Transfer of spectral phase from near infrared ultrashort pulses to deep ultraviolet (UV) sub-30-fs pulses through four-wave mixing process is demonstrated. Micro joule UV pulses at 237 nm were generated by nonlinear mixing of second harmonic pulses of Ti:sapphire laser output and near infrared pulses from a noncollinear optical parametric amplifier. Chirp of the near infrared pulse was transfered to the UV pulse with the opposite sign. A positively chirped near infrared pulse was used for generating a negatively chirped UV pulse, which was compressed down to 25 fs by a magnesium fluoride window.
©2010 Optical Society of America
Ultrashort laser pulses are among the most effective tools for fundamental studies in physics and chemistry. Ultraviolet (UV, <300 nm) pulses are widely employed in chemical dynamics study. For example, in time-resolved photoelectron spectroscopy, such pulses are used to pump a valence electron up to unoccupied orbitals that induces chemical reaction and also to eject an electron during the course of the reaction.
For many studies, shaped pulses are preferred to their transform limited analogues . For instance, properly tailored pulses can control a chemical reaction to lead to specific products . However, shaping, or chirp management, of very short pulses (<30 fs) in the UV region is one of the biggest issues, since convenient pulse shaping devices such as spatial light modulators  or acousto-optic modulators  are only available in visible or near infrared (NIR) regions. Recently, an acousto-optic modulator for UV region, down to 260 nm has been developed and pulse shaping in the wavelength range has been demonstrated experimentally [5–7]. However, it is almost impossible to extend to the wavelength region shorter than 250 nm since these devices are based on dielectric material. Ultrashort UV pulses would easily form color centers even in fluoride crystals (ex. MgF2), which are transparent down to ~110 nm.
Indirect pulse shaping would be a solution for pulse shaping in the UV region. Spectral phase transfer through sum frequency generation (SFG) in solid crystals has been demonstrated by several groups [8–10]. However, the method is still not suitable for ultrashort pulse (<30 fs) generation in the wavelength region shorter than 250 nm since dispersion of solid crystals in this wavelength range is so large that broadband phase matching is impossible even using achromatic SFG with angularly dispersed geometry [9, 11].
Four-wave mixing in gases is a simple and efficient way to generate ultrashort pulses in the wavelength region shorter than 250 nm. A pioneering work of UV pulse generation through four-wave mixing of fundamental and second harmonic (SH) of Ti:sapphire laser output was performed with a hollow core fiber in 1999 . Using a NIR optical parametric amplifier (OPA), it was possible to tune the wavelength of UV pulses  down to 215 nm. However, no pulse shaping of UV pulses shorter than 250 nm has been demonstrated so far.
Recently, we have developed four-wave mixing through filamentation in gases [14, 15]. The output UV pulse energy is much higher than that from the hollow core fiber method and moreover, the alignment is considerebly simpler since fibers are not necessary. These features make the filamentation method more convenient for practical applications. Based on the filamentation scheme, we have generated UV pulses as short as 12-fs and applied them to time-resolved photoelectron spectroscopy [16, 17].
In this paper, we demonstrate spectral phase transfer to ultrashort UV pulses by four-wave mixing through filamentation. By four-wave mixing of SH of Ti:sapphire laser output and NIR OPA output, ultrashort UV pulses at 237 nm were generated with micro-joule pulse energy. Linear chirp and third order dispersion (TOD) of NIR OPA output were transferred to UV pulses as expected. Employing this indirect chirp control, we generated nearly transform limited 25-fs pulses at 237 nm without complex compressors. In principle, this strategy can be applied to the chirp control of vacuum ultraviolet (VUV) pulses.
2. Spectral phase transfer through four-wave mixing
In this section, we discuss about spectral phase transfer through four-wave mixing with a simple theory. Here, we consider four-wave mixing process, ω SHG + ω SHG − ω NIR → ω fwm, where ω SHG, ω NIR, ω fwm are angular frequencies of SH of Ti:sapphire laser, output from NIR OPA, and generated UV pulses through four-wave mixing, respectively. Assuming instantaneous response of the nonlinear medium and perfect phase matching condition in the whole wavelength region, the generated complex electric field E fwm(t) is proportional to the product of the input fields, E 2 SHG(t)E*NIR(t), where the complex electric fields of SH and NIR are E SHG(t) and E NIR(t), respectively. The Fourier transform of the field is written as follows,
where ω′ + ω″ = Ω′ and E FHG(t) = E 2 SHG(t). Ẽ X(ω) denotes Fourier transform of E X(t) for each subscript. This equation is essentially the same as the idler wave of OPA, or difference frequency generation (DFG), when we assume that E FHG(t) and E NIR(t) are pump and signal fields, respectively. Actually, indirect pulse shaping through OPA or DFG has been used for shaping mid-infrared pulses [18, 19]. The significant difference between the indirect shaping schemes through SFG and DFG is the sign of transfered chirp. The chirp direction of the generated pulse becomes opposite to the signal pulse with the OPA scheme. This is interesting feature in our four-wave mixing scheme since UV pulses usually experience positive chirp when they propagate in air or pass through glass windows. Such positive chirp for the UV pulses can be precompensated by adding certain positive chirp to the NIR pulses before the four-wave mixing, which is much easier than post-compensating the chirp of the generated UV pulses. One typical demand of such experiment is that the generated UV pulses which pass through the rear window of the four-wave mixing gas cell is compressed without any complex compressors, for example, a grating compressor.
Another important point is that only even orders of spectral phase are transfered to the DFG signal with opposite sign whereas odd orders of spectral phase are transfered with the same sign. Since we would like to present a simple discussion about how the spectral phase of the NIR pulse is transfered to the UV pulses, here we assume monochromatic pump wave (a much longer pump pulse than the signal pulse), Ẽ FHG(ω) = Ẽ FHG δ(ω − 2ω SHG). Then, eq. (2) is simplified as follows,
Here we expand the spectral phase of NIR pulse ϕ NIR(ω) by Tayor series,
Then, the phase of the four-wave mixing signal can be written as
where ω fwm = 2ω SHG − ω IR. Comparing with eq. (4), it is clear that odd-order phases are transfered as it is to the UV pulses, but the even-order phases are transfered with opposite sign.
In reality, the SH spectrum has a finite bandwidth. As a result, the transfered spectral phase is basically smoothed by convolution with the SH spectrum. The effect was also discussed in Ref.  for idler wave of an OPA process.
3. System Overview
To implement UV-pulse chirp control, we need a rather long pump pulse and a broadband NIR OPA. In addition, a high energy OPA in NIR region (>0.1 mJ) is required for an efficient frequency-conversion with filamentation scheme. A noncollinear OPA (NOPA) with ~100-fs pump pulse would be ideal for our purpose. The schematic overview of the whole system is shown in Fig. 1. ~80-fs fundamental pulses were generated from a cryogenically cooled Ti:sapphire regenerative amplifier system (2.6 mJ, 792 nm, 1 kHz). The output beam was split into two replicas with a ratio of 7:3. The high-energy portion was delivered into a two-stage NOPA system generating broadband NIR pulses, and the low-energy portion was frequency-doubled in a β-BBO crystal. Both NIR and SH pulses were then mixed in a gas-cell to generate UV pulses through four-wave mixing.
3.1. Noncollinear optical parametric amplifier in near-infrared region
For broadband pulse generation NOPA is a well-established means, with which visible pulses can be generated with a duration down to 4-fs . G. Cerullo and coworkers extended the concept of broadband phase matching in NOPA geometry to NIR region . In an 800 nm pumped NOPA using periodically poled stoichiometric LiTaO3 (PPSLT), they amplified a spectrum spanning the 1.1–1.7 µm range, and then compressed the broadband pulse down to 8.5-fs with a few µJ pulse energy . Nonlinear optical crystals, such as LiNbO3 and especially PPSLT satisfy the broadband phase matching condition for the 800 nm pump NOPA. However, in our system we cannot use PPSLT because the aperture is limited by poling procedure and hence this crystal cannot afford a high-energy output. So we at first employed a LiNbO3 crystal with Type I phase matching. Unfortunately, the expected gain was not observed in our experiment. The reason is not clear, yet parasitic four-wave mixing process would be one of the possible reasons . Then, we chose BBO crystals with Type II phase matching. The gain bandwidth was not as broad as PPSLT, nevertheless it was still possible to afford ~30-fs pulses with a certain noncollinear angle.
The detailed system is shown in Fig. 2. Basically, the system consists of a two-stage NOPA. The pump energies for the 1st and 2nd stages are 11 µJ and 1.5 mJ, respectively. The white light seed was produced by focusing a small potion of the pump pulse (<1 µJ) into a sapphire plate (t = 3 mm) by a parabolic mirror (f = 100 mm). The collimated white light was precompressed by a SF10 prism pair compressor, and visible and fundamental parts of the white light were blocked in the compressor. In the first amplification stage, pump beam was gently focused by a concave mirror (r = 3000 mm) and the seed beam was down-collimated to ~1 mm diameter. The propagation direction of the pump beam forms an angle of 4.2°(internal 2.1°) with that of the seed beam in a BBO crystal (θ = 29°, t = 3 mm). Under this condition, the phase matching is best satisfied and the gain attained a maximum (104-fold, ~300 nJ).
After passing through the 1st-stage NOPA, the signal beam was slightly divergent. An f = 1 m concave mirror collimated the preamplified beam to a suitable size for the 2nd-stage high-energy NOPA. The remaining 1.5 mJ fundamental beam was initially upcollimated to ~15 mm diameter because large pump beam size is required for the 2nd-stage NOPA to avoid self-focusing effect during the propagation. To prevent damage on the crystal surface, the beam size on the BBO crystal should be >3 mm. Such large pump beam size would introduce a significant spatial chirp in the amplified seed pulses because the pump pulse fronts do not match the signal pulse fronts in NOPA geometry . As a result, the amplifying efficiency will be low and the seed pulse duration will be broad. To overcome the pulse-front mismatching, we tilted the pump pulse-front with a Brewster fused silica prism. A telescope further magnified the tilting angle to make it coincide with the optimal noncollinear angle. By such pump pulse-front tilting, the amplifying efficiency was dramatically improved.We obtained ~0.3 mJ (with 2-mm BBO) NIR pulses finally, meaning a 20% efficiency. These are comparable output energy and efficiency with a high energy SH (400 nm) pump visible NOPA . Amplified spontaneous parametric fluorescence generated without the white light seed was negligible comparing with the amplified signal with the seed.
The output pulse was compressed by a SF10 prism (apex angle 60°) pair compressor with a prism separation of 750 mm (shown in Fig. 3). The first prism was mounted on a translationstage, which enabled us to adjust the pulse chirp.With the maximum bandwidth, it was possible to achieve 25-fs pulses, however, we observed a significant mode distortion under this condition. So we operated the NOPA with slightly narrower bandwidth, which can produce 30-fs pulses with optimum adjustment of the prism compressor.
3.2. Four-wave mixing in gases
The schematic of the four-wave mixing system is shown in Fig. 3. In the SH generation branch, the other fundamental beam, 0.8 mJ, was frequency-doubled in a thin BBO crystal (θ = 29°, Type I, t = 0.5 mm). Two pieces of fused silica glass (t = 8 mm) were put into the fundamental beam path with Brewster-angle to compensate the pulse chirp. The BBO crystal was placed as close as possible to the end so as to minimize the SH propagation in air and to avoid chirping of the SH. The pulse width was ~80-fs, which was measured by a home-built dispersion-free transient-grating frequency-resolved optical gating (TG-FROG) system .
The SH and the NIR pulses were gently focused by concave mirrors (f = 2 m) independently, overlapped through a dichroic mirror, and delivered into a stainless-steel gas cell (L =~1.5 m). The front window was a CaF2 plate (t = 1 mm) with Brewster angle whereas the rear window was a MgF2 plate (t = 0.57 mm, c-cut) with normal incidence. In front of the gas-cell, pulse energies of SH and NIR were measured to be ~350 and ~200 µJ, respectively. The two concave mirrors were used so that the focal regions of SH and NIR beams fully overlapped. We examined neon and argon, and found that four-wave mixing efficiency is the highest in neon at ~80 kPa. Probably, dispersion of argon is too high for our experimental condition. Orange colored plasma column from ionized neon with ~8 cm length was seen when the time and spatial overlap between SH and NIR pulses was optimized. In this system, the thin rear window compensates the dispersion of the generated UV pulses that is initially negatively chirped by the spectral phase transfer through the four-wave mixing. The gas cell was directly connected to a vacuum chamber. The output beam was filtered by a few reflections of dichroic mirrors, and introduced into another TG-FROG system in vacuum.
The output energy of UV pulses through ω SHG + ω SHG − ω NIR → ω fwm was 1.5 µJ at maximum. The efficiency was much less than the previous system, namely, mixing 30-fs SH with 25-fs fundamental [14,15]. This low efficiency was not due to a longer pulse (~80 fs for the SH pulse) than before since we have achieved similar order of efficiency as the previous system by mixing SH and fundamental with the current light source (~13 µJ@265 nm). The reason for the low efficiency would be mode quality of NOPA output and/or phase matching condition of the nonlinear mixing. Coherence length of the phase matching (1/Δk) is half of the previous four-wave mixing process. A typical spectrum of the UV pulse is shown in Fig. 4(a). The bandwidth supports ~25-fs pulses at the transform limit. As is expected from the previous system, signal from a cascaded process, ω fwm + ω SHG − ω NIR → ω cas, was also observed, where ω cas is angular frequency of the generated field by the cascaded process. In contrast to the previous system, the wavelength range of the signal of the cascaded signal is VUV region (~168 nm). A typical spectrum of the VUV pulse is shown in Fig. 4(b). The transform-limited pulse of the VUV spectrum is shorter than 20-fs. It was not possible to measure the pulse energy by our thermal sensor (3A-P, Ophir), whose minimum detectable level was ~100 µW (100 nJ@1kHz). Interestingly, we did not observe obvious sum frequency mixing signal, ω SHG + ω SHG + ω NIR → ω sfg, which should appear at around 170 nm. It is rather surprising since the product of the three fields used for the sum frequency mixing (E SHG(t)E SHG(t)E NIR(t)) is much more than that of the cascaded process (E fwm(t)E SHG(t)E*NIR(t)). The reason could be that the coherence length of the sum frequency process is about four times shorter than that of the cascaded process, which is similar situation as our previous system .
4. Experimental Results
The generated UV pulses were sent to the TG-FROG device and therein characterized. The pressure of the vacuum chamber was kept ~1 kPa. We controlled the chirp of the NIR pulse by changing the insertion of the first prism in the compressor. At each prism position, we compensated the delay between the SH pulse and the NIR pulse to have the same UV spectrum. We also characterized NIR-pulse chirps through SH-FROG with a 50-µm thick BBO crystal. Although the SH-FROG has an ambiguity in the direction of time, we may readily guess it since SF10 has positive dispersion in the wavelength range. The spectral phases of the UV pulses and the NIR pulses are shown in Fig. 5. At the first glance, the spectrum shapes are mirror symmetric with each other, which fact reflects eq. (3). Actually, the UV spectrum is slightly broader than the NIR spectrum, which is basically due to convolution effect with the spectral width of the SH pulse. The convexities (up or down) of the spectral phase at the main part of the spectrum are opposite with each other suggesting chirp directions of the pulses are opposite with each other. Concerning the TOD, high frequency components present larger concavity compared with low frequency components in both cases. Therefore, the sign of the TOD was kept the same.
Figure 6 shows group delay dispersion (GDD) of NIR and UV pulses calculated from the FROG measurements. GDDs were calculated by polynomial fitting of retrieved spectral phases from FROG. Negative correlation between NIR and UV pulses is very clear. The slope steepness of the GDD of the UV pulses is ~30% smaller than that of the NIR pulses, which can be also explained by the convolution effect with the SH pulses. Quantitative analysis of the TOD was not successful because fitting results were very sensitive to the fitting spectral region. Probably the values of the TODs were not large enough to be accurately measured with the bandwidth. The output energy of the UV pulses does not change within this prism insertion range.
By manipulating the chirp of NIR, we were able to control the chirp of UV pulses and succeeded in compressing the UV pulse without complex compressor, like a grating compressor. By using slightly positively chirped NIR, the UV pulses in the gas cell were negatively chirped and then, were compressed after passing through the MgF2 window. According to the fitting result of the prism insertion dependence of the GDDs in Fig. 6, when the GDD of the UV pulse is zero, the GDD of the NIR pulse is 66.5 fs2, which is good agreement with the GDD value of the 0.57 mm thick MgF2 window, 65.6 fs2. A typical FROG trace of the most compressed UV pulse is shown in Fig. 7. The pulse width was 25-fs that is almost transform limited.
We have demonstrated spectral phase transfer through four-wave mixing process. This scheme is very similar to the spectral phase transfer to idler wave through OPA process. We have succeeded in generating nearly transform limited 25 fs pulses at 237 nm without complex compressors. Very recently, the same idea was applied to generate sub-10-fs, 300 nJ pulses at 270 nm by four-wave mixing in hollow core fiber . However, it is important to demonstrate the technique to the wavelength range shorter than 250 nm where acousto-optic modulators cannot be applied for pulse shaping.
One of the most interesting issues of this scheme is characterization of the VUV pulses generated through the cascaded process. In principle, similar phase transfer, that is, even order phase of the NIR pulse is transfered with opposite sign, must have occurred for the VUV pulses. In the current experimental condition, it was not possible to demonstrate the phase transfer due to the difficulty of pulse characterization of the VUV pulses. In the wavelength range, it is not clear whether the TG-FROG system can be applied. One has to prepare a very thin nonlinear medium for transient grating to avoid pulse broadening due to the medium or phase mismatch. In addition, the alignment procedure can be extremely difficult. An alternative characterization method is FROG with non-resonant multiphoton ionization . Although the method is free from pulse broadening due to the nonlinear medium and phase mismatch, it would be very time consuming measurement since one has to measure photoelectron spectrum from a non-resonant process at each delay time. The difficulty can be understood with the fact that there is no publication concerning characterization of ultrashort pulses at ~160 nm with a kind of FROG schemes since 1999 . There are still a lot of room for investigation of pulse characterization schemes in the wavelength range.
The unique feature of the phase transfer through four-wave mixing can be very helpful for experiments in vacuum condition. In a typical spectroscopy system with ultrafast UV or VUV pulses, inconvenient differential pumping or a extremely thin window is necessary to separate a high pressure gas target for high harmonic generation from the sample chamber . In contrast, with our light source, it is possible to put some glass windows with reasonable thickness for pulse compression and hence, dramatically reduce difficulty of vacuum systems. Even with a very chirped or intricately shaped signal pulse (NIR pulse in the current system), efficiency of the frequency conversion does not drop too much, at least much better than direct harmonic generation with a shaped pulse. In addition, the wavelength of the UV and VUV pulses is basically tunable by tuning the wavelength of the NIR OPA, as was demonstrated in similar systems before [13, 30].
After some improvement of the efficiency for generation of the VUV pulses and precise VUV pulse characterization, the system must become one of the most ideal light sources for time-domain investigations of the fundamental dynamics of atoms and molecules in physics, chemistry, biology, and material sciences.
P. Z. acknowledges a fellowship from the Foreign Postdoctoral Researchers (FPR) program of RIKEN.
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