1. Introduction

Advanced nonlinear optics allows the generation of extremely short light pulses tunable from the UV to the infrared. The pulse duration approaches the period of the carrier wave [1]. In this regime the control of the pulse spectrum and the spectral phase becomes increasingly important. The technical capability of deliberate pulse shaping opens new opportunities of optimal compression [2], coherent control [3,4] and two-dimensional spectroscopy [5].

Various methods for ultrafast pulse shaping have been demonstrated: 4-f shapers based on liquid crystal displays (LCD) [6] and on acousto-optic modulators (AOM) [7] as well as more direct acousto-optic programmable dispersive filters (AOPDF) [8]. Due to technical reasons these methods were largely limited to the visible and infrared spectral range. A vast class of molecules and attractive materials does, however, require UV light for electronic excitation or manipulation of reaction dynamics. Advanced devices promise to improve this situation [9,10], they await their combination with competitive tunable UV sources.

Direct frequency doubling of shaped sub-100 fs visible or NIR pulses allows only selected pulse shapes in the UV [11]. More flexibility is given by sum frequency mixing of shaped pulses with stretched fixed frequency auxiliary pulses and resulted in tunable 19 fs shaped UV pulses [12] and 150 fs at the third harmonic of a Ti:Sa laser [13]. However, coupling between the shaping and the efficiency is still encountered. With micromirrors (MEMS) direct shaping of UV pulses has been demonstrated, yet at very low duty cycle and efficiency. The reported results are so far limited to 78 fs at 404 nm [14], 104 fs at 266 nm [15] and 30 fs in a limited range around 324 nm [16]. Despite reasonable efficiency and a predicted operational range down to 180 nm, the use of a fused silica AOM in a 4-f setup has only been shown for 88 fs pulses at 400 nm [10] and 55 fs at 260 nm [17].

With the newly available AOPDF for UV operation, that is based on a KDP crystal [18], significant progress can be expected. The principal applicability of the new unit to UV pulses on the 50 to 100 fs range has already been demonstrated [19]. Compression close to the Fourier limit can, however, not be derived from the figures and information given in the report. In the present contribution we report on a detailed investigation of the use of this compact and easily adjustable device for the full range from 250 to 400 nm. The UV pulses are derived from the broadband visible pulses of a noncollinear optical parametric amplifier (NOPA). Compression to below 20 fs as well as complex pulse structures are obtained and the pulses are fully characterized. Contrary to most previous shaping efforts the collimation and focusing of the beams into interaction region of the spectroscopic experiment was considered explicitly. This proved necessary since proper pulse compression was not possible with the initially chosen beam geometry. The correct combination of geometric and Gaussian optics proved to be crucial for the generation of clean pulses.

2. Experimental setup

The basis for the shaped UV pulses and their characterization (see Fig. 1 ) are two single-stage NOPAs pumped by a 1 kHz Ti:Sa amplifier system (CPA 2001; Clark MXR). The output of NOPA 1 is compressed by a prism compressor (PC) and then focused by mirror M1 into a 30 µm thick BBO crystal for type I second harmonic generation (SHG). The SHG potentially creates angular dispersion, because the maximum efficiency for every wavelength depends on the incident angle. Thus the recollimated UV beam would have a spatial chirp in the vertical direction. A further possible source of angular chirp is a nominally imperfect alignment of the NOPA. The angular dispersion is equivalent to a pulse front tilt [20]. We compensate the horizontal component by a slight rotation of the second prism in the PC [21] while monitoring the UV beam with a fiber coupled spectrometer. To precompensate the vertical chirp caused by the SHG, we slightly change the angle of the amplifier crystal in the NOPA from the nominally correct value for achromatic phase matching and utilize the slight divergence of the seed light.

 

Fig. 1 Setup for the generation and characterization of shaped UV-pulses. PC: prism compressor; SHG (DFG): second harmonic (difference frequency) generation; λ/2: half-wave plate; M1 to M3: spherical focusing mirrors; L1 and L2: lenses; IBW: intermediate beam waist.

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The UV polarization is rotated by an achromatic half-wave plate. Half of the material dispersion of the AOPDF is compensated by an UV-PC. This permits a higher temporal shaping window and a larger bandwidth of the AOPDF because the acoustic wave is less chirped and thus less elongated within the crystal length.

Mirror M2 cannot lead to a perfect collimation of the UV beam propagating toward the UV-PC and the AOPDF due to the inherent divergence of the Gaussian beam. The quasi-collimation can only be adjusted for a nearly parallel beam in some selected region and an intermediate beam waist (IBW in Figs. 1 and 3 ) downstream. To position the location of the IBW behind the AOPDF and to adjust the beam size inside the AOPDF suitably, we use a refractive telescope (L1 and L2) in front of the AOPDF.

 

Fig. 3 Geometric and Gaussian optics relevant for the use of the AOPDF. (a) Spatial chirp and parallel displacement of diffracted subpulses, e.g., for a double pulse. (b) Focusing of three transversally shifted Gaussian beams without proper positioning of the intermediate beam waist (IBW). (c) Measured beam profile of a triple pulse in the Gaussian focus with improper (top) and adjusted (bottom) collimation.

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The AOPDF (Dazzler^TM model T-UV-250-400; Fastlite) [18] is based on a 50 mm long KDP crystal and offers a temporal shaping window of 4 - 3 ps in the spectral range of 250 - 400 nm. The previously reported 75 mm crystal renders a somewhat longer shaping window, yet at the cost of additional linear and higher order dispersion, independent of the pulse duration. The efficiency of the shaper is typically 20% at the 1 kHz repetition rate of the system. The shaped diffracted beam is geometrically separated from the direct beam.

For pulse characterization we use either ZAP-SPIDER [22] or type I difference frequency cross correlation and XFROG. Visible auxiliary pulses for the cross correlation are provided by NOPA 2 tuned to 530 nm. The pulse is compressed by a combination of a PC and Brewster-angled chirped mirrors [23]. The Gaussian pulse duration was determined with an autocorrelator [24] to 13.5 fs FWHM. Cross correlation with the shaped UV pulses is done in 25 to 62 µm thick BBO crystals and measured with an integrating photodiode or - for the XFROG - a spectrometer.

The combination of NOPA and SHG allowed us to produce tunable UV pulses over a wide range in the UV. Modulated and unmodulated broadband output spectra of the AOPDF are shown in the Fig. 2 . Fourier limits down to 14 fs were obtained, representative values are indicated at the top of Fig. 2. The minimal pulse length at short wavelength is limited mainly by the phase matching bandwidth of the BBO. For the longest wavelength the spectrum is structured due to the proximity to the Ti:Sa fundamental. Amplitude shaping can be used, e.g., to produce clean Gaussian pulse shapes (spectrum at 380 nm) or selective excitation of different electronic molecular absorption bands or vibrational modes (260 nm or 350 nm). The diffracted UV pulses have an energy of typically 10 - 50 nJ depending on the spectral shaping.

 

Fig. 2 Spectra of shaped frequency-doubled NOPA pulses tunable between 250 and 390 nm and their Fourier limit. Top: unmodulated; bottom: modulated by the AOPDF.

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3. Focusing geometry alignment: Gaussian vs. geometric optics

A broad spectrum and a flat spectral phase are indispensable prerequisites for a Fourier-limited ultrashort pulse. Equally important is the fact that all spectral components spatially overlap, generally in the focus of a lens or mirror used to concentrate the pulse in the interaction region of the spectroscopic experiment. The AOPDF displaces parts of the pulse diffracted at different positions along the KDP crystal differently. Consequently a properly designed beam focusing geometry is needed that is described in the following.

The acousto-optical interaction rotates the polarization from the extraordinary to the ordinary axis. At the same time, it deflects the wave-vector and the Poynting vector of the light, yet not in the same manner, which is due to the crystal walk-off. The angle of the Poynting vector determines the beam path inside the acousto-optical crystal and therefore possible lateral spatial effects: The subpulses of a pulse sequence are diffracted at different positions and therefore are emitted from the AOPDF with a parallel shift of up to 960 µm [see Fig. 3(a) for a double pulse]. The angle between the diffracted and the directly transmitted beam after the AOPDF is, however, purely determined by the wave-vectors. For simplicity, the refraction of the beams at the crystal/air interface is ignored in Fig. 3(a). Not only well separated double pulses but also the components of a compact pulse are affected by this effect. In addition, the AOPDF is typically used to compensate its intrinsic material dispersion by a strongly negatively chirped acoustic signal. This means that different spectral components are scattered at different locations and a spatial chirp results even for an optimally compressed pulse. Interestingly this issue is not addressed in the dominant application of AOPDFs, the phase correction for shortest amplified light pulses [2].

It has been argued that an analogous complication is also encountered in LCD based 4-f shapers [25]. The optical layout described below might also be helpful in these setups. In principal, the parallel shift can be compensated by a double pass geometry, however, at the cost of a dramatically lowered overall efficiency. We therefore choose an alternative approach depicted in Fig. 3(b).

The transversally displaced components propagate in parallel after exiting the AOPDF. The are focused to the interaction region of the spectroscopic experiment or the pulse characterization (mirror M3 in Fig. 1 or lens in Fig. 3) and intersect in the geometric focus. The highest intensity is reached in the Gaussian focus of each subbeam or subpulse. The challenge is to overlap the two loci. In our initial setup the three subpulses generated by the AOPDF did indeed not overlap in the Gaussian focal plane as shown in the upper part of Fig. 3(c). By variation of the input signal to the AOPDF we confirmed that indeed each one of the spots corresponds to one of the delayed subpulses. This was also corroborated by cross correlation measurements. When a large size of the visible auxiliary beam was used, the full triple-pulse was found. Only a single sub-pulse was observed, however, when the beam size was adjusted to the one of the individual UV subbeam.

The propagation of a Gaussian beam through a focusing lens can be calculated analytically in the paraxial approximation. We consider a beam with an intermediate beam waist (IBW) $w_0$ at the distance $d_0$ in front of the lens and an incident Rayleigh length $z_0=\pi ·w_0{}^2/\lambda$. The distance $d_1$ of the Gaussian focus after the lens with focal length f is given by Eq. (1) [26].

This formula implies that the position of the Gaussian focus depends not only on the distance of the IBW from the lens, but also on the waist size. For geometric optics $z_0$ is zero and Eq. (1) reduces to the well known lens formula. If the distance $d_0$ can be chosen to be identical to f, $d_1$ becomes identical to f and the Gaussian focus will coincide with the intersection of the parallel rays, i.e. the geometrical focus.

We chose a position of the focusing mirror at roughly its focal length behind the IBW and fine tuned the collimation telescope (see Fig. 1) to set $d_0=f$. To optimize the alignment, a beam camera is placed into the geometric focus. This location is determined by the position where pulses with different delay generated by the AOPDF overlap. Subsequently, the Gaussian focus is positioned in the same plane by moving one of the lenses in the telescope. The perfect overlap shown in the lower part of Fig. 3(c) results. Finally, the lack of any remaining spatial chirp is confirmed by the use of the AOPDF as a tunable narrow spectral filter. This means that there is no more spatio-spectral coupling. Together with the demonstrated temporal compression very close to the Fourier limit (see Sec. 4), we can conclude that there is no more relevant spatio-temporal coupling.

We note that it has been suggested to place the focusing lens after a 4-f shaper one focal length after the shaper's last grating [27], in close analogy to our situation. To avoid the reflection losses and the chirp introduced by the telescope, in principle the recollimation mirror after the SHG could be used to adjust the focal position. Unfortunately, the given beam size and the length of the UV compressor make this impractical.

4. Sub-20 fs tunable UV pulses and arbitrary spectral and temporal shapes

The generation of arbitrarily shaped UV pulses requires Fourier limited input pulses and the application of well known amplitude and phase filters [6,13]. In our setup the input pulses generated by SHG of the NOPA are not Fourier limited and we therefore use the AOPDF both to compress and shape them. For this purpose the alignment considerations detailed in Sec. 3 are applied. Before we demonstrate the extensive shaping capabilities, we first describe the optimal compression of the tunable UV pulses.

Figure 4(a) shows the spectrum of a pulse centered at 260 nm together with the measured cross correlation (CC) curve. No amplitude shaping was used and progressive orders of the phase filter applied by the AOPDF were optimized for the shortest possible CC time. From the Gaussian shape of the spectrum we conclude that the temporal shape is also Gaussian. With the measured FWHM of the CC we can use a straight forward deconvolution procedure [28] utilizing the pulse length of the visible auxiliary pulse to determine the actual length of the UV pulse of 19.5 fs. This is within 10% of the Fourier limit despite the very short wavelength. Even for such a short pulse the pulse lengthening in the CC crystal by the group velocity dispersion can be neglected and only the group velocity mismatch between UV and visible pulse and the timing jitter of 1.3 fs added by the AOPDF electronics have to be considered.

 

Fig. 4 (a) Cross correlation and spectrum of a pulse at 260 nm compressed to 19.5 fs FWHM. (b) ZAP-SPIDER measurement of a 16.8 fs pulse at 319 nm. (c) Cross correlations and spectra of double pulses at 260 nm with 100 fs (blue) and 150 fs (black) interpulse delay. The subpulses of the latter are in-phase (black spectrum), and opposite in phase (red spectrum).

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Pulses at 320 nm could readily be compressed to 16.8 fs as measured by ZAP-SPIDER [22]. The identical value was found by the CC measurement and the comparison confirms the validity of our deconvolution procedure. Both in the spectral and the temporal domain the phase vanishes nearly perfectly [see Fig. 4(b)].

The optimal compression at a selected wavelength renders the necessary phase filter to compensate all unbalanced dispersion encountered by the UV pulses. This filter is applied as an acoustic pulse with the appropriate fine structure and synchronization to the AOPDF. A straight forward addition of a filter function renders any desired pulse shape. This is demonstrated in Fig. 4(c) for satellite free double pulses at 260 nm. In this case the above mentioned acoustic pulse is applied twice with the acoustic delay corresponding to the optical delay of 100 or 150 fs. For the double pulses separated by 100 fs (shown in blue) the resulting spectrum is modulated with a 10 THz spacing. The pulse spacing of 150 fs decreases the spectral period (see lower part of Fig. 4(c). The relative phase of the two subpulses with respect to the carrier wave determines the position of the fringes: for in-phase pulses there is a maximum at the center of the spectrum (black curve) while for pulses with opposite phase two equal height maxima are found symmetrically displaced (red curve).

Multiple subpulses at 319 nm, with an individual length of 21 fs and without additional satellites outside the displayed window are shown in Fig. 5(a) . Out of the 7 pulses individual ones can be left out, shifted and broadened (by chirp) at will. In Fig. 5(b) we show pulses at 260 nm with a distinct flat top temporal profile and a staircase one. These pulses are chirped to utilize the energy contained in the broad spectrum of the input pulses.

 

Fig. 5 Cross correlation of structured pulses at 319 nm (a) and 260 nm (b, c). (a) Pulse trains of 21 fs pulses subsequently manipulated. (b) 1 ps square pulse (violet), stairs with 300 fs broad equal amplitude steps (blue), 500 fs square pulse (black). (c) Value of the speed of light encoded on a pulse train via the subpulse intensity.

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It should be noted that not only the subpulse spacing but also the energy of all the subpulses can be precisely controlled. For equally intense subpulses the acoustic power has to be properly limited to avoid nonlinear amplitude filtering. The high degree of amplitude control is elaborated in Fig. 5(c) where the SI value of the speed of light is encoded to 9 digits with about 4 bit vertical precision. For this equally spaced pulse sequence the energy contained in each subpulse was adjusted with a single iteration.

So far we have shown pulse sequences with identical spectral content for all subpulses. For coherent control experiments shaped pulses are needed with differing spectra of the subpulses. This can be readily achieved with our setup. Figure 6(a) shows a pair of 58 fs pulses generated from a common input pulse (black spectrum on the right). The XFROG measurement agrees very well with the CC trace [Fig. 6(b)] and the individual spectra of the subpulses. To decrease the spectral smearing in the XFROG, the probe pulse was spectrally narrowed.

 

Fig. 6 Cross correlation of double pulses with differing wavelength. (a) XFROG (left) of pulses with disjunct spectra (right) and input spectrum (black). (b) Corresponding cross correlation and pulse durations. (c) Cross correlation (bottom) and spectra (top) of subpulses with 12 nm bandwidth; colored: individual spectra; black: double-pulse spectrum.

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For subpulses with overlapping spectra [see Fig. 6(c)] the joint spectrum is modulated in the center according to the temporal separation of the sub-50 fs pulses. The phase of the fringes can be adjusted by the relative phase of the two pulses.

5. Conclusions and perspectives

In this work we have demonstrated that the combination of a broadband NOPA with SHG in a thin BBO crystal and direct pulse shaping in a commercially available AOPDF allow the generation of fully tunable UV pulses with a duration below 20 fs or an arbitrary temporal shape. A further shortening of the pulses could be reached with achromatic phase matching [1]. Since the UV Dazzler^TM is specified for an instantaneous bandwidth of 15% of the optical carrier frequency, we can expect pulses or pulse structures as short as 6 fs. This is well in the regime of vibrational time scales needed for the most demanding coherent control schemes [3,4].

Increased output pulse energy could be achieved by sum frequency mixing of the NOPA pulses with a sizable fraction of the pump pulses. This would come at the cost of reduced tuning at short wavelengths. Alternatively a two-stage NOPA should provide higher output, but at present it is quite challenging to operate it with a clean enough spatial mode.

The crucial issue that was solved in this work was the proper combination of geometric and Gaussian optics. As with any cutting-edge ultrafast setup, the desired ultrafast pulses are only assured at one position along the beam propagation. This is not only necessary and ensured with respect to the spectral components but also in the spatial domain. In the described setup this position is presently at the focus of the cross correlation or the ZAP-SPIDER. The envisioned spectroscopic investigations will be performed in this spot.

The direct shaping in the AOPDF delivers fully controlled UV pulses with unprecedented shortness and full tunability. The operational principle of the AOPDF intrinsically avoids the generation of replica pulses encountered in pixelated devices like LCDs in a 4-f shaper [29]. This will be of great advantage for 2D UV spectroscopy that now can be implemented readily with the phase locked double pulses [5]. The presently limited update rate of the AOPDF is only due to the technical implementation but can easily be upgraded to the kHz repetition rate of the laser system. A 100% duty cycle will then be available for the most demanding experiments.