3.1 Overview

Figure 2 shows a schematic of the PTAS and is true to scale. The beam entering from the right is the leakage light of the last turning mirror (transmission = 0.5%) of the main beam. We estimated the B-integral in the bulk material of the mirror for a pulse of 200 J and 500 fs duration using an image of the NF (see Figure 3). The result was (0.261 $\pm$ 0.075) radians in the mean, peaking at 0.555 radians. This is still within tolerable limits.

Figure 2 Scale schematic of the PTAS. The intermediate focal diagnostic is not shown for clarity. The other main components are labeled (‘L’ for lenses) and described in the text.

Figure 3 The NF (left) and absolute, uncorrected WF (right) at the PTAS, recorded on-shot using the largest possible aperture.

At this point, the main beam features a diameter of up to 280 mm, depending on the selected aperture. The main demagnification happens using a compact 8:1 OAP telescope, described in Section 3.2, while still being in vacuum, as the intensity at the intermediate focal spot would be sufficient to ionize gas. The alignment is done with an intermediate focal diagnostic (not shown in Figure 2), which is described in Section 3.4.

The energy is optionally attenuated with another leaky mirror, where the beam paths are overlapped using a Mach–Zehnder style configuration and a shutter to select the beam path, described in Section 3.3. At this point, the energy is already low enough to make the contribution to the overall B-integral in the material of the leaky mirror insignificant.

Afterwards, the beam leaves the vacuum chamber and passes two motorized, reflective neutral density filters for further energy attenuation, which is standard at PHELIX. The beam is then further demagnified about a factor of 3.3 by a regular Kepler telescope, composed of achromats. It passes through a continuously variable attenuator, using a $\lambda$ /2 waveplate and polarizer combination, and another achromatic Kepler telescope, which applies final demagnification by a factor of 2.4 and images the DM into a camera box, featuring both NF and far field (FF) cameras and a custom Shack–Hartmann sensor (SHS) for WF measurement.

3.2 Demagnification and imaging

The decision to demagnify the beam using an OAP telescope follows from the requirement of compactness, while the decision for an f ${}_1$ = 400 mm, 45 ${}^{\circ}$ OAP as the first optical element was made due to compliance with PHELIX standards.

For the second OAP, the main aspects considered were its damage threshold and producibility. As 0.5% of the main beam is transmitted through the leakage mirror towards the PTAS, a hypothetical demagnification of 14:1 would yield the same NF fluence in the main beam, which we consider the limit in order to avoid the risk of damage.

On the other hand, an OAP equivalent to the first one but a factor of 14 smaller is very difficult to produce due to the strong curvature of the substrate. After a comprehensive survey, we found that a focal length of f ${}_2$ = 50 mm seemed to be an acceptable trade-off between size and accuracy. Furthermore, the beam diameter of 35 mm after the telescope is still large enough to slow down the formation of hot spots until the beam has been attenuated. We also chose coatings that could tolerate any conceivable fluctuations in local intensity up to that point.

Our OAP was milled from a 2” copper substrate (LT Ultra GmbH, Germany), featuring a surface error of less than 150 nm peak-to-valley (PtV) and a roughness of less than 5 nm RMS. This is still relatively large and shows that the estimated alignment errors are not the limiting factor for the transmission beam quality of the PTAS.

Thanks to the smaller beam diameter after the OAP telescope, the rest of the imaging and demagnification can be done with off-the-shelf achromats, given that the energy is sufficiently attenuated before, as even large F-number telescopes will not stress the space constraints. The second telescope is composed of one f = 500 mm and one f = 150 mm achromatic doublet (labeled ‘L1’ and ‘L2’ in Figure 2). The third telescope brings the beam diameter down to 4.4 mm using one f = 300 mm and one f = 125 mm achromatic doublet (labeled ‘L3’ and ‘L4’ in Figure 2, respectively) and images the surface of the DM onto the image plane of the camera box. The chromatic defocusing over the full width at half maximum (FWHM) of the PHELIX spectrum introduced by these lenses is less than $0.01\lambda$ RMS, which is better than the alignment precision of the OAP telescope.

In Figure 3, the NF and WF at the PTAS are shown. These were recorded on-shot using the largest possible aperture at PHELIX. In the NF, the clipping of the beam on the last compressor grating (see Section 5.1) is visible on the left- and right-hand side of the beam, together with grating imperfections at various places in the NF. This demonstrates the NF imaging quality of the PTAS. The according WF shows that high-order aberrations dominate the beam, while astigmatism and defocusing are mostly absent.

3.3 Energy attenuation

The range of available energies in the target chamber of PHELIX goes from 400 $\mu \mathrm{J}$ for the alignment beam to 200 J for a full energy shot, while most energies in between can also be achieved. The dynamic range that has to be covered by the PTAS is therefore 5×10⁵, which has to be achieved with several attenuation stages.

The first attenuator is a Mach–Zehnder setup right after the OAP telescope (labeled ‘MZI-Atten.’ in Figure 2). Here, the first beam splitter is a leaky mirror with a reflectivity of 99.3%, while the recombination beam splitter has a reflectivity of 40% (for s-polarization, as present in the PTAS). A motorized shutter can block either one or the other beam path, enabling the selection between transmissions of 59.58% and 0.28%, respectively, creating a dynamic range of 2.13×10².

Outside of the vacuum chamber, before the beam gets further demagnified, two reflective attenuators with a neutral density of 1 can be inserted into the beam, increasing the dynamic range to 2.13×10⁴.

The rest of the dynamic range is given by the last attenuator, which is a combination of a $\lambda /2$ wave plate and a single polarizer and is easily capable of attenuating the energy by the required factor of 24.

In order to avoid ghost images, we applied standard measures to this setup. Specifically, all planar optics except the neutral density filters are wedged and the ghost images are removed from the beam path by a pinhole in the intermediate focal plane between L1 and L2. The neutral filters, however, feature plane-parallel surfaces, as the beam displacement introduced by the first filter has to be compensated by the second one. Here, an anti-reflective coating with a reflectivity of less than 0.2% mitigates ghost images to an insignificant amount.

With most of the coatings being susceptible to polarization, the PTAS proved to handle linear polarization well, achieving the desired extinction ratio at any pulse energy that can be delivered by PHELIX and thus being able to measure over the whole energy range.

3.4 Alignment strategy

The alignment of the beam path outside of the vacuum chamber was done using a back-propagating reference beam, generated by a fiber laser, which was injected next to the camera box (see Figure 2). Using a 0 ${}^{\circ}$ turning mirror after the second telescope, it was used in a double-pass configuration to optimize the alignment with the WF sensor of the camera box.

However, the alignment beam stayed in place afterwards for the alignment of the OAP telescope, using the alignment scheme described in our previous work^[ Reference Ohland, Zobus, Eisenbarth, Zielbauer, Reemts and Bagnoud ^{18 ]}, where the intermediate focal spots of the main beam and the back-propagating alignment beam were overlapped spatially.

In order to do so, an etched tungsten needle on a motorized stage is used to mark the position of the focal spot (see Figure 4). The focal plane then has to be observed in both beam directions with a vacuum compatible microscope that is able to resolve the intermediate focal spot. Due to the small focal length of the second OAP, this setup has to be rather compact in this case, generating the necessity of two small mirrors that can be placed in the beam after the focal spot for each propagation direction, respectively (see Figure 5) in order to deflect the beam into the microscope.

Figure 4 An etched tungsten needle is used to mark the position of the focal spot (center). A bit of dust has stuck on its tip. The large caustics are created by backlighting, which is used in order to see the shadow of the needle.

Figure 5 Scale schematic of the intermediate focal diagnostic in side view (left) and top view (right), observing the backwards propagating alignment beam. The needle and the diagnostic mirrors can be moved in and out of the beam, while the microscope can be moved in three axes in order to change the viewing position. The other possible states of the diagnostic are drawn as transparent overlays.

Our microscope is composed of a 20× Plan Apo NIR infinity-corrected objective (Mitutoyo Corp., Japan) combined with an f = 200 mm plano-convex lens and a 12-bit CMOS camera (Manta G-235B, Allied Vision Technologies GmbH, Germany). Cooling the camera under vacuum is significantly simplified by the fact that this board-level camera is split into a sensor and a connector board, connected by a flexible flat cable. As most of the heat is only generated on the connector board, it can easily be mounted to a dedicated heat sink.

4.1 Cross calibration

As mentioned earlier, the optimization of the focal spot requires a calibration routine for the WF sensor. As the PTAS inherently measures the leakage of the beam, the calibration has to be done separately, sampling the actual focused beam.

To do so, we developed a module named Calibrator for Laser systems with Absolute Wavefront Sensing (CLAWS). This module is depicted schematically in Figure 6. The strength of CLAWS lies in its ability to be self-calibrated in situ using a pinhole^[ Reference Wang, Wang, Zou and Zhang ^{20 –} Reference Gao, Jiang and Li ^{22 ]} in the focal plane, creating a spherical WF as reference. In addition, the system is compact and can be moved to the target chamber center (see Figure 7) at the beginning of the experiment to cross-calibrate the PTAS with the least amount of interference with the experimental setup.

Figure 6 Schematic of the CLAWS concept.

Figure 7 Sketch of the target chamber area, indicating a possible configuration during the calibration routine.

In practice, CLAWS is aligned to catch the full beam with a high-numerical-aperture microscope objective. Then, a (1+0.25/–0.10) $\mu \mathrm{m}$ blackened stainless steel foil pinhole, manufactured by Thorlabs Inc., USA, is placed in the focus to generate a close-to-perfect spherical wave. Using this ideal point source, a reference is taken using CLAWS. Afterwards, the pinhole is removed and the AO runs an optimization loop to this reference (see next section for results). Once the best WF is reached, the WF measured by the PTAS is saved as the new PTAS WF reference, corresponding to the best accessible focus at the target position. After this procedure, CLAWS can be removed.

4.2 Optimization results

The focal spot before and after the optimization using CLAWS is shown in Figure 8. After we completed the calibration routine for the first time, the peak fluence in the focal plane increased by roughly a factor of three, promising more than 10²¹ W/cm² for a typical PHELIX shot of 100 J and 500 fs. The improvement is obvious, as most of the scattered energy is moved back into the center of the focal spot. This becomes especially apparent when looking at the encircled energy, shown in Figure 9, as the curve of the optimized focal spot lies consistently above the unoptimized one. The radius of 50% encircled energy, for example, is only half as large as prior to the optimization.

Figure 8 The unoptimized (left) and optimized (right) focal spots of a copper OAP at the target position, recorded with a 16-bit CMOS camera, installed in CLAWS. The intensity is estimated for a 100 J, 500 fs pulse.

Figure 9 The encircled energy over the radius from the point of largest intensity, taken for the focuses shown in Figure 8.

The WFs in CLAWS, associated with these focuses, are shown in Figure 10. The remaining high-order aberrations, relative to the pinhole reference, are visible on the right. These aberrations, combined with steep slopes at the edges of the beam and some yet uncharacterized chromatic aberrations that cannot be corrected using a DM, are accountable for the deviations of the optimized focal spot from the diffraction limit.

Figure 10 The unoptimized (left) and optimized (right) WFs corresponding to the focuses shown in Figure 8, recorded using CLAWS. The WFs are measured relative to the reference generated using the pinhole. The unoptimized WF features an RMS of 0.202 $\lambda$ , while it is reduced to 0.052 $\lambda$ after optimization.

By now, CLAWS can only be operated in air, which leads to some uncertainty in the estimation of the on-shot intensity after the target chamber has been evacuated. Doing quantified measurements of the associated alignment deviations of the focusing OAP relative to the incoming beam, we found these uncertainties to yield a correction factor of 0.84 ${}_{-0.03}^{+0.16}$ , which we applied to all findings presented in the following.

5.1 Image quality of the PTAS

While the PTAS does not need to deliver a true FF intensity distribution representation of the beam due to the calibration procedure using CLAWS, it was designed to allow a high-fidelity low-distortion imaging of the sampled beam to the detectors. To check this point, we needed to compare the FF at the PTAS with a reference. The focal spot in the target chamber is, however, not suitable for this, as the OAPs are changed and realigned between experiments, drastically changing the aberrations in the chamber. Therefore, we compared FF images recorded at the PTAS with images recorded at the compressor beam sensor, which uses a high-F-number (f = 6 m) lens as the first optic for imaging (see Figure 11). Figure 12 shows a snapshot of the FF here (left) and at the PTAS (right). The images were recorded at the same time and without any beam correction.

Figure 11 A sketch of the PHELIX compressor, including the gratings, the DM and the directions to the compressor beam sensor (‘COS’) and the PTAS.

Figure 12 A qualitative comparison between FFs (a) measured at the compressor exit and (b) measured at the PTAS at the same time. No beam correction was applied.

The focal fluence distributions show obvious qualitative similarities, while deviations indicate some difference between the beam paths. This is presumably composed of astigmatism and defocusing, but cannot be quantified due to the lack of a WF sensor at the compressor exit sensor. Still, the similarity shows that the PTAS can be used as a sensor calibrated to a relative reference, while at the same time aiding the laser operation by providing an approximation of the FF at the target position.

The statement that these deviations are not the limiting factor in the FF approximation holds especially true when considering the difference between the uncorrected FF recorded at the compressor and the PTAS (Figure 12) and the uncorrected FF at the target position (Figure 8, left). This difference is due to the aberrations introduced by the imperfections of the focusing optic (in this case, an OAP milled from copper). It will persist even if the focal spot is optimized and change if the focusing optic is replaced.

5.2 On-shot intensity gain

Finally, we conducted an experiment to verify the increase in on-target intensity. During this campaign, we investigated the impact of the higher intensity on the laser–target interaction. Specifically, we used the PTAS and the AO loop to control and estimate the on-shot intensity for the different configurations described below while keeping the pulse energy constant and varying the thickness of the foil targets made of polystyrene.

Under our experimental conditions, a higher laser intensity increases the hole-boring effect^[ Reference Hornung, Zobus, Roeder, Kleinschmidt, Bertini, Zepf and Bagnoud ^{23 ]}. Therefore, we expect the transmission of the laser light through the target to depend on the target thickness and the intensity reached on-shot, where lower thicknesses and higher intensities increase the transmission. The results of this measurement are shown in Figure 13, plotting the transmission through the target over the foil thickness in the range from (55 $\pm$ 9) nm to (3186 $\pm$ 15) nm for various operation conditions.

Due to the Treacy architecture^[ Reference Treacy ^{24 ]} of the PHELIX compressor (see Figure 11), the pulse is spatially chirped when entering the target chamber and the PTAS. This leads to some ambiguity in the data of the SHS and makes calculating the exact fluence distribution in the target plane a complicated task. Therefore, we estimated the intensity by viewing the focal spot with a 16-bit CMOS camera after the calibration routine, applying the expected error arising from the pump-down, as discussed in Section 4. We then used the on-shot deviation of the WF at the PTAS compared to the calibration reference to derive a multiplicative factor (Strehl) for this intensity. The result is color coded in Figure 13. Note that the choice of using a color bar for the intensity prevents us from showing the error of the intensity, which is within +28% to –18% and contributes to the scattering of the data points along the y-axis.

Figure 13 Transparency of the polystyrene foil targets, plotted over their thickness. The estimated intensities are color coded, while different shot configurations are indicated by the shape of the data points. The data set displayed as triangles was taken from a previous beam time (P155).

The diamonds and triangles correspond to two different experiments without AO, yielding similar results and intensities of about (1.4–3.6)×10²⁰ W/cm². Using the AO loop in combination with the copper parabola increases the on-target intensity by a factor of three to five (squares), while using a glass parabola increases the intensity even more up to 1.4×10²¹ W/cm² (green dots). This indicates that the AO loop cannot fully correct for the high spatial frequency defects that are present on a milled copper OAP, pointing out the advantages of polished glass OAPs.

While one expects a transmission of 100% in the limit of an infinitely thin target, we only reach about 80% in this experiment, where the shots using the glass OAP may indicate some form of saturation. This can be explained by the lower intensity parts of the focal spot, which do not contribute to the hole boring and are rather reflected by the plasma. However, we could not investigate this as no targets thinner than 55 nm were available.

A clear correlation between intensity and transmission through the target is apparent, where the target becomes transparent at smaller thicknesses and for higher intensities, which matches our expectations. The greatest impact of the intensity is visible at target thicknesses around 300 nm, increasing the transmission from about 30% to 65% using a copper OAP with AO and almost 80% if a glass OAP was used instead. This shows the robustness of the WF sensing and the AO loop.

Note that the shots with the glass OAP for target thicknesses over 500 nm are of lower intensity. These were the first shots with AO, where the shot routine still needed to be debugged. Due to time constraints, these shots could not be repeated.