since 2010, when the first use of the EPM on short pulse lasers was demonstrated [11], there has been steady experience gained on the use of such optics on glass laser systems with pulse lengths of the order of a ps [12,13].
The optimal geometrical parameters like eccentricity and angle of incidence of the EPM to achieve the desired magnification under paraxial approximation 35 have been described earlier [15]. The only remaining parameter for designing the EPM is its scale size, which is set to optimize the reflectivity of the main laser pulse on the EPM [13]. This paper describes the design of an EPM for the PEARL laser facility [16,17] at Nizhny Novgorod, Russia. The laser uses large-aperture nonlinear DKDP crystal for optical parametric order to align the front surface. An alternative method is to align the front surface of the target with using a retro imaging system which has been demonstrated to work well with precision comparable to the Rayleigh length of the 60 focusing optic [18]. Alignment based on retro reflection has the advantage of being immune to surface irregularities on the target introduced while mounting the target. This paper describes a retro imaging system for aligning a solid target to the tightly focused output from an EPM. The performance of the retro alignment system is bench-marked against an alternative alignment technique 65 based on monitoring the near field of the beam being obstructed by the target.
This paper is structured as follows. Section 2 describes the geometry of the EPMs and characterizes their performance. Section 3 describes two different procedures for aligning the target at the output focus of the EPM. Finally, the paper concludes with section 4. target is at the focus, the entire near field profile diminishes simultaneously as seen in the figure (4b, right). If the target thickness (3 µm in our case) is comparable to the Rayleigh length (expected to be around 3 µm for the output 130 of EPM at the PEARL facility) then two shadows approaching from either side on the near field can also be observed and the shadow from the front side of the target (figure 4b center) can be distinguished from the shadow from the rear side of the target. On the PEARL facility, front side of the targets were aligned by monitoring the shadow from the front surface and placing the front surface 135 at the focus. When shot with the full energy beam, a significant increase in the X-rays and the maximum ion energy were measured as compared to normal OAP shots. These results will be described in subsequent publications.
Target alignment by retro imaging. The retro imaging system, which is useful for aligning thicker targets was assembled only on the test bench in order to 140 bench-mark its performance. A 0.8 µm thick Al target was chosen to compare the two alignment procedures, as the target thickness was comparable to the Rayleigh length on the test bench (see figure 2b). Initially the target was aligned at the focus by monitoring the near field as described in the previous paragraph.
Subsequently, the axial location of the target was varied around this reference 145 location. The location of the target was absolutely measured using a Fabry-Pérot interferometer based displacement sensor. Figure 5 shows the average brightness of the measured spot on the retro imaging camera as a function of target displacement. The result shows that optimizing the target location for maximizing the average intensity measured in the retro imaging camera can be 150 used for aligning the target at the focus of the EPM within the Rayleigh length (approximately ±1 µm on the test bench). Such a retro imaging system is planned to be implemented on future campaigns involving thicker targets with EPMs. It should be noted that on high power facilities, the pellicle will have to be removed from the beam path before the full power 155 shot in order to avoid the beam wavefront distortion due to nonlinear interaction of high intensity laser beam with the pellicle.
Retro imaging setups on existing facilities [18] utilize the focusing OAP to collect light reflected from the target front surface. However, the retro imaging setup described in this paper uses the EPM to collect the reflected light. The

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EPM in this configuration for collecting the reflected light acts like a high mag-nification objective to create an image at the front focus which is then imaged on the retro imaging camera with a lens. The pellicle beamsplitter used in the alignment process introduces significant wavefront errors in the reflected light, but as is evident from figure 5 the alignment procedure is still robust.