1. Introduction

In the recent decades we have witnessed not only a tremendous progress in laser technology but also more and more applications of laser in various fields ranging from fundamental research to biological, chemical, medical and industrial application. The same is especially true for the field of ultrafast laser pulses being the driving motor in atomic and molecular physics with femtosecond (fs) and attosecond pulses and becoming increasingly common in medical or industrial applications. Kerr lens mode locked Ti:Sapphire lasers [1] are the major source of ultrafast laser pulses. Along with the chirped pulse amplification scheme [2] the high energy regime is accessible. The limitation of the output pulse duration of common amplifiers, which is governed by the bandwidth of the gain medium, can be circumvented by spectral broadening of femtosecond laser pulses in gas-filled hollow-core fibers (HCF) followed by a compression stage [3] enabling pulses consisting of only a few optical cycles.

In this paper we report on a modified approach to the conventional self-phase modulation (SPM) induced broadening in atomic rare gases, namely using a molecular gas as nonlinear medium offering additional vibrational degrees of freedom. Sulfur hexafluoride (SF₆) has been a prominent example for ultrashort pulse generation via molecular phase modulation [4], dual-wavelength pumping [5, 6] and filamentation [7] in recent years. However, for an efficient compression either one or two laser pulses with mJ pulse energy or already ultrashort pulses in the order of 30 fs are necessary for exploiting the beneficial properties of SF₆ as nonlinear medium. These requirements can be met with a more complex laser system limiting a wider use of molecular gases as nonlinear medium. On the other hand many of the recently developed laser systems based on Yb doped thin disks [8] or fibers [9, 10] deliver sub-100 µJ and sub-500 fs laser pulses at very high repetition rates offering also turn-key, hands-off operation paving the way for applications in non-laserlab, medical or industrial environments. However for many applications the pulses from Yb based lasers are too long and must be efficiently compressed. The necessary spectral broadening is achievable either by advanced fiber designs, e.g. gas-filled Kagome type hollow-core photonic crystal fibers [11, 12], or choice of an appropriate gas to fill a HCF. In this paper we will show that we can compress sub-mJ pulses longer than the Raman period in the same manner as in rare gases but at reduced gas pressure or peak intensity using SF₆ as nonlinear medium.

In section 2 we discuss the limitations of using SF₆ as nonlinear medium in ultrafast science. The pulse compression experiments are presented in section 3 before we present a summary and short outlook in section 4.

2. Raman active gases as nonlinear medium in ultrafast science

Spectral broadening in a gas-filled HCF is based on SPM due to the intensity dependent refractive index $n(I)$ of the gas medium:

Here $n_2$ is the nonlinear refractive index, which is (1.4 ± 0.2)∙10⁻¹⁹cm²∙W⁻¹ for argon. As a result of propagation through a gas-filled HCF a bandwidth-limited laser pulse experiences an additional nonlinear phase shift to the temporal phase, which usually leads to spectral broadening and temporally positive chirp. This positive chirp can be compensated by introducing negative group delay dispersion, e.g. by means of a prism compressor or dielectric chirped mirrors. For SF₆ the nonlinear index of refraction is (1.6 ± 0.3)∙10⁻¹⁹ cm²∙W⁻¹ [13], which is comparable to argon, but has a more complex behavior. SF₆ is a symmetric molecule, hence the nonlinearity has no rotational contributions unlike for diatomic molecules. However, stretching vibrations have to be taken into account for SF₆ with particular importance on the A_1g vibrational mode being the strongest Raman active one. The fundamental frequency of 775 cm⁻¹ corresponds to a temporal period of 43 fs. To benefit from SF₆’s Raman activity there are, among others, two prominent possibilities: i) pulses much longer than the vibrational period are focused into SF₆ and the newly generated phase-locked Raman sidebands are subsequently compressed using a prism compressor setup with multiple mirrors as delay lines [14] or a spatial light modulator [15]; ii) pulses shorter than the vibrational period of 43 fs are used for impulsive excitation and then a probe-beam propagates through that dressed molecular medium resulting in a phase controllable spectral broadening. Thereafter, the probe-beam contains sidebands from both Stokes and anti-Stokes scattering. The pump-beam also contains signatures of molecular modulation resulting in a redshift and a pulse-train at the vibrational frequency of the excited mode [16]. Impulsive excitation can be also understood as the total pulse bandwidth of the exciting pulse being larger than the Raman separation ${\Omega }_{Raman}$. In this contribution we investigate the intermediate regime, i.e. the laser pulse duration is longer than the Raman oscillation period but shorter than the dephasing time $T_2$ of the SF₆ molecule. This operation regime is referred as transient or non-stationary scattering [17] and is limited by

3. Experiments

3.1 Spectral broadening at 800 nm wavelength

For the current experiments laser pulses from a commercial laser system (Spectra-Physics Spitfire®) with 0.9 mJ pulse energy and a pulse duration adjustable between 70 fs and 300 fs were focused into a HCF (250 µm inner diameter, 78 cm length) that was situated in a gas cell with adjustable gas pressure between 0 and 2000 mbar. The spectra of the broadened pulses were measured with an Oceanoptics USB4000-VIS-NIR spectrometer (350 nm to 1000 nm wavelength range).

Pressure scans of argon and SF₆ for 850 µJ input pulse energy and 78 fs pulse duration are shown in Fig. 1.In case of argon (Fig. 1(a)) symmetrical spectral broadening is observed. Increasing the pressure leads to increased total spectral bandwidth. However, it has to be mentioned that the full width at half maximum (FWHM) of the spectrum does not increase anymore at a certain pressure level limiting the compressibility of the pulse. Compared to the spectra obtained with argon three observed features cannot be addressed to pure SPM in SF₆ (Fig. 1(b)). First, the FWHM of the spectral width is larger for SF₆ than for argon at the same pressure below 400 mbar. Hence using SF₆ instead of argon for the same amount of spectral broadening either the gas pressure can be reduced by a factor of 2 to 3 or the peak power can be decreased by the same amount. Second, the blueshift of the spectrum is more pronounced for SF₆ than for argon, which will be beneficial for spectroscopic applications drawing on shorter wavelengths. Third, the spectrum contains sidebands at fixed positions that can be attributed to the A_1g vibrational mode. This leads to a smooth broadening of the spectrum resulting in a larger full width at tenth part maximum (FWTM) value than for argon. All these three features can be well explained by not only considering SPM but also ionization and SRS, as will be discussed below. However, for an application attention has to be drawn to HCF throughput that can be decreased e.g. by losses of higher order fiber modes or self-focusing at the HCF entrance. As indicated by the intensity drop in the logarithmic color scale, the spectral broadening above 600 mbar is achieved at the cost of a several percent reduced HCF transmission. For estimating the achievable pulse duration it is convenient to calculate the Fourier transform of the spectrum under assumption of a flat spectral phase. For argon (FWTM bandwidth 2800 cm⁻¹) and SF₆ (FWTM bandwidth 5000 cm⁻¹) this results in 9 fs and 4 fs pulse duration (FWHM) respectively (outlines in Fig. 1).

 

Fig. 1 Comparison of spectral broadening in a argon (a) and SF₆ (b) filled HCF for different gas pressures. Parameters of the input laser pulses and the HCF remain unchanged (see text). A normalization was done for the output pulse energy of the HCF and the resulting spectral intensity is shown in a logarithmic color scale. For SF₆ the generation of Raman sidebands is observed by vertical lines with higher amplitude at fixed positions and corresponds to the A_1g vibrational mode as indicated by the dotted lines. Above the pressure scans outlines at 1000 mbar for both gases are depicted.

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The above mentioned laser parameters result in a peak power of 10 GW. The intensity at the entrance of the HCF is in the order of 10¹³ W∙cm⁻² being sufficient for multiphoton ionization for both gases having their first ionization potential at 15.8 eV (Ar⁺) and 15.3 eV (SF₅⁺), respectively. The probability for double ionization is negligible for argon (27.6 eV). However, for SF₆ further ionization levels are located at much lower energies namely at 16.9 eV and 18.3 eV making an additional ionization much more likely [22]. As a result the ionization rate of SF₆ will be much higher as indicated by an enhanced additional blueshift [23] compared to argon. At a certain pressure the Raman sidebands corresponding to the A_1g vibrational mode become dominant in the spectrum and the anti-Stokes lines are more prominent than the Stokes lines. This can be explained by SRS in the HCF. Due to SPM and the plasma blueshift the modified laser pulse contains now frequency components matching to the Raman levels, whereas the unperturbed input pulses covering the spectral range from 770 nm to 820 nm does not overlap with them. Furthermore, the higher Raman differential cross section for higher frequencies has to be considered.

The observed features have been observed in a wide range of laser pulse parameters: the input pulse energy has been varied from 100 µJ to 850 µJ and the pulse duration from 75 fs to 300 fs by chirping the pulses. In the whole parameter range we obtained similar spectra after increasing the gas pressure accordingly. In Fig. 2 an energy scan and a variation of pulse duration are shown for a fixed gas pressure of 1000 mbar.

 

Fig. 2 Spectral broadening in a SF₆-filled HCF for different laser input pulse energies (a) and different pulse durations (b) for a fixed gas pressure of 1000 mbar. The input energy was varied using neutral density filters, while the pulse duration was constant at 78 fs. In (b) the pulse duration was varied by positively chirping the spectrally unchanged lasers pulse, which had 850 µJ pulse energy.

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Comparing the achieved spectral broadening in Fig. 1(b), 2(a) and 2(b), it is obvious that a smooth spectral broadening, slight blueshift and high HCF transmission can be realized by choosing an adequate parameter set of pulse energy, pulse duration and gas pressure.

Inspecting the spectra in Fig. 1 the question raises, which pressure region is best suited for ultrashort pulse compression, i.e. what will be the shortest pulse duration and how many post-pulses will be generated via SRS and what is the energy and duration of these pulses following the main pulse. For this it is reasonable to choose the pressure of SF₆ such that one gets a broad spectrum while keeping HCF transmission high. To answer the above mentioned questions we characterized the temporal amplitude and phase of the output pulses with a GRENOUILLE (Swamp Optics Near-IR GRENOUILLE 8-20-USB). The device has a time ambiguity, which can be easily solved because the generation of pre-pulses can be ruled out in presence of strong SRS. After optimization we achieved a fiber transmission in the order of 60% and a throughput of the fused silica prism compressor of 90% resulting in a compressed pulse energy of 450 µJ for 300 mbar gas pressure.

In Fig. 3 the retrieved intensity and phase in the spectral and temporal domain from the GRENOUILLE measurement are depicted. The pulses have a spectral width of 57 nm (FWHM) and were compressed to 26 fs. The main pulse is followed by an additional post-pulse, which is delayed by 38 fs and has a pulse duration of 15 fs, which is very close to the FTL (Fig. 3(b)). The 38 fs delay between the maxima of the two compressed pulses agrees well with the 43 fs Raman period of the A_1g vibrational mode. The main pulse contains 94% of the energy corresponding to peak power of 15 GW compared to 1.7 GW of the shorter post-pulse. For many spectroscopy applications relying on a nonlinear interaction the influence of the post-pulse will be negligible. In addition to that it should be pointed out that the generation of post-pulses is related to SRS, so working in a more SPM pronounced regime, i.e. lower pressure or lower peak intensity the post-pulse energy could be further reduced, at the expense of a slightly lower compression factor.

 

Fig. 3 Measurement of spectrally broadened pulses after prism compressor: (a) Using 300 mbar SF₆ a broadening to 57.2 nm (FWHM) is observed. After compression a residual cubic spectral phase remains. (b) The temporal profile shows the main- and post-pulse separated by 38 fs. The main pulse contains 94% of the energy and has a duration of 26fs, compared to 15fs of the less energetic post-pulse. The spectral phase and temporal profile were retrieved from a GRENOUILLE measurement.

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Besides the spectral and temporal characterization the usability of the compressed beam is strongly connected to its spatial beam quality. The beamprofile was measured using a Coherent LaserCam-HR (1024x1280 pixels, 6.7 µm pixel pitch) and is shown in Fig. 4.The measurement shows a circular beamprofile having Gaussian lineouts in horizontal and vertical direction. The measured effective beam diameter is 5.01 mm. The collimation of the beam was realized compensating the divergence of the HCF output by a spherical mirror.

 

Fig. 4 Measurement of the beamprofile: Raw image and lineouts in horizontal and vertical direction of a spectrally broadened pulse after compression using two prisms. The effective diameter of the collimated beam is 5.01 mm.

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In conclusion the setup of an argon-filled HCF and subsequent compression using prisms can be directly transferred to SF₆. The well-known beam quality of such a setup remains in case of using SF₆, which has additional spectral benefits. For estimation of the practical usability beyond Ti:Sapphire lasers these results have to be checked at other wavelengths, e.g. 400 nm, and lower peak powers.

3.2 Spectral broadening at 400 nm wavelength

In addition to the experiments at the fundamental wavelength of Ti:Sapphire lasers spectral broadening was also investigated for the second harmonic at 400 nm central wavelength. Using an argon-filled HCF spectral broadening and compression is the same successful setup as for 800 nm [24, 25] (Fig. 5(a)).The frequency conversion was done by focusing the output pulses of the laser into a 70 µm thick BBO crystal. After filtering the fundamental wavelength with high-reflective mirrors for the second harmonic, the resulting blue pulses (140 µJ, 60 fs) were then focused into the HCF. For this parameter set we observed just SPM induced symmetric spectral broadening for both gases. Due to the reduced peak intensity of 4∙10¹² W∙cm⁻² at the entrance of the HCF no substantial blue shift has been observed and SRS was negligible too due to the small initial bandwidth (775 cm⁻¹ correspond to 12.4 nm bandwidth at 400 nm) in case of SF₆ (Fig. 5(b)).

 

Fig. 5 Comparison of spectral broadening in argon (a) and SF₆ (b) for laser pulses with 400 nm wavelength. Due to the reduced peak power compared to experiments in Fig. 1 just SPM occurs for both gases. However in case of SF₆ reduction of the HCF transmission becomes dominant at pressure levels above 400 mbar indicated by the intensity drop in the logarithmic color scale.

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Again, the same broadening in SF₆ has been achieved with half the pressure as for argon. However, reduced HCF transmission becomes very prominent in case of SF₆ when the pressure is increased above 400 mbar. Again, as for 800 nm, a compromise between spectral broadening and HCF throughput has to be found. For 300 mbar SF₆ the input pulses (6 nm FWHM bandwidth) could be broadened to 15 nm corresponding to a FTL pulse duration of 16 fs. The output pulses were compressed with a prism compressor resulting in 23 fs measured pulse duration (Fig. 6) with 45 µJ energy.

 

Fig. 6 Interferometric autocorrelation trace for spectrally broadened and compressed pulses at 400 nm central wavelength: The pulse duration is in the order of 23.3fs and due to missing SRS no post-pulses occur.

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The pulse duration was determined using an interferometric autocorrelator with a GaN diode for two photon absorption of 400 nm light [26]. The fringe resolved autocorrelation trace (FRAC) has been averaged giving the intensity autocorrelation (IAC) that was fitted assuming Gaussian pulses. The achievable energy can be easily increased to 75 µJ when suitable anti-reflection coated windows at the gas cell and high-reflective mirrors are used instead of silver mirrors having a low reflectivity at 400 nm that leads to an increase of peak power to 3 GW. Compared to results generated using impulsive excitation (1.5µJ, 4fs) [4] the pulses are longer but with the much more compact setup we were able to increase the peak power by a factor of 10.

3.3 Application to high power disk and fiber lasers

The obtained results at 800 nm and 400 nm allow a transfer to commercial available Yb based ultrafast lasers. Since the Raman differential cross section is smaller for longer wavelengths a SPM pronounced operation regime can be easily accessed. The lower peak power of these lasers can be compensated with increase of gas pressure. Here SF₆ provides the same spectral broadening using only half the pressure compared to argon. This is advantageous ensuring a simple gas cell construction avoiding a high differential pressure to air. Compared to an argon-filled HCF and prism compression changing to a molecular medium preserves the advantages of such a setup, e.g. good spatial beam quality and temporal compression by a factor of three.

4. Conclusion

In conclusion, our experiments showed that even pulses longer compared to the Raman period could be efficiently compressed in SF₆-filled HCFs. We obtained a compression of a factor of 3 for pulses at either 800 nm or 400 nm resulting in an increased peak power in both cases. The major advantage of a molecular gas compared to e.g. argon is the same broadening for either a lower gas pressure or a reduced input peak intensity. The latter offers the possibility to achieve the same broadening in larger diameter HCFs, having a higher linear transmission and hence offer the possibility of a higher output pulse energy. A further advantage on the performance of larger diameter HCFs is less sensitivity to fluctuations of the input beam pointing. Thus an optimized pulse compression setup based on a SF₆-filled HCF will be very promising tool for ultrafast real world applications.