Shaping femtosecond laser pulses at short wavelength with grazing-incidence optics.

We present the design of an extreme ultraviolet (XUV) pulse shaper relying on reflective optics. The instrument will allow tailoring of the time-frequency spectrum of femtosecond pulses generated by seeded free-electron lasers (FEL) and high-harmonic generation (HHG) sources down to a central wavelength of ~15 nm. The device is based on the geometry of a 4f grating compressor that is a standard concept in ultrafast laser science and technology. We apply it to shorter wavelengths using grazing-incidence optics operated under ultra-high vacuum conditions. The design blaze angle and the line density of the gratings allow the manipulation of all different harmonics typical for seeded FEL and HHG photon sources without the need of realignment of the instrument and even simultaneously in multi-color experiments. A proof-of-principle pulse shaping experiment using 266 nm laser light has been performed, demonstrating relative phase-control of femtosecond UV pulses.


Introduction
In the last decade a new window of opportunities has opened-up using intense free-electron laser (FEL) pulses in the extreme ultraviolet (XUV) and soft X-ray regime for photon science applications [1]. Pioneering work has been done at FELs like FLASH at DESY in Hamburg [2], LCLS at SLAC in Stanford [3], and FERMI at Elettra in Trieste [4]. The implementation of so-called seeding schemes at these facilities [5][6][7], which allow for the generation of fully coherent photon pulses, paved the way towards applying coherent nonlinear X-ray spectroscopy and quantum control methodologies at FELs ( [8,9] and references therein). First experiments were conducted at FERMI, tuning the machine parameters in order to tailor the photon pulse characteristics [10][11][12]. Research and development of photon pulse shaping capabilities at FELs enables the transfer of advanced experimental techniques from the optical spectral range (IR, visible and UV) to the short-wavelength limit, e.g. four-wave mixing [13] and coherent control of quantum phenomena [14].
Tailoring the temporal shape of femtosecond (fs) pulses in the optical spectral range at the push of a button has resulted in a great variety of pulse-shaping experiments that control the photo-induced motion of electrons and ions in atoms, molecules, clusters and solid-state samples [15]. The generation of arbitrarily shaped waveforms, i.e. the manipulation of the time-frequency spectrum of the electromagnetic wave, is possible by controlling the spectral phase, amplitude and polarization of the electric field in the frequency domain [16]. Often, a pixelated spatial light modulator (SLM) based on liquid crystals (LC) is placed in the Fourier plane of a zero-dispersion compressor, which is used to spatially disperse and re-collimate the spectrum of the ultrashort laser pulse. By applying distinct voltages to separate pixels the refractive index across the spectrum can be manipulated. Upon transmission of the fs laser pulse through the LC array a frequency dependent phase and/or amplitude modulation is acquired. By virtue of an inverse Fourier transform this results in shaped pulse envelopes in the time domain with tailored frequency distribution. Alternatively, acousto-optic modulators (AOM) [17,18] or acousto-optic programmable dispersive filters (AOPDF) [19,20] can be inserted. These devices rely on synthesized radio-frequency waves changing the optical properties of the modulator material and thus controlling the transmitted light wave characteristics.
Conventional transmissive pulse shapers allow for tailored photon science applications down to about 250 nm wavelengths. The main obstacle towards experimental studies at even shorter wavelength with refractive optics is the limited transparency range and laser-induced damage of the modulator medium. However, the availability of shaped pulses in the deep UV would already allow for a multitude of interesting applications, because many organic compounds exhibit strong absorption bands in this spectral range [21]. For instance, gaining a mechanistic understanding of the remarkable photostability of DNA has been based so far on multiphoton interaction with intense near-infrared (NIR) laser fields. In these dynamic studies of the electronically excited states lifetime [22], either the multiphoton pump or the timedelayed multiphoton probe pulse may significantly perturb the multidimensional potential energy landscapes under investigation. Multiple absorption events complicate unravelling details of the weak field excitation and subsequent energy dissipation processes, which are the photophysical and photochemical relevant scenarios in nature. Furthermore, multiphoton stimuli impede the ability to achieve control over the phase of the excitation without modifying the transition probability as a function of laser intensity [23,24].
In order to access deeper UV spectral regions down to ~200 nm for pulse shaping pioneering work using micro-electro-mechanical system (MEMS)-based mirror arrays was carried out by Hacker et al. [25]. In recent years MEMS technology has been pushed forward [26,27] and adapted to XUV amplitude modulation in high-harmonic generation (HHG) covering approximately 30 -90 nm in first experiments [28]. The quest for shaped XUV pulses comes from the dream of physico-chemists to steer chemical reactions at the level of electronic motion on the attosecond timescale. It refers to the holy grail of 'attochemistry', where shaped pulses might be used to control the fate of coherently coupled cationic eigenstates produced by ultrashort pulses with a short central wavelength [29].
In this contribution, we present a feasibility study of an XUV pulse shaper relying on grazing incidence optics and its realization within the limits of current technology. A 2 m long compact version of the instrument has been built, optimized for use down to a central wavelength of approximately 15 nm. The expected overall transmission is on the order of 1% Tr = , suitable for most experiments at seeded FEL facilities and laboratory-based HHG sources. Both lasing schemes make use of a highly nonlinear frequency up-conversion process that is driven by intense optical laser pulses interacting with relativistic electrons in linear accelerators and bound electrons of atoms in gas cells/jets, respectively. The line density and the blaze angle of the shaper's dispersive elements (the gratings) have been designed, in order to allow its operation at each harmonic of the optical seed (drive) laser pulse without realignment of the zero-dispersion compressor. Furthermore, this approach allows for simultaneous shaping of several co-propagating harmonics enabling e.g. fundamental third harmonic coherent control experiments like the ones pioneered by Chan, Brumer and Shapiro [30].

Experimental setup
The zero-dispersion compressor in the 4f geometry, also known as 'zero dispersion line' or '4f-line', was first proposed in 1983 by Froehly and associates [31]. It is an optical layout consisting of four elements: two identical gratings (G 1 , G 2 ) and two identical cylindrical lenses or mirrors (CM 2 , CM 3 ) with focal length f. The four elements are arranged in a symmetric configuration, as sketched in Fig. 1. The symmetry plane is called the Fourier plane, because the frequencies within the spectral bandwidth of the pulse are spatially separated due to an optical Fourier transform. It provides spatially encoded access to the spectral amplitude ( ) A ω and phase ( ) φ ω , and thereby to the full electric field function ( ) out E ω of the transmitted waveform. The complex representation of the field is particularly useful, because any action of a mask can be represented as a product of a frequencydependent function ( ) M ω and the incident field distribution ( ) in E ω : The distance between each optical element and the next, the Fourier plane included, is equal to the mirrors focal length f (hence the name '4f'). The XUV pulse shaper design described in the present contribution hosts two additional focusing mirrors (CM 1 , CM 4 ) added at the extremities of the beam path to decrease the beam footprint on the optics in the center of the shaper setup in the plane perpendicular to the dispersion direction, in particular on the reflective shaping mask. The advantage is that the active area (length) of the mask along the beam path is reduced which allows for shorter phase/amplitude masks. The general layout is very similar to a time-delay-compensated monochromator [32]. A phase/amplitude mask located in the Fourier plane of the zero-dispersion compressor allows tailoring the time-frequency spectrum (shape) of femtosecond pulse indicated in purple. A lamellar mirror assembly acting as a phase/amplitude mask and operating under grazing incidence is highlighted. Tip, tilt and translation of the moveable lamellar mirror on the nanometer scale allow for pulse shape control of the XUV output.
An ultrashort laser pulse is dispersed by the first grating G 1 in the plane relevant for pulse shaping. The setup is designed to employ gratings with a line density of 333 lines/mm and blaze angle b 9.9 θ =°. With an incidence angle of i 5 θ =°(measured with respect to the grating surface), the first order of a femtosecond laser pulse 0 ( 266 λ = nm) will be diffracted at where d is the grating period, i.e. 3 µm, n is the diffraction order, and c λ is the central wavelength of the incident light wave. It follows that all n-th diffraction orders of n-th  of the 266 nm seed (drive) laser wavelength will be diffracted at the same angle θ d with the highest efficiency and increasing spectral dispersion for the shorter wavelengths. This allows for multicolor shaping experiments using different harmonics from seeded FELs and intense HHG sources. When the dispersed beam is focused in the 4f-line by the subsequent mirror CM 2 , each 'monochromatic bundle of rays' within the spectral bandwidth is focused onto a different position in the Fourier plane. Because all but the central frequency are not focused in the mirror focal point, small aberrations are introduced. In principle, they are compensated by the symmetric optics set-up in the zero-dispersion line and no net effect should remain in the output pulse. However, side effects, which relate to the process of light modulation in the Fourier plane, need to be considered when simulating the expected performances of implemented shaping masks. Delaying a monochromatic bundle by a time t results in an additional linear phase term ( ) (1) t φ ω ω = , leading to a pulse front tilt behind the Fourier plane. As a consequence of this spatio-temporal coupling of the 4f-line, shaped pulses exhibit a spatial chirp in the transverse coordinate across the output beam. The effect has been studied in great detail for LC and AOM masks (see for instance [33], and references therein) and will be detailed below. It limits the capabilities to generate tailored waveforms, i.e. the spectral resolution and accessible temporal window, respectively. The position k X of each frequency component k ω in the Fourier plane is given by: where α is derived from geometric considerations as: where c is the speed of light and d is the grating period. According to Gaussian optics the focus width 0 x Δ of each monochromatic component in the Fourier plane can be derived from: where f is the focusing distance and in x Δ is the diameter of the incoming beam. Thus, the resolution can be expressed as: The calculated value δω represents a lower limit for the spectral resolution of the pulse shaper. Typically, the actual resolution of a 4f pulse shaper is not limited by the focus size in the Fourier plane, but by the size of the active optical elements (e.g. liquid crystal pixel size) of the phase mask. The frequency resolution δω of a pulse shaper relates to a temporal period by Fourier transformation. The resulting time interval determines the temporal window T that can be shaped with minimal distortion. It is given by: where v has the dimension of a velocity, and is given by: For the present XUV pulse shaper setup the magnitude of the spatio-temporal coupling as given by the parameter v is roughly on the same level as for pulse shapers in the visible spectral range (see Table 1), which gives rise to comparable spatial chirps. We note in passing that the 0 x Δ , δω , T as well as values for the laser pulse durations refer to the full width at half maximum (FWHM) of the intensity envelope throughout the manuscript. The achievable resolution of the present set-up was simulated using the software package Optics Studio/Zemax taking into account optical aberrations. Table 1 summarizes the results for short wavelength laser pulses at a central wavelength of c 38.1 λ = nm using the 7th diffraction order of the grating. The focusing optics and grating specifications are given in Table 2 and Table 3, respectively. The instrument is shown in Fig. 2.    The focusing mirrors (CM 1 -CM 4 ) are made of polished silicon substrates with < 0.5 nm surface roughness. The mirror pairs (CM 1 , CM 4 and CM 2 , CM 3 , respectively) are cut from the same piece of silicon after polishing, ensuring perfect pairwise matching of the curvatures. The overall transmission of the XUV pulse shaper of ~1% takes into account the optics reflectivity under grazing incidence and a filling factor of 80% of the lamellar mirror assembly depicted in Fig. 1. The modular arrangement of the optical components in individual vacuum tanks enables the adjustment of the focal distance f between them without constraints, e.g. to compensate for divergence of the incoming beam. Furthermore, a future upgrade of the shaper in order to increase the spectral resolution in the Fourier plane or moving towards shorter wavelength is easily possible by replacing the gratings and the mirrors. Increasing the relative distances at shallower grazing incidence results in increased spectral resolution and transmission, respectively. Currently, the relative distance between the central optics (focal length f) is 330 mm.

Results
The present study was performed using femtosecond pulses at 266 nm central wavelength that were generated by nonlinear frequency up-conversion of near-infrared (NIR) pulses from a commercial Ti:Sa femtosecond laser system. An 800 nm beam with a diameter of 5 mm propagates through a set of nonlinear crystals (Eksma Optics) for third harmonic generation (THG). In the THG-kit a calcite crystal delays the residual NIR pulse with respect to the 400 nm radiation initially generated in a first β-BBO (β-BaB 2 O 4 ) crystal of 0.5 mm thickness. According to the design, both colors overlap in time and space in a second β-BBO crystal of 0.15 mm length for sum-frequency generation of 266 nm light with a pulse duration of ~130 fs. A few tens of microjoule in the third harmonic with a spectral bandwidth of the order of 1% has been achieved, which is sufficient for pilot UV pulse shaping experiments using the all-reflective 4f -line. The goal of the present study is to demonstrate the overall functionality of the device and a first experimental performance test in the UV spectral range that is crosschecked by optics simulations. A bandpass mirror installed behind the THG unit filters most of the residual 800 nm and 400 nm light and the remains are removed by the first grating of the pulse shaper. As a temporary installation, of-the-shelf UV gratings (Richardson/Newport) with 300 lines/mm operated in the first order have been used for G 1 and G 2 , respectively. The resulting dispersion in the Fourier plane with f = 330 mm is 3.8 nm/mm. The gratings are blazed at 10.4°, which is close to the design value discussed above, achieving diffraction of 266 nm light into the first order with highest efficiency (nearly specular reflection). The gratings are made of BK-7 glass coated with aluminum. The aluminum coating is protected from oxidation by a thin layer of magnesium fluoride. Such a coating has approximately 90% reflectivity at 266 nm.
At the heart of the 4f-line a lamellar mirror assembly comprised of two interleaved mirrors with a filling factor of 80% has been placed in the Fourier plane of the pulse shaper acting as a mask that is capable of modulating spectral phases by controlling path length differences on the nanometer scale. The filling factor is given by the 100 µm-wide reflective stripes of 5 mm length (uncoated silicon wafer) separated by 150 µm gaps. The flatness of the comb-like reflective mask is crucial because otherwise additional spectral phase delays along the footprint in the Fourier plane would be introduced. The surface quality of the mask in the illuminated area was characterized by means of white-light interferometry [35]. It shows a root mean square deviation of a few nanometers from a perfect plane [36]. In the present shaping experiment we have chosen to modulate the spectral amplitudes by tilting one of the lamellar mirrors off axis, i.e. by removing certain frequency components from the beam path.
The resulting modulated UV spectrum of the beam is recorded at the shaper exit and compared to simulations, which describe the effects of a periodic amplitude mask M(ω) acting on a Gaussian beam. The simulation code is based on equations that have been developed by Thurston et al. [37]. They were modified by replacing the linear approximation of the grating dispersion Eq. (4) with the exact non-linear form: where k X is the position on the Fourier plane, with k 0 X = being the center of the shaping mask, f is the focus length of the 4f-line, d θ is the grating diffraction angle and c λ is the central wavelength of the laser pulse. The diffraction angles are calculated using the grating Eq. (2). For the sake of completeness, we note that the experimental data from the spectrometer is compared to the simulated spectrum right behind the lamellar mirror in the pulse shaper, while the spectral modulation was experimentally characterized at the shaper exit, i.e. the simulation assumes a perfectly symmetric setup. A linearly chirped 130 fs Gaussian pulse with the experimentally determined UV spectral bandwidth is taken as input for the simulation. The measured data shown in Fig. 3 can be reproduced reasonably well by assuming a focus size 0 75 x Δ = µm for the monochromatic bundles of rays, which is much worse than the optimal spectral resolution given by the carefully aligned optics (~5 µm at 266 nm), and by adding an incoherent background to the simulations. Obviously, the spectral resolution is rather determined by the 'sharpness' of the amplitude mask than by the optics specifications. Due to the mechanical dicing by a rotary diamond saw, surface damage ('chipping') is present close to the edges of the reflecting stripes, with surface sections up to tens of micrometer wide missing. The extent of the damage on the mirror stripes is shown in Fig. 3 on the right. Furthermore, chipping smooths the edges of the transmitted spectral bands and increases stray light adding up incoherently in the spectrometer. The simulated spectra in frequency domain matching the experimental results have been used to calculate the resulting temporal profile of the shaped pulse sequences keeping the experimental spectral bandwidth constant but changing the compression of the pulses. In Figs. 4(a)-4(d) the resulting temporal envelopes are compared for the input pulse duration of 33 fs at the Fourier limit (a), chirped pulses of duration of 60 fs (b), 100 fs (c) and 130 fs (d) assuming a 'spectral resolution' 0 x Δ of 5 μm and 75 μm in the Fourier plane, respectively. It can be seen that if the duration of the input pulse is small compared to the peak separation (213 fs), the replicas will have a Gaussian shape identical to the initial pulses. If the duration of the initial pulse is comparable to the peak separation, complex interference patterns will arise. tails of different spectral components centered on the gaps are still reflected. As a result, no spectral components are completely removed from the pulse. In the time domain, this reduces the intensity of the satellite pulses with respect to the central one.
A well-defined UV pulse sequence at a central wavelength of 266 nm comprising of sufficiently compressed optical stimuli is interesting for controlling light-induced dynamics in many-body quantum systems, especially considering that the parametrization and more sophisticated tailoring of its time-frequency spectrum are rather simple. For instance, a defined relative phase jump between the central lobe and the side lobes can be introduced, while keeping the overall temporal envelope constant [38]. This is achieved by moving the lamellar mirror along the dispersion plane, which shifts the reflective elements into positions of different frequency components. Measured spectra of different pulse shapes, which are phase-shifted in steps of π/9 are shown in Fig. 5. The spectra have been filtered through a 5point moving average filter, in order to reduce the effect of the camera thermal noise. Gaussian fits of the pulse envelopes and the lines indicating their fixed center-of-mass and 1σ points are included for comparison. The overall effect of the spectral amplitude modulation on the relative phase in time domain can be calculated analytically. Assuming linear dispersion in the Fourier plane and a perfectly flat amplitude mask with sharp edges and no dead spaces between the reflective elements (stripes or pixels), the electric field of the shaped pulse is given by [39]: δ is the spectral distance between mask pixels in the Fourier plane given by the 250 µm period of the lamellar mirror and g v δ is the spectral resolution with which the lamellae are 'sampled' given by the monochromatic focus width 0 x Δ . The total number of pixels in the mask is given by N . The amplitude (phase) change introduced by the n-th pixel is given by ( ) n n A φ , whereas n B is the spectral amplitude of the unshaped pulse at the n-th pixel. The measured spectra and simulated temporal profiles of four shaped pulses, with π/2 relative phase-shift steps and assuming 60 fs pulse duration for the unshaped pulse, are shown in Figs. 6(a)-6(d). Fig. 6. Shaping of the time-frequency distribution of 60 fs-long UV pulses. Four differently shaped pulses, each generated by a quarter stripe-period difference in the shaping mask position (a). They obey the same temporal electric field envelope (b), but exhibit different relative phases of the first (c) and last lobe (e) with respect to the central one (d). The intensity has been scaled in Fig. 6(d) in order for the four waves not to overlap. The spectra shown in (a) are measured single-shot spectra, while the remaining graphs show simulated data.
While each of the carrier waves is in phase at the peak of the central pulse (d), in the leading (c) and trailing (e) pulse the phase advance or delay of the carrier is equal to the phase difference in the position of the striped mirror. This allows monitoring of photophysical and photochemical processes in molecules by imaging the reaction products (electrons, ions or photons) as the spectral distribution is continuously swept over the full range of 2π in a systematic manner [38]. We have to emphasize that the absolute phase is, of course, not known and will (without phase stabilization) in any case vary from pulse to pulse. However, recording the molecular response as function of relative phase changes between the central pulse and side bands from -π to + π during an experiment provides important information. Only mechanisms that involve coherence in the excitation of molecules will be sensitive to such phase changes between the successive pulses driving electronic and nuclear dynamics. In other words, such a protocol offers a tool to discriminate between coherent and incoherent effects and to select the control strategy accordingly. Photoreactions, which are typically driven by incoherent processes, mainly depend on the excitation wavelength or on secondary processes occurring after the laser matter interaction, while coherent control uses the advantage of coherent properties of the laser field for manipulation by constructive and destructive interference [38]. Those schemes were pioneered in atomic excitation by Meshulach and Silberberg [40] and have been exploited in great detail to coherently control the photoionization of potassium atoms [41], but work even in the light-harvesting antenna complex LH2 from Rhodopseudomonas acidophila. In this photosynthetic purple bacterium it was possible to steer the energy flow in a condensed-phase environment [42]. The possibility to cleave pre-selected backbone bonds in amino acid complexes that may be regarded as peptide model systems as a function of light phase has been demonstrated using intense 800 nm pulses [38]. These experiments were carried out on different amino acid chromophores and shed new light on NIR laser-induced relaxation pathways. The observation of protonated species in the mass spectra indicated that coherent control may even be useful in particular cases to study intramolecular reactions such as hydrogen-or proton-transfer. However, for a detailed mechanistic understanding of these important photochemical reactions explaining, e.g., photostability of DNA, future experiments will benefit from state selectivity in the excitation process at short wavelength. For instance, peptide-bond absorption in molecular building blocks of life sets in at λ < 230 nm [21], thus the present pulse shaper relying on grazing-incidence optics may open new perspectives for biophysical and biochemical research.

Conclusion and outlook
In the present contribution the design of an extreme ultraviolet (XUV) pulse shaper based on the 4f geometry of a zero-dispersion grating compressor well-known in ultrafast laser science and technology has been described. The mobile instrument relies on grazing-incidence reflective optics and is operated under ultra-high vacuum conditions. Therefore, it enables tailoring of the time-frequency spectrum of femtosecond pulses down to a central wavelength of ~15 nm. The design blaze angle and line density of the gratings implemented in the 4f-line allow the manipulation of all the different harmonics typical for seeded free-electron lasers (FEL) and high-harmonic generation (HHG) sources without the need of realignment of the instrument. Even simultaneous multi-color control experiments are within reach keeping in mind that amplitude and phase of specific spectral components can be manipulated with high precision in the Fourier plane by means of micro-electro-mechanical system (MEMS)-based mirror arrays [26][27][28]. A proof-of-principle pulse shaping experiment using 266 nm laser light has been performed, demonstrating relative phase-control of femtosecond UV pulses. The study paves the way towards future experiments at seeded XUV and soft x-ray FEL sources worldwide.

Funding
Cluster of Excellence 'The Hamburg Centre for Ultrafast Imaging' of the Deutsche Forschungsgemeinschaft (DFG) -EXC 1074 -project ID 194651731 and the collaborative research center 'Light-induced Dynamics and Control of Correlated Quantum Systems' (SFB925); Federal Ministry of Education and Research of Germany (BMBF) through collaborative research projects FSP 302 (05K13GU4) and LoKoFEL (05K2016).