In this section we perform an experimental characterization of the spatiotemporal behaviour of an ultrashort pulse after passing through a Gaussian to flat-top beam (FTB) diffractive converter. We aim to introduce a proof of concept experiment to test the chromatic artifacts introduced by a commercial DOE under femtosecond illumination. The election of a flat- top converter DOE is not arbitrary. The use of FTBs instead of Gaussian beams may be advantageous in some applications involving ultrashort lasers. Experiments in high-field physics have benefited from FTBs, where they have been demonstrated to lead to more efficient proton acceleration [146]. In atto-science, FTBs have been employed to generate isolated attosecond pulses and controlled high-order harmonics, reaching broadband extreme UV beams with extremely low divergence [37, 42].
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When the optical system includes DOEs, the response depends on the wavelength and therefore knowing the pulse dynamics in its spatial and temporal coordinates is critical. This is especially important when the resulting beam is used in a second stage where the spatiotemporal profile of the pulse is an important parameter. For this purpose, we carried out the complete spatiotemporal dynamics and propagation of femtosecond FTBs. In this way, 30-fs input pulses were shaped by a Gaussian to FTB converter DOE and characterized by means of the STARFISH technique [17], which is explained below. As a DOE, we used a commercial flat-top shaper (TH- 033, HOLO/OR). This shaper does not need a Fourier lens, since the diffractive pattern is integrated on a refractive lens. It is designed to operate at λ=800 nm and a working distance WD of 200 mm, for a 6 mm input Gaussian beam diameter (Din). The final size of the flat-top pattern is around 3 mm (Dout). In Fig. 5.1 it is shown a schematic of the diffractive device.
The diffractive flat-top beam shaper is a phase element that transforms the Gaussian input beam into a uniform spot with sharp edges at a specific working distance WD. It is important to note that the flat-top spot is not at the minimum spot location (minimum waist), but near it.
The experimental setup for the spatiotemporal characterization of the beam is shown in Fig. 5.2. In this case we used a different laser than in previous experiments. This laser corresponds to the amplifier output of the
Figure 5.1. Schematic of the Gaussian to FTB converter. The DOE is inserted inside a focusing lens.
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HE Pro CEP laser (see annex). It delivers pulses centred at 800 nm of around 23 fs duration, with 1 kHz repetition rate and energy up to several mJ. A spatial filter allowed us to obtain a fairly good Gaussian beam profile. This is achieved with two lenses, L1 and L2, of focal lengths 𝑓1=250 mm and 𝑓2=300 mm respectively. It allows us to obtain a 6 mm (Din) Gaussian beam at the input of the DOE as it is required by the design specifications. The wavefront sensor (WFS) is placed in order to check the collimation of the resulting beam before the flat-top DOE.
The measurement of the spatiotemporal light distribution at the flat- top beam plane was performed by using the STARFISH technique [19]. This reconstruction technique consists of spatially resolved spectral interferometry using a fiber optic coupler as interferometer. Here, the light from the ultrafast laser source is split in two arms: the reference and the test beam. The reference and the test beam are collected into the fiber input ports. The test arm spatially scans the transverse profile at the output plane of the DOE and the reference arm controls the relative delay between the pulses required for the interferometry (around 2 ps in the experimental conditions of the present study). For each transverse position, both pulses are combined inside the fiber coupler and leave it through the output
Figure 5.2 Experimental setup for the spatiotemporal characterization of the DOE. The beam splitter (BS) divides the beam into the reference and test lines. The dotted curved arrows in some mirrors means that they are flip mirrors. These mirrors are used to deviate the beam to the wavefront sensor (WFS), the CCD camera and the FROG measure system.
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common port that is directly connected to a standard spectrometer where the interference spectrum is measured (resolution 0.1 nm, AvaSpec-2048, Avantes). The reference beam is not scanned and its spectral phase is obtained on-axis just by means of a conventional frequency-resolved optical gating measurement (FROG). From the spectral interference, the spectral phase and amplitude at each point are obtained by data processing using conventional algorithms. Finally the temporal profile is recovered by Fourier transformation.
In Fig. 5.3 we show a set of measured results corresponding to the plane which is 200 mm away from the DOE. In the part a) of the figure the recorded spatio-spectral phase for the test beam is shown in logarithmic scale. From this representation it is clear that the DOE response is wavelength dependent. Lower wavelengths are less spatially dispersed than higher ones.
In the part b) of Fig. 5.3 the spatiotemporal reconstructed trace is represented also in a logarithmic scale. At a first view, a curved structure is observed. This implies that light from the outer part of the pattern is delayed
Figure 5.3 Experimental analysis of flat-top beam generation. a)
b)
c)
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approximately in 50 fs with respect to the central part of the beam. In the part c), we show the spatial pattern of the flat-top beam. In the part d) we plot the profile of the spatial part of the beam that corresponds to the vertical dotted line of part c).
From the analysis of Fig. 5.3, we can extract several conclusions. First, it is clear that each individual wavelength of the pulse experiences a slightly different propagation after passing through the flat-top DOE. It affects the spatial profile at the output plane, which is narrower for shorter wavelengths (Fig. 5.3a). Second, from the analysis of Fig. 5.3b we can assume that the temporal width of the pulse is homogeneous for almost the whole spatial profile, but present some inhomogeneities and a delay in the wings. It supposes an evidence of temporal distortions, since the spatiotemporal profile of the beam is not completely uniform. The last conclusion is related to the particular operation principle of the considered DOE. As we have stated in the first two conclusions, the effect of chromatic artefacts are appreciable both in space and time. However, it is clear that they do not introduce strong distortions that completely destroy the dynamics of the beam. The main reason is that only low spatial frequencies are involved in this experiment. The flat-top converter generates a circle of light symmetrically distributed along the propagation axis, as it is appreciated in Fig 5.3c. In fact, in the intensity profile of Fig. 5.3d, a peak of light is observed in the middle of the light distribution that can be interpreted as a “zero non-diffracted order”. Therefore, the lack of high spatial frequencies result in the presence of small spatiotemporal distortions. This conclusion is fully developed in the next section of this chapter.
The characterization carried out by the STARFISH technique must be taken into account for forward applications where this DOE is used with ultrashort illumination, as for example, to assess the validity of flat-top shapers for femtosecond laser processing. Although the distortions appear to be low, it is necessary a careful consideration about how critical are for each particular application. The characteristics of the pulse and the type of DOE influence the final response of the optical system. As we will see in
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the next section, the use of ultrashort pulses and DOEs is not necessary translated into high spatiotemporal distortions. However, when high spatial frequencies and very short pulses are involved, these distortions become significant and may need active correction for further applications.