Four-Fold, Cross-Phase Modulation Driven UV Pulse Compression in a Thin Bulk Medium

Abstract

Generation of high energy few-fs pulses in the ultraviolet (UV) still represents challenges due to compression and phase control difficulties in this spectral range. Presented here is a pulse compression approach utilizing cross-phase modulation within a thin solid-state medium induced by a strong, spatially and temporally controllable near-infrared (NIR) pulse acting on a weaker, 400 nm UV pulse. Through this method, four-fold compression is attained within a single fused silica plate, resulting in a 13 fs UV pulse with preserved beam quality. With some further technical adjustments, this method’s applicability could be extended to deep or even vacuum UV, where direct compression is difficult.

1. Introduction

The advancement of ultrashort-pulse UV light sources holds significance in exploring the intricacies of atoms, molecules, solids, and even certain biological processes at the femtosecond scale [1,2]. Continuously shortening pulse durations not only enhances temporal precision, but also gives access to GW level peak power already at pulse energies in the tens of µJ range. Expanding the ultrashort light source availability into this less explored parameter space (due to technical challenges mainly related to light sources) opens new pathways to atomic and molecular transitions. It has also been shown that driving high harmonic generation with a shorter wavelength pulse can boost the typically very low efficiency of this process by two orders of magnitude [3,4]. Another application, which requires an intense few-cycle UV pulse and is also the main motivation behind this work, is a recently proposed method of significant shortening of pulse duration of externally seeded free electron lasers (FEL) overcoming the electron slippage limit [5].

While few-cycle pulse generation and compression techniques are readily available in near infrared, their application to UV pulses is challenging. The usual way to prepare a UV ultrashort pulse is frequency converting a few-cycle NIR pulses, previously compressed exploiting a self-phase modulation (SPM) in a noble gas filled hollow-core fiber or multi-pass cells, into the UV in the nonlinear medium through harmonic generation (in a single or multiple steps). Unfortunately, in order to preserve the bandwidth, nonlinear crystals have to be very thin or noble gases have to be used instead [6,7], in both cases leading to poor conversion efficiencies. While conversion efficiency can be increased in the case of four-wave mixing in noble gases, available pulse energies are still limited to a few µJs [8]. An alternative is a direct pulse compression in UV, either in hollow-core fiber [9,10], often with low coupling efficiency, or in (multiple) thin glass plate(s) [11,12], where the broadening factor is limited with the onset of spatial distortions or eventually even beam break-up [13]. Wavelength-tunable, µJ-level, few-fs long DUV pulses can also be generated through resonant dispersive wave emission [14]. However, this involves a more complex experimental setup including a two-stage nonlinear interaction inside a noble-gas-filled hollow-core fiber.

It is well known that cross-phase modulation (XPM)-based spectral broadening of a weak probe pulse by a strong co-propagating pump pulse in a non-linear medium can be used for pulse compression [15]. A non-linear temporal phase

$${\mathsf{\Phi }}_{NL}(t)=\frac{2\gamma }{L}{\int }_0^L{I}_{pump}\left(0,t+{\eta }_{\mathrm{G}\mathrm{V}\mathrm{M}}z-{\tau }_{\mathrm{d}\mathrm{e}\mathrm{l}\mathrm{a}\mathrm{y}}\right)dz$$

is imposed on a probe pulse generating new spectral components by the second, pump pulse, where γ is a nonlinearity coefficient, I_pump is the pump pulse intensity, η_GVM is the difference of inverse group velocities of pump and probe pulse, τ_delay is the relative delay at the input of nonlinear medium of a length L. As is seen, the induced phase can be controlled by the parameters of the pump pulse both in space and in time. A detailed theoretical study on the impact of each of them was done by Agrawal et al. in [15]. Surprisingly, the method has not been largely explored experimentally. XPM-driven pulse compression in noble-gas-filled hollow-core fibers in the UV [16], and very recently also in the DUV [17], enabled generation of few-fs pulses in the sub-1 and 10 µJ range, respectively. The use of a thin solid plate instead of a gas-filled fiber as a nonlinear medium offers the potential of compactness, easier alignment and long-term stability. However, the only demonstration in solid state medium [18] uses XPM as a bandwidth-broadening mechanism in the visible in parallel with four-wave mixing, so the scheme required phase-matching and compressed pulse energy was limited to 1 µJ. Here, we demonstrate the applicability of XPM for a pulse compression in a solid thin plate for more energetic pulses (in the range of tens of µJ). It is important to emphasize that, compared to SPM-based compression schemes, the proposed XPM-based one has the intrinsic advantage of giving access to higher compressed pulse energies due to the added degrees of freedom of the parameters of the interacting pulses, namely energy and diameter ratio, relative delay, pulse shape and different central wavelength. The pump beam energy and spot-size can be (much) larger than the probe and with pump central wavelength being in the infrared, the high peak power levels needed for high nonlinear spectral broadening can be obtained at reduced spatial gradients, and small-scale self-focusing and nonlinear absorption (strong limiting factors in the visible and UV) can be kept low as well. At the same time, across the smaller probe beam, the spectral broadening is more homogeneous. In the present work, we take advantage of the described concept and demonstrate a 4.5-fold compression in a single 150 µm thick fused silica plate resulting in a 13 fs long, 18 µJ pulse (after compression) at a central wavelength of 396 nm.

2. Materials and Methods

The experimental setup is shown in Figure 1. We started with 2.3 mJ, 60 fs long pulses from a titanium sapphire regenerative amplifier running at 50 Hz repetition rate with a beam diameter of 10 mm. The beam was first split in two branches, with 82% being reflected to be used as the pump while the transmitted 18% was for conversion by second-harmonic generation (SHG) into the probe. In the ‘pump’ branch, a variable attenuator (a half-wave plate and a pair of thin-film polarizers) allowed independent control of pump beam intensity. The delay between pump and probe pulse could be adjusted in 1 fs steps. To achieve looser focusing of the pump with the roughly similar distance of focusing elements as in the probe branch, beam size was reduced by an iris right before the focusing lens with a focal length of 1.5 m. The final pulse energy used for results presented here was 470 µJ.

In the ‘probe’ branch, polarization of fundamental could be adjusted by a half-wave plate in order to control the energy of second harmonic (SH) pulse that was generated in a 350 µm thick β-BBO crystal cut at 29.2 degrees. While up to 50 µJ of SH could be generated, we used 40 µJ in the reported experiment to reduce the effect of SPM of the probe pulse. The residual fundamental after SHG was filtered out by reflection from two dichroic mirrors with high reflectivity in 350–450 nm and low in the wavelength range of the fundamental. The SH beam was focused with a 2-lens telescope (f1 = 300 mm, f2 = −250 mm) to increase the focal spot size, while keeping the setup relatively compact. The use of iris in that branch was avoided, because the presence of diffraction rings was found to lead to beam break-up at moderate compression factor in agreement with small scale self-focusing theory [19].

The beams from both branches were overlapped on a dichroic mirror reflecting probe (400 nm) and transmitting pump (800 nm). Part of the beam could be picked up by a wedge and sent to a CCD camera to observe beams in the virtual focus. Beam profiles of the overlapped beams in the focus are shown in Figure 2b. The pump beam was larger, perfectly round with a diameter of 400 µm, while the probe beam was slightly elliptic, with a diameter of 140 and 190 µm in horizontal and vertical directions, respectively. The corresponding confocal parameters were 31 cm for pump and approximately 10 cm for probe beam. The size of the pump therefore does not significantly change along the Rayleigh range of the probe. In the focus of the two beams, a 150 µm thick uncoated fused silica plate was placed at a normal incidence. The thin plate sat in a low vacuum (approx. 10 mbar) to avoid nonlinear effects in air. Vacuum tube was closed by two 0.5 mm thick Brewster windows. After exit from the tube, the probe beam was collimated by a 750 mm focal length aluminum coated spherical mirror and sent through dispersion compensator consisting of two anti-reflective coated fused silica wedges and 12 reflection from chirped mirrors (Ultrafast Innovation’s CM82 with −50 fs2 per reflection). Transmission through the dispersion compensator was around 65% and could decrease slightly due to beam clipping in conditions when probe beam was larger due to the cross-focusing effect of nonlinear interaction. The compressed pulse was characterized by a home-build self-diffraction FROG and imaging spectrometer. The pulse spectrum collected by an integrating sphere was measured independently with another spectrometer. To observe beam changes after the nonlinear interaction, a weak part of a beam, back-reflected from the first surface of the first prism of dispersion compensator was sent to a camera, optionally with another lens inserted to analyze far-field spot.

Both pump and probe pulse were characterized by SD-FROG right before entering the vacuum tube so that all dispersion and SPM effects in the beam path would be present. Temporal and spectral intensities at the input are shown in Figure 2. The pump pulse was 54 fs long and chirp-free, while the probe was slightly positively chirped (due to dispersion of telescope’s lenses) and 69 fs long. Longer probe pulse was chosen intentionally in order to decrease impact of temporal walk-off (estimated to 23 fs) between pump and probe pulse during nonlinear interaction in the thin plate. Some modulation of probe pulse as recognizable from its spectrum was present already at the input of the vacuum tube. This is due to SPM with an equal contribution coming from the waveplate of variable attenuator and the recombining dichroic mirror.

3. Results

While several parameters can be tuned in order to achieve a particular goal, we only explored some of them. Namely, the intensity of pump in the focus was only changed by changing the energy of the pulse, while the diameter of the beam was kept constant. The thin plate’s position was adjusted within the confocal parameter of the probe. While there was no significant impact on temporal properties within this range, there was notable impact on spatial properties due to some cross-focusing effect. Another crucial parameter is the delay between pump and probe. It was found that at the largest spectral broadening (at the zero pre-delay), the pre- and after pulses of the compressed pulse are very strong due to a highly non-linear phase, which cannot be compensated with chirped mirrors. Delay was therefore adjusted with pump preceding probe by 13 fs as a compromise between broadening and good compressibility. The SD-FROG results are shown in Figure 3. Low G-error of G = 0.0089 and good agreement between measured and retrieved spectrum confirm successful pulse reconstruction. This is also evidence of homogeneous broadening across the beam as the two replicas for FROG measurement are taken from different parts of the beam edge. The reconstructed temporal intensity has a 13.1 fs long central peak with a pre- and post-pulse with intensity below 15% of the central one. From the comparison with the Fourier-transform-limited pulse, which has only slightly shorter duration but weaker satellite pulses, we can conclude that the origin of this satellites is the oscillatory spectral phase, which cannot be easily compensated. We observed that at only slightly smaller compression factors with compressed pulse duration of 15.5 fs, the intensity of satellite pulse dropped below 7%.

Homogeneity of spectral broadening across the beam was checked with a home-built imaging spectrometer that had a 3 mm high, 10 µm wide slit at the input. For better visual representation, the spectrums at each height z of the spectral image in Figure 4 are normalized. The average value of overlap integral [20] between spectra at different heights and the integrated spectrum is 0.972 and has only two moderate drops in two middle parts of the beam with not well understood origin. In Figure 4b, spectra at four different selected heights (including the latter two) show a good similarity in terms of bandwidth with some variation of energy distribution among three spectral peaks.

Beam profile of compressed pulse was measured after collimation (see Figure 5a), and its shape depended mostly on the position of the thin plate and the delay between pump and probe. The first one is due to variation of ratio between the pump and probe beam sizes and consequently the amount of nonlinear lens introduced by XPM. The reason for the second one is believed to be additional XPM in the vacuum window. While estimated size of pump beam at the exit window is six to seven times the one in the thin plate, the effective window is almost four times thicker than the thin plate. On the other side, the probe beam is much larger (even larger than the pump), so the XPM effect has a much more pronounced impact on spatial properties then on temporal/spectral ones. This is demonstrated by an intense beam quality degradation at positive pre-delays of pump that result in pulses’ temporal overlap inside the exit window. However, we were able to set the pre-delay such that beam quality of probe remained preserved (or even slightly improved), with the beam in the far-field being only slightly elliptic without noticeable features outside the main central beam (see Figure 5a).

4. Discussion

To conclude, we presented here an approach to achieve relatively high compression factors while preserving beam quality based on χ⁽³⁾ spectral broadening in a single fused silica plate. This is achieved by employing XPM as the main mechanism for spectral broadening, which is both stronger and independently controllable compared to SPM. It is worth noting that performing the presented measurements at 50 Hz repetition rate was imposed by the control system of our facility needed for triggering of lasers and all diagnostics. We expect that all presented results should remain valid also at the standard repetition rate of our regenerative amplifier, i.e., 1 kHz. There remain several straightforward technical improvements in our setup that should increase overall efficiency and compression factors and are under development. This includes improving the pump laser beam quality and optimized pump beam resizing by a telescope eliminating the iris. Thus, higher pump energy would be available giving access to higher compression factors or enabling the use of thinner medium for obtaining the same compression. In a thinner medium, the temporal walk-off between pump and probe pulse is reduced and opens the way to use the scheme in deep UV. The improved pump beam quality should at the same time improve the probe’s focal spot and further increase the homogeneity of spectral broadening across the beam. Another foreseen improvement is introducing a noble gas rather than low vacuum in the tube hosting the thin glass plate, which has been reported in the literature [12] to be beneficial both in reducing damage on the plate and providing additional spectral broadening. With thinner vacuum windows, undesired nonlinear effects should be suppressed and number of reflections per chirped mirror would be reduced eliminating beam clipping and therefore increasing overall compression efficiency.

An important point is that the concept is extendable to other wavelengths that are generated through nonlinear frequency conversion, where residual, non-converted infrared beam can be applied as a pump, e.g., for higher harmonics (third or fourth) and also to wavelength tunable pulses delivered by OPA. The temporal walk-off between pump and probe pulse will be one of the main limiting factors for satellite-free pulse at shorter wavelengths in DUV range using such approach. This would require thinner nonlinear medium or even more complex solution like temporal pre-shaping of the pump pulse [21]. Despite this, we believe that the additional degrees of freedom to control the pulse interaction intrinsic to the XPM hold promise for obtaining interesting results also in that spectral range.