Compact 200 kHz HHG source driven by a few-cycle OPCPA

The CEP stabilized octave-spanning Ti:Sa oscillator (VENTEON, 80 MHz, 6 fs) is the front end of the OPCPA. Its spectrum is used to seed both the parametric amplifier and the fibre CPA, inherently optically synchronizing the two. The frequency doubled output of the fibre CPA serves as pump for the parametric amplifiers.

A narrow fraction of the oscillator spectrum around 1030 nm is selected with a dichroic mirror to seed the fibre amplifier chain, which consists of a chirped fibre Bragg grating for pulse stretching, a fibre preamplifier, two parallel rod-type amplifiers, and two grating compressors. In the preamplifier, the seed is amplified to 600 mW and the repetition rate is reduced from 80 MHz to 200 kHz with the help of three amplification stages and two pulse pickers. The output of the preamplifier is divided into two pulses with the same power to seed two Yb-doped rod-type amplifiers in parallel (NKT-DC-285/100-PM-Yb-ROD). The rod-type amplifiers deliver 150 μJ pulse energy before compression. With an 80% efficiency of the grating compressor, the output of the fibre amplifiers is 24 W each. Thermal management and appropriate cooling is essential to obtain high power and good mode quality from the rod-type amplifiers. Note that for the results presented in this work only one rod-type amplifier was used.

The pulse duration of the fibre CPA output pulses is approximately 350 fs, measured with an auto-correlator assuming a Gaussian-correction factor. For second harmonic generation the output of the fibre amplifier is focused into a 1 mm long type-I β-barium borate (BBO) crystal, resulting in 11 W at 515 nm, corresponding to 48% conversion efficiency. The pulse duration of the second harmonic is estimated to be approximately 250 fs. By using a λ/2-plate and a thin-film polarizer the second harmonic is divided into two beams to pump two NOPAs.

The parametric amplification part is comprised of a pulse shaper, two NOPAs built in the Poynting-vector walk-off compensation geometry, chirped mirrors for intermediate and final compression, and a f-to-2f interferometer for slow drift control of the CEP.

2.3.1. Pulse shaper

2.3.2. NOPA1

The pump for the first NOPA stage, 3 W, is focussed into a 2 mm type-I BBO (θ = 26.6°) crystal (beam diameter is approximately 350 μm), resulting in 125 GW cm⁻² peak intensity. The seed pulse diameter in the BBO crystal is slightly smaller. For this NOPA stage the non-collinear angle between pump and seed is approximately α = 2.4°, ensuring broadband amplification. A motorized translation stage in the seed path compensates for temporal drifts between the pump and the seed (more information about the delay stabilization is given in section 3.4).

The first NOPA amplifies the 10 mW (80 MHz) seed to 260 mW (200 kHz), which corresponds to an efficiency slightly below 10%. In figure 2(a), the output energy of NOPA1 is plotted versus the pump energy. The red data points were obtained by measuring the average power of the full beam. Above a pump energy of 15 μJ, the amplified signal spectrum starts to show undesired parasitic effects. At that point, the efficiency curve changes its slope. The black circle marks the chosen working point for NOPA1. With only 3 W pump power, NOPA1 works in a very relaxed condition, which leads to good temporal and spatial properties. The inset in figure 2(a) shows the measured beam profile. Spatial and temporal characterization of the first NOPA stage are shown in section 3. The dispersion of a 2 mm thick BBO crystal stretches a compressed <7 fs pulse to approximately the length of the pump pulse. Thus, the seed pulse must be recompressed before NOPA2. Two reflections from a double-chirped mirror pair (Venteon DCM7) slightly over-compensate the dispersion; this is balanced by 2 mm of fused silica and about 60 cm of air between the NOPA stages.

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2.3.3. NOPA2

The spectral power at different stages in the system is shown in figure 3. The spectrum originating from the oscillator (grey line), seeding the first NOPA stage, is slightly modified by the reflectivity of the gratings in the shaper and furthermore cut at the edges due to the hard aperture of the LCD display. The transmission through the hard aperture is chosen in order to match the amplification bandwidth of the parametric amplifier, i.e. 640–1100 nm (or 270–470 THz).

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The first NOPA covers almost the whole bandwidth of the seed and amplifies it from 0.125 nJ to 1.5 μJ per pulse. Apart from the well-known parasitically phase-matched SHG around 340 THz [16] in the Poynting-vector walk-off compensation geometry, the shape of the spectral amplitude is maintained in the parametric amplification process, reflecting the absence of strong parasitic and undesired wave mixing processes. The second stage also covers the whole bandwidth of the seed spectrum (see red curve in figure 3), but shows first signs of nonlinear distortions, e.g. strong amplification at the edges of the spectrum, a strongly modulated structure around 440 THz as well as new peaks and dips around 300 THz and the filled gap at 320 THz [17]. The black curve presents the output spectrum in a linear scale.

The duration of the NOPA output pulse is characterized with the d-scan technique [12]. Since this method requires the pulses to be focussed into a nonlinear second harmonic generation crystal, we simulate the focus conditions, which are present in the HHG setup. For the reasons discussed in section 4, we focus the pulses with an achromatic lens. The NOPA pulses are therefore characterized not behind the first compressor after the two NOPA stages (see section 2.3.3), but behind the second chirped mirror compressor, a BK7-wedge pair as well as a vacuum window and an (identical to the HHG setup) achromatic focussing lens. Figure 4(a) shows the measured and reconstructed d-scan traces without an additional phase applied to the phase shaper. The fundamental spectrum was measured with a calibrated optical spectrum analyser (OSA, Andor). The tilted shape of the d-scan traces indicates that the different spectral components of the broadband pulse cannot be compressed simultaneously.

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Figure 4(c) shows the spectral power (dotted black line) and phase (dotted blue line). The pulse suffers from ringing in the spectral phase, originating from uncompensated dispersion components, e.g. from double chirped mirrors. The reconstructed temporal profile is shown in figure 4(d) (blue dotted curve, 6.3 fs pulse duration). It is obvious that the pulse cannot properly be compressed, which is mainly reflected by the fact that the peak power is much lower than for the Fourier-transform-limited case (grey line).

Because the pulse shaper is placed before the first parametric amplifier, the dynamic range of the phase that can be applied is limited. Applying the exact spectral phase, necessary to obtain a Fourier-transform-limited pulse behind the two NOPA stages at the HHG focus, is unfortunately not possible, because it would significantly change the temporal shape of the seed pulses for the NOPA. Consequently, the pulse durations of the pump and seed pulses would not be matched anymore, which will reduce the efficiency of the par-ametric amplification. As a compromise, a spectral phase is applied, which cleans the output pulses from the OPCPA, i.e. leading to less satellite pulses and more power in the peak of the pulse, while not impacting the parametric amplification too much. The measured and reconstructed d-scan is shown in figure 4(b). The d-scan trace is not tilted anymore, indicating that the pulse can be better compressed temporally. The spectrum (figure 4(c), filled red curve) supports a Fourier-transform-limited pulse duration of 5.7 fs. With the shaper, the pulse could be compressed to 6.1 fs, (figure 4(d), red line) and the pulse peak power could be increased to 75% of the Fourier-transform-limited power. Taking this into account, we conclude that of the 9 μJ pulse energy emitted by the laser, about 6.75 μJ are contained in the main pulse, resulting in a peak power of 1.1 GW.

In this section, we present a spatio-temporal characterization of the output pulses from the OPCPA. Optical parametric amplification naturally introduces spatio-temporal coupling, which can be kept small in the so-called magic angle configuration [16, 18]. A misaligned NOPA stage increases distortions to the spatial and the spectral phase and leads to stronger spatio-temporal couplings, which impact the performance of subsequent NOPAs and ultimately reduce the intensity to which the OPCPA output can be focused. Therefore, spatio-temporal characterization is a very powerful tool to measure and understand the impact of phase distortions and spatio-temporal couplings and to avoid them as much as possible during the amplification process in a NOPA.

As mentioned in section 3.1, the amplified spectrum after the second NOPA stage (see figure 3) shows spectral features, which are not related to the oscillator seed spectrum. This indicates the presence of parasitic effects during the amplification process. One prominent parasitic effect is the second harmonic generation of a fraction of the signal (and the idler) in the Poynting-vector walk-off compensation geometry [16], which leads to distortions of the spectral amplitude and phase of the signal (and idler). Furthermore, the second NOPA stage operates in saturation for some spectral parts which might lead to back-conversion to the pump frequency and local distortions to the spectral phase and amplitude. This will affect the compressibility of the output pulse [17, 18]. Since in a non-collinear optical parametric amplifier spatial distortions are expected as well, originating e.g. from (i) the angular-frequency dependent nonlinear gain distribution, (ii) a pulse front miss-match of the pump and the signal beams [18, 19] and (iii) from the birefringent nature of the amplification crystal (BBO), temporal distortions are strongly coupled to the spatial coordinates of the beam.

In contrast to previous spatial and temporal characterization techniques applied to high-repetition rate NOPAs based on e.g. SPIDER measurements taken at different positions of the beam [20], imaging spectrometry [20] or spatially resolved spectral interferometry [21], we apply a homemade technique based on spatially-resolved Fourier transform spectrometry, capable to measure the spatio-spectral phase over large apertures [13, 14]. With this technique, we can access the full information of the pulse regarding the amplitude and phase in space and time at arbitrary planes. A similar approach based on the SEA-F-SPIDER technique was recently applied to the characterization of another high-repetition rate, few-cycle OPCPA laser [22, 23].

Spatio-temporal couplings originating from NOPAs employing uniaxial crystals, e.g. BBO, are expected to occur in the plane, where the seed and pump beams are non-collinearly mixed, i.e. the walk-off plane or x–z plane, if the z-direction is the propagation direction of the pump (see figure 5(a)). In the y–z plane, no strong spatio-temporal distortions are expected and observed in our analysis. The most prominent spatio-temporal distortion, originating from NOPA stages detuned from the magic angle configuration, should be angular dispersion, which also causes pulse front tilt and potentially spatial dispersion in the far-field. For a detailed discussion of spatio-temporal couplings and their different representations, we refer to an article by Akturk et al [24]. The analysis of our measurements concentrates on distinguishing the following spatio-temporal coupling contributions:

• Spatial dispersion where the coupling $\gamma$ is found in the amplitude

$$\begin{eqnarray*}&&E(x+{\gamma }_{x,\omega },y+{\gamma }_{y,\omega },\omega ){{\rm{e}}}^{{\rm{i}}\varphi (x,y,\omega )}.\end{eqnarray*}$$

• Angular dispersion where the coupling $\gamma$ is found in the phase

$$\begin{eqnarray*}&&E(x,y,\omega ){{\rm{e}}}^{{\rm{i}}\varphi (x+{\gamma }_{x,\omega },y+{\gamma }_{y,\omega },\omega )}\\ &&\,\to \tilde{E}\,({k}_{x}+{\tilde{\gamma }}_{{k}_{x},\omega },{k}_{y}+{\tilde{\gamma }}_{{k}_{y},\omega },\omega ){{\rm{e}}}^{{\rm{i}}\tilde{\varphi }({k}_{x},{k}_{y},\omega )}.\end{eqnarray*}$$

Here, k_x, and k_y are the transverse wavenumbers in x- and y-direction, respectively, which can be obtained by Fourier transforming the electric field E of the pulse along the space coordinates. Angular dispersion, such that different frequencies propagate into different directions, will be visible as asymmetry (tilt) in a (k_x,y, ω)-representation of a pulse. Spatial dispersion, such that the frequency content of the pulse is not evenly distributed in space, will be visible as asymmetry in a (x, y, ω)-representation.

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For our spatio-temporal analysis, we distinguish three different planes, which are illustrated in figure 5(b), i.e. the NOPA plane (x₁, y₁), where the couplings originate from, the far-field (x₂, y₂), where we perform the characterization and the near-field (x₃, y₃), which is obtained by refocusing the pulses either with the purpose of generating high-order harmonics or to couple to an additional NOPA. Our characterization technique measures the phase and amplitude of the pulse $E({x}_{2},{y}_{2},\omega )\,$in the far-field [13], i.e. after collimation at some distance away from the BBO crystals. By simple Fourier operations, we can obtain the pulse in any other representation, i.e. (x₂, y₂, t) and $({k}_{{x}_{2}},{k}_{{y}_{2}},\omega )$, and by numerical propagation also in any other plane, e.g. in the near-field at the focus of our HHG setup.

We start by characterizing the spatio-temporal couplings originating from the first NOPA stage (NOPA1), which is built with very relaxed pumping conditions. The measurement is performed after collimating the diverging beam from NOPA1, i.e. in the far-field. We characterize two different conditions of NOPA1: first, it is aligned to the best of our abilities and second, we deliberately detuned the angle between the pump beam and the crystal axis in order to generate angular dispersion and pulse front tilt as well as spatial dispersion in the far-field. For the first condition, we optimized the NOPA stage by carefully choosing the pump conditions regarding the pump beam size and the power, by that making sure that this stage works far from saturation (see section 2.3.2). This can be tested by a pump-signal efficiency curve and by avoiding distortions in the amplified spectrum. At the same time, the non-collinear angle is optimized for broadband amplification. Figure 6 summarizes the extracted data from the spatio-temporal characterization of NOPA1. Figure 6(a) shows the spatially integrated spectral power (blue line), (b) the intensity in (x₂, ω)-representation (i.e. a cut for y₂ = 0), and (c) the intensity in $({k}_{{x}_{2}},\,\omega )$-representation (cut at ${k}_{{y}_{2}}=0$) for the well aligned NOPA1 on the left side and with deliberate misalignment on the right side ((e)–(g)). Also shown in figures 6(a) and (e) is the spectrum measured with an OSA (red line). The spectra agree well in both cases, which is a very important confirmation that our Fourier transform spectrometry approach gives reliable data. For the well aligned NOPA, no distinct asymmetry is observed, neither in the (x₂, ω)- nor the $({k}_{{x}_{2}},\,\omega )$-representation of the measured pulse, indicating that there is no significant spatio-temporal coupling. The situation is different when NOPA1 was deliberately misaligned. Figure 6(f) shows a clear asymmetry of the pulse in the (x₂, ω)-representation, i.e. spatial dispersion originating from angular dispersion in the NOPA plane. This is accompanied by a slight tilt of the angular spectrum, which however is less obvious, see figure 6(g).

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We investigate the focusability by numerically propagating the pulses for the well-aligned and misaligned NOPA1 to the near-field, assuming aberration-free and dispersion-free focussing conditions. We follow a procedure, outlined by Giree et al [18], where the spectral phase is not explicitly considered and where the pulses are assumed temporally transform-limited on-axis. Off-axis, however, the spectral phase can be more complicated, as the phase difference between the on-axis and off-axis phases is kept in this analysis. This allows us to disentangle the impact of the introduced spatio-temporal couplings on the focusability from the impact on the pulse duration. For the numerical propagation from the far-field to the near-field, an angular plane wave decomposition is used [25], providing the pulses in (x₃, y₃, ω)-representation (see figure 5(b)). A Fourier transform in the frequency direction, finally gives the focused pulses in (x₃, y₃, t)-representation, from which we can extract the maximum intensities. The focused pulses are illustrated in space and time for the well-aligned and misaligned NOPA in figures 6(d) and (h), respectively.

While the differences are subtle in visual comparison, the impact of the misalignment becomes obvious when comparing the maximum intensities with each other as well as with an idealized case for which we numerically removed all spatio-temporal couplings (see [18] for a discussion of the procedure). This can be understood as a three-dimensional Strehl ratio, relating the actual focal intensity, compromised by phase distortions and spatio-temporal couplings, to the focal intensity of a pulse with identical pulse energy, identical spatial profile, but clean spatial phase. For the sake of easy comparison, we normalize the pulses from the well-aligned and deliberately misaligned NOPA1 to the same pulse energy, ignoring the fact that the misaligned NOPA1 gives less pulse energy. By this procedure, we obtain a Strehl ratio of approximately 0.81 for the well-aligned NOPA1, while the value for the misaligned NOPA1 is approximately 0.63. Taking into account the strongly nonlinear intensity dependence of HHG, such difference in focal intensity can largely impact the HHG signal and its conversion efficiency. Furthermore, spatio-temporal couplings might impact the performance of subsequent NOPA stages.

Finally, we also characterized the pulses after the second NOPA stage. Again, the characterization was performed in the far-field after collimation. For this measurement, both the first and the second NOPA were aligned to the best of our abilities. Figure 7 summarizes the results. The averaged spectra measured with the OSA (red line) and the Fourier transform approach (blue line) are in good agreement again (figure 7(a)). In the two middle ((b) and (c)) and the two bottom rows ((d) and (e)), we plot the intensity in (x₂, y₂, ω)- and $({k}_{{x}_{2}},{k}_{{y}_{2}},\,\omega )$-representations, respectively. Spatio-temporal distortions should be expected in the direction of non-collinear wave mixing in the NOPAs, i.e. the x-direction. This is confirmed by the characterization. In figure 7(b), a slight asymmetry in the spectral distribution along the x₂-direction is observed, i.e. a sign of spatial dispersion, as well as a slight tilt in the $({k}_{{x}_{2}},\,\omega )$-representation (figure 7(c)), i.e. a sign of angular dispersion. In the y-direction (figures 7(d) and (e)), no distinct asymmetries can be observed, neither in the (y₂–, ω)- or $({k}_{{y}_{2}},\,\omega )$-representations of the intensity, indicating that the pulse should focus cleanly in the y-direction. The difference in the focusability of the x- and y-directions becomes obvious, if we interpret the $({k}_{{x}_{2}},\,\omega )$- (figure 7(c)) and $({k}_{{y}_{2}},\,\omega )$-representations (figure 7(e)) as rescaled versions of the near-field (x₃, ω)- and (y₃, ω)-representations. This is valid if we assume that the far-field and the near-field are connected via their spatial Fourier transforms, i.e. that diffraction in the Fraunhofer regime is valid [25]. From this comparison, it is clear that the transverse size of the focus in the near-field, e.g. the HHG interaction region, is larger in the x- than in the y-direction. This is confirmed by a three-dimensional illustration of the spatio-temporal intensity distribution in the focus, obtained from numerical propagation, which is shown in figure 7(f). The obtained Strehl ratio is approximately 0.71.

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If we now additionally consider the measured spectral phase of the pulses reflecting the temporal pulse shape at the HHG interaction region, as discussed in section 3.2, only about 75% of the total pulse energy is contained in the main pulse. This additionally reduces the focused intensity compared to an undisturbed pulse, which is transform-limited both in space and time. Behind both NOPAs, including the effect of the spectral phase, we obtain a total Strehl ratio of 0.53. The reduction of the peak intensity should have considerable impact on the efficiency of HHG. Please note that even for a carefully aligned, few-cycle OPCPA, as demonstrated in this section, the maximum focused intensity is barely half the possible intensity (not including the spatial-temporal aberration coming from a focussing element). This underlines the importance of spatio-temporal characterization techniques in order to optimize the alignment of optical parametric amplifiers.

3.4.1. Active delay stabilization

For long-term stable output power of the OPCPA laser, active delay stabilization between the pump and the seed/signal is essential. As a result of the short pump pulse duration, in our case about 250 fs, small fluctuations of the relative timing of the two beams will translate to the amplified output spectrum, the central frequency, the power, and the CEP. The active delay stabilization is based on recording the frequency-doubled, angularly dispersed idler spectrum as emitted from the first NOPA, with a camera. The frequency-doubling originates from a parasitic phase-matching effect. A typical measurement is shown in figure 8(a).

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If the timing between pump and signal in the crystal changes, the position of the centre of mass of the idler spectrum on the camera chip will move. The active delay stabilization continuously computes the centre of mass, compares it to a saved reference, and generates an error signal, which is used to move a translation stage that controls the delay of the seed pulses to the pump. This stabilization system, running at approximately 5 Hz, mostly corrects for thermal path length differences originating from the fibre laser part, which in total is some tens of meters long. Since the largest contribution to the delay instability is addressed with the active stabilization of the first NOPA stage, an active stabilization for the second NOPA is not necessary. With the active delay stabilization, the standard deviation of the average output power over 2 h is less than 0.5%, see figure 8(b). The shot-to-shot energy stability over 2 h is 2% rms.

3.4.2. CEP-stability

The gas supply system is designed to deliver a high gas density to a small medium's length. This is crucial for efficient generation of high-order harmonic radiation in a tight focusing geometry [26].

A sketch of the nozzle system is given in figure 10(a). It provides a very localized, high-pressure gas target without contaminating the surrounding vacuum. It is comprised of two nozzles: one for gas injection and one for gas extraction. The injecting nozzle forms a supersonic gas jet through a small, 50 μm diameter hole. According to Monte Carlo simulations (computed with DS2V [27]), the resulting pressure in the interaction volume is estimated to be one order of magnitude lower than the backing pressure. Thus, a backing pressure of 10 bar (up to 40 bar is possible) approximately results in 1 bar (4 bar) pressure in the interaction region. The extraction nozzle is connected to a roughing pump, which is supposed to capture most of the injected gas in the generation chamber. The extr-action nozzle has a hole of 1 mm diameter and is placed 0.2 mm away from the injection nozzle. The generation chamber is additionally pumped with a large turbo pump, resulting in a background pressure of below 10⁻² mbar, despite the large amount of injected gas.

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The simulations suggest that with the current nozzle design the estimated target length approximately 100 μm away from the ejection nozzle, i.e. in the middle between ejection and extraction nozzle, is 200 μm. Outside that length the gas pressure has fallen to below 30%. Thus, the effective gas length is comparable to the confocal parameter of the laser. Figure 10(b) shows the harmonic yield in argon as a function of the backing pressure. The XUV signal is absorption limited and saturates beyond 12 bar. Every time the pressure was changed during the measurement, the nozzle position had to be re-optimized because of a recoil force from the gas jet, which pushes the nozzle away from the laser focus. The dip of the XUV yield at 18 bar backing pressure thus can be attributed to a not carefully enough optimized nozzle position.

4.2.1. XUV spectra

The high-order harmonic radiation is characterized using a homemade XUV-spectrometer consisting of a grating and a MCP (see figure 9). The grating (Hitachi, 001-0640) is an aberration-corrected concave grating with variable groove spacing. The XUV beam is simultaneously focused and spectrally dispersed in the horizontal direction, while it is unaffected in the vertical direction. Thus, the vertical direction (not focused) carries information about the divergence of the beam, while the horizontal direction (focused) carries the spectral information.

Figure 11(a) shows harmonic spectra, i.e. photon energy versus divergence, for neon, argon, and krypton. For all three gases, the nozzle position was optimized for the highest cut-off energy in the high-order harmonic spectra. For argon and krypton, contributions from the long trajectories to the HHG spectrum can be identified. Since long and short trajectories differ in their divergence, i.e. the long trajectories are more divergent, their contributions become obvious for large angles. We select the short trajectory contribution to our HHG spectra by integrating in the vicinity of the optical axis. Figure 11(b) shows the HHG spectra integrated between the two grey lines marked in (a). Except for neon, all other measurements were performed with an aluminium (Al) filter placed before the grating (see figure 9). As a result, the low energy sides of the argon and krypton spectra are shaped by the Al-transmission window and by the transmission through a few nm thick oxide-layer, usually covering the filter on both sides [28]. The neon spectrum is influenced around 25 eV by the frequency dependent diffraction efficiency of the grating. Krypton shows distinct harmonics from the filter edge around 22 eV (H15) to the cut-off at 53 eV (H33). In argon, the spectral amplitude decreases around 50 eV due to the presence of the Cooper minimum. The argon HHG cut-off reaches H39 (60 eV). For the measurement of the neon HHG spectrum, no filter was used to suppress the strong IR field because the higher absorption edge of aluminium around 72 eV would remove the cut-off of the neon HHG spectrum. The spectrum from 20 to 40 eV overlaps with the second-order diffraction from higher photon energy harmonics. The spectrum from 50 to 90 eV features a continuous structure, which can be attributed to the limited resolution of the spectrometer in this range. Only the presented spectrum in neon was measured with a locked CEP of the amplifier. However, locking the CEP and changing it leads to rich interference pattern in the spectrum of all three gases (not shown here) [35].

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4.2.2. Beam profile

4.2.3. Photon flux