Abstract
1 Introduction
High-power lasers have proven to be very efficient drivers for plasma physics studies, ever since the invention of lasers in the early 1960s, because of the ability to focus the laser beams to extremely small surfaces, reaching in turn the necessary intensities for laser–plasma interactions[
Up to now, the use of RPPs has been restricted to nanosecond high-energy lasers[
A second more obvious reason is the technical complications related to implementing an RPP in a short-pulse laser. In such a case, the standard technique that consists in adding the RPP close to the last focusing optical element cannot be done because the thickness of such an optical element introduces too much deleterious nonlinear Kerr effect. Hence, new strategies for using RPPs with short-pulse high-intensity lasers need to be developed.
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In this paper, we discuss the implementation of RPPs with short-pulse lasers, including beam smoothing techniques. In particular, we show and experimentally demonstrate the implementation of a phase plate at the PHELIX laser facility[
2 Considerations on the use of random phase plates in short-pulse lasers
Nowadays, the peak power available at laser facilities enables conducting experiments with large laser-intensity distributions of many tens of micrometers in diameter[
Laser type | Nonlinear index | Beam max. | Max. thickness |
---|---|---|---|
( | fluence ( | ( | |
500 fs, 1054 nm | 0.6 | 510 | |
50 fs, 800 nm | 0.3 | 93 |
Table 1. Maximum RPP substrate thickness for typical short-pulse lasers.
For this reason, the enlargement of the focus with the help of an RPP as used at nanosecond laser facilities comes in question. Beams generated by an RPP are, in general, not ‘flat top’ but exhibit a speckle pattern of high spatial frequency. This drawback is compensated for by the nanosecond dynamics of the laser–plasma interaction that yields a smoothing of the speckle-pattern effect. For short-pulse lasers, we have verified that such a smoothing effect can be expected in many cases too. For instance, Figure
As stated in Section
A second approach to circumvent the B-integral issue is to write the phase element directly on a reflective optical element (mirror) to be located close to the last focusing element. When considering this option, we faced the problem of the impact of the phase pattern on the damage threshold of the phase mirror and the following optics. Indeed, a decent beam-shaping effect is obtained with a binary phase element, which is cost effective compared to the more advanced technique necessary for continuous-phase-element generation. However, the phase discontinuity locally induces weakness points in the mirror coating. This requires a thorough study of the laser-induced damage mechanisms on the mirror. In addition, strong and uncontrolled intensity modulations appear on the laser beam, already a few centimeters after the phase element, that put the following optics at risk. For this reason, we did not follow this option.
The third possibility is to locate the phase plate where both damage threshold and nonlinear effects are not a problem. This location needs to be before the compressor and, for obvious economical reasons, we studied the possibility to locate the RPP early in the system, near an image plane, where the beam is still small. This strategy has the advantage to isolate the beam modulation stage from the expensive and damage-threshold-sensitive last optical elements with spatial filters. To do so, the laser system must be adapted to allow for the propagation of a beam that is significantly larger at the far-field location, i.e., in the spatial filters, and exhibits some modulations in the near-field. In addition, the compression of the pulse should not be impacted by the spatial phase of the beam. This condition is fulfilled as long as the spatial gradients in wavefront do not impact the optical path of the single rays in the beam and compression remains homogeneous across the beam in the compressor. This option has been used in the experimental realization at PHELIX and is detailed in the following sections.
3 Design of a phase plate for the PHELIX facility
As explained in the previous section, the entrance of the laser pre-amplifier has been chosen for the location of the RPP as shown in Figure
One of the aspects of this work is the assessment of the compressor behavior in the case of a spatially modulated beam. Indeed, phase gradients are at the center of concerns because they correspond to a spatially varying change in the local beam-propagation direction
The results are depicted in Figure
Another spatio-temporal effect that can impact the pulse shape comes from the compressor configuration found at PHELIX where it is known that a single-pass compressor introduces a pulse front tilt in the far-field[
We obtained the RPP from a commercial source (SILIOS Technologies) that produces discrete eight-level phase plates inscribed in high-quality substrates with a damage threshold compatible with the operation at a high-power laser facility. The phase mask provides the right beam shaping in the far-field away from the optical axis to avoid a residual peak of intensity in the zeroth order with a high diffraction efficiency. Unfortunately, the phase mask includes spatial discontinuities, i.e., vortices, that translate into speckle-like modulations in the near-field of the beam, as soon as high-spatial frequencies are filtered out, which happens already in the first spatial filter. This is shown in Figure
The last feature of the RPP that we employ is a beam-shaping function for the near-field. Indeed, it is possible to apply an additional spatial-phase modulation to the mask in order to introduce a smooth intensity shaping in the near-field[
For the beam alignment, switching from the standard serrated aperture to the phase plate requires the use of a pinhole of a different size in the first telescope and its re-alignment to select the
4 Experimental validation
The phase plate is made on a square 25 mm 1-mm-thick fused-silica substrate and is anti-reflection coated. It is inserted in lieu of the standard serrated apodizer in the same motorized holder for transversal centering. The beam has to be tilted to select its first order via the first telescope and a spatial filter (see Figure
We conducted a series of shots with and without the RPP. Figure
The corresponding far-field intensity distribution is presented in Figure
Compared to the standard case, the far-field distribution created when the RPP is used shows a large spot of the expected dimension. In this area, the intensity shows a speckle pattern with a few hot spots. The correlation of the intensity distribution shows a typical speckle grain size of
In the temporal domain, the characterization of the laser pulse is not trivial. Indeed, the phase plate creates a nonuniform pulse compression in the far-field. In order to study this, a device capable of spatially resolving the pulse duration across the far-field intensity distribution would be necessary. Our calculation shows that the pulse lengthening with the phase plate used at PHELIX should remain below 10% at the edge of the far-field distribution, which is relatively small and makes this effect even more complicated to measure. As a rough consistency check, a scanning intensity autocorrelator was used in the diagnostic arm after the compressor to characterize the unamplified beam at 10 Hz. In addition to spatially averaging the above-mentioned spatio-temporal coupling, the intensity autocorrelator setup introduces a blurring effect due to combined interaction angle and non-negligible spot size of the beam in the doubling crystal (windowing effect), which can be significant with a focal spot about 40 times the diffraction limit and introduces an artificial lengthening of the signal. In the case of the autocorrelator at hand with an internal interaction angle of
5 Conclusion
We have experimentally investigated the implementation of an RPP at a short-pulse laser facility. For such lasers, the RPP cannot be located at the end of the laser chain because of nonlinear pulse distortions and beam self-focusing. Instead, we have proposed and demonstrated that an RPP located at the beginning of the amplifier is technically feasible and provides a far-field intensity distribution as expected. The main drawback associated with this particular RPP design is a reduction of the maximum allowed energy by nearly a factor of 2 because of phase discontinuities in the near-field. This phase plate has been used in a dedicated beam time where a uniform illumination of a target was necessary for ion and X-ray generation[
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