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Abstract
We introduce hydrofluorocarbon molecules as an alternative medium to noble gases with low ionization potential like krypton or xenon to compress ultrashort pulses of relatively low energy in a conventional hollow core fiber with subsequent dispersion compensation. Spectral broadening of pulses from two different laser systems exceeded those achieved with argon and krypton. Initially 40 fs, 800 nm, 120 μJ pulses were compressed to few optical cycles duration. With the same approach a compression factor of more than 10 was demonstrated for an ytterbium-based laser (1030 nm, 170 fs, 200 μJ) leading to 15.6 fs.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Over the last decades, the quest to study light-matter interaction at increasingly short time scales and high intensities promoted the development of ultrashort laser sources and few-cycle pulses are now routinely generated. The generation of few-cycle pulses typically requires an external pulse compression stage due to the limited gain bandwidth of optical amplifiers, which restricts the shortest durations achievable directly from the laser system. One of the most common techniques consists in increasing the bandwidth through self-phase modulation (SPM) in a noble gas-filled hollow core fiber (HCF) followed by dispersion compensation, via e.g. chirped mirrors [1]. First introduced in 1996 by Nisoli et al. [2], this technique is now well-established and enables to compress pulses with a wide variety of parameters [3–6].
More recently, there has been a rising interest for diode-pumped Ytterbium (Yb)-based laser systems. These lasers can work with very high repetition rates, generating amplified pulses of femtosecond duration [7–11]. Their innovative geometries (thin-disk, slab, or fiber) allow operation at high average power by reducing thermal load, yet the bandwidth remains limited by the gain medium. Therefore, there is a real need for efficient compression techniques suitable for ultrashort pulses with lower energy, in the range of tens to hundreds of microjoules. Such lasers represent an ideal driver for generating coherent XUV with high flux through high-harmonic generation [9,12,13].
Kagomé-type hollow core photonic crystal fibers represent one approach to compress very low energy pulses delivered by high average power diode-pumped Yb-based laser systems. These micro-structured fibers enable compression of few microjoule pulses to sub-10 fs duration and can even be designed to support higher energies [14–18]. Despite major progresses, it remains nonetheless challenging to use these fibers [19]. An alternative to these rather complex Kagomé fibers lies in the use of low ionization potential (IP) noble gases, like krypton and xenon, in traditional hollow core fibers [10,20–23]. Simple HCFs can support both lower and higher energy pulses as well as being very versatile and robust. So far, the proposed technique has focused on noble gases, neglecting molecular gases because they are subjected to a delayed nonlinear response from the excitation of rotational or vibrational modes such as reported for SF6 [24] or N2 and O2 [25].
In this article, we propose a distinct category of molecular gases, hydrofluorocarbons, to efficiently compress low-energy pulses using HCFs. These molecules represent a valuable alternative to rare gases like krypton and xenon. First, we demonstrate that nonlinear propagation of ultrashort pulses using hydrofluorocarbons results in similar spectra as for noble gases, despite the fact that they have a complex molecular structure in comparison with atoms. Then, with such a molecular gas, we achieve sub-20 fs post-compression starting from 200 μJ, 170 fs initial pulses of an ytterbium-doped potassium-gadolinium tungstate (Yb:KGW) amplified laser system.
2. Spectral broadening of the Ti:Sa laser pulses
First of all, we have investigated the spectral broadening evolution of ultrashort pulses under the nonlinear response of the targeted molecular gases using 40-fs-long pulses centered at 800 nm, at a repetition rate of 2.5 kHz delivered by a Ti:Sa laser system. As depicted in Fig. 1, the pulses are focused in a 1 m long gas-filled rigid HCF of 250 μm core diameter to be spectrally broadened. To avoid perturbation of the beam coupling at the fiber input, vacuum is maintained in the entrance cell, as the setup is employed in a differential pressure configuration. The gas flows from the output (right) to the input of the HCF (left), where the vacuum pump is connected, thus creating a gradient of pressure. The pressure was measured using two digital pressure gauges (910 DualTrans, MKS) connected on both cells. The pressures reported in this paper correspond to the output cell pressure, while the entrance cell was maintained close to vacuum between 0.5 – 5 Torr, depending on the gas flow and pressure gradient. Throughout the measurements, the fiber transmission was around 60%.
Fig. 1 Schematic of the experimental setup (from left to right): spectral broadening in the gas-filled HCF followed by the compression stage and the characterization of the output pulses.
The spectral broadening upon propagation in the HCF was studied for three molecular gases: 1,1-difluoroethane (C2H4F2, also known as R152a), 1,1,1,2-tetrafluoroethane (C2H2F4, also known as R134a), and ethylene (C2H4), a small hydrocarbon molecule. These gases have relatively low IPs (see Table 1), and are therefore expected to exhibit high polarizabilities and suitable nonlinear responses for pulse compression at low input pulse energies. In parallel, reference measurements were taken for two atomic gases, argon and krypton. The spectral broadening at different input pulse energies as a function of gas pressure was characterized before the compression stage using a spectrometer (HR4000, Ocean Optics).
Table 1. Ionization potential (IP) of the different gases under investigation
Figures 2(a) and 2(b) present typical spectra measured after the nonlinear propagation through the gas-filled HCF. The initial spectrum is shown in shaded grey. The angular frequency axis is provided for visualization purposes only, as the spectra were measured with respect to the wavelength. In Fig. 2(a), energy and pressure parameters were chosen to obtain broadened spectra with equal bandwidth for each gas. As observed in Fig. 2(a), the broadened spectra extend from the visible to the near infrared (550 nm to 950 nm) over approximately 400 nm, corresponding to a broadening factor of 5. In comparison, the initial spectrum has a spectral width of 80 nm, extending from 750 nm to 830 nm and centered around 790 nm. Also in Fig. 2(a), the spectra obtained for all gases, except for ethylene, exhibit highly similar shapes with smooth SPM lobes at the same wavelength positions. For ethylene, in contrast to all the other gases, the spectral extension appears strongly diminished at shorter wavelengths. Considering that shorter wavelengths are generated at the pulse trailing edge, through self-phase modulation, we infer that this part of the pulse undergoes a different nonlinear response. On the other hand, we observe for the red side that the spectrum is nearly identical to that of all the other gases. This finding suggests that ethylene may be somehow modified at the peak of the pulse, thus resulting in a different electronic response seen by the pulse trailing edge. For this reason, we would not consider this molecule for laser pulse compression. This feature is not observed for hydrofluorocarbon molecules and atomic gases, in which the broadened spectra are smooth and regular, such as expected from the instantaneous Kerr nonlinear response.
Fig. 2 (a) Comparison of spectra for different gases in the SPM regime: R152a (120 μJ, 475 Torr), R134a (160 μJ, 525 Torr), ethylene (80 μJ, 575 Torr), argon (320 μJ, 750 Torr), and krypton (200 μJ, 550 Torr); (b) Comparison of spectra for different gases beyond the SPM regime, all at a pressure of 760 Torr (1 atm): R152a (200 μJ), R134a (200 μJ), ethylene (120 μJ), argon (320 μJ), and krypton (240 μJ). The spectrum of the initial pulse before broadening is shown in shaded grey. The spectra were measured with respect to the wavelength and the frequency axis is provided for orientation purposes only.
In Fig. 2(b), parameters were set to study spectral broadening at higher levels of nonlinearity. For this, we increased gas pressures and pulse energies. In those conditions, we observe new features as the spectra become asymmetric around the central wavelength and present more complex structures with new peaks arising. This is the case for both atoms and molecules. In particular, we note the extension of the blue side of the spectra. Such a blue-shift has already been associated experimentally to self-steepening [26,27] and can also be an indicator of ionization [28, 29]. It was also shown in previous work that the excitation of molecular vibrational states may lead to periodic modulations such as those observed in the spectrum of R152a in Fig. 2(b) [24]. On the other hand, such modulations are not necessarily observed for R134a or ethylene, for which the effect of a delayed response or vibrational modes would have been expected as well. Therefore, it is not trivial to identify the exact combination of mechanisms leading to this particular spectrum, given that the behavior is observed for a high level of nonlinearity where several effects may be coupled. Quantitatively, the spectra broadened in R152a and R134a at a pressure of 760 Torr (1 atm) and input energy of 200 μJ extend over 600 nm (from 400 nm to 1000 nm). As a comparison, higher input energy (240 μJ) is required to broaden krypton from 400 nm to 950 nm. In the case of ethylene, the spectrum in Fig. 2(b) shows the maximal broadening achieved in our conditions. Here, the broadening saturates at low energy (120 μJ at 760 Torr), and the spectrum gets more irregular without broadening anymore when the energy is increased. At the same time, transmission in the fiber starts dropping significantly, thus further underlining that ionization plays a role at higher intensity.
In order to further compare the nonlinear propagation, we quantified the total bandwidth Δω as a function of pressure for all gases under investigation. For fixed laser parameters, 800 nm, 40 fs pulses, the output spectra were measured while varying the pressure by small increments, up to 760 Torr. Throughout this paper, the total bandwidth Δω is a parameter defined by applying the following numerical method. The frequencies at levels of 1%, 50% and 99% of the integrated intensity with respect to frequency were determined for each pressure. They correspond respectively to the bottom, middle, and top dotted lines on Fig. 3(a). For this study, we have defined the parameter Δω as the difference between frequencies corresponding to 1% and 99% of the total integrated energy (bottom and top dotted lines). We observe that the center of mass remains constant for all pressures in R134a. It is also the case for the other gases studied in this paper, including ethylene. Presenting the results on an angular frequency ω axis allows us to observe the evolution of broadening. For self-phase modulation, the broadening is expected to be linear and symmetric in frequency. As observed on Fig. 3(a), the spectrum expands with pressure more rapidly for higher frequencies, as opposed to the case of lower frequencies. This is assumed to be related to self-steepening. In Fig. 3(b), the total bandwidth Δω for each pressure is obtained by applying the numerical method described above, that is from the difference between the angular frequencies corresponding to 1% and 99% of the integrated energy. It shows the total bandwidth Δω obtained with 800 nm, 120 μJ, 40 fs pulses in R152a (green squares), R134a (red diamonds), ethylene (purple circles), and krypton (blue upward triangles) and for 240 μJ for argon (orange downward triangles). Compared to the initial pulse bandwidth, we observe a broadening factor of approximately 3 for argon and krypton at 760 Torr. The broadening is significantly stronger for molecular gases, as we achieved factors of approximately 6, 7, and 8 respectively for R134a, ethylene, and R152a.
Fig. 3 (a) Experimental spectral broadening in R134a (120 μJ input pulse energy) as a function of pressure; (b) Quantitative measurement of the total bandwidth as a function of pressure for all investigated gases for an input pulse energy of 120 μJ (except argon, for 240 μJ).
As expected from the linear dependence of n2 on pressure [30], the measured spectral broadening Δω scales almost linearly as a function of pressure, as shown in Fig. 3(b). In general for atoms, lower ionization potentials can be associated to higher nonlinear indices. In fact, there is no direct equation linking the IP to the nonlinear index n2, and therefore to Δω. Theoretical models have been developed to calculate the nonlinear index based on the particle density and the ionization potential, but are only valid for noble gases [31]. More complex models would be required for molecular gases and calculations should take into account the electronic polarizability in different spatial orientations [32]. This is not trivial and goes beyond the scope of the work presented here. However, Fig. 3(b) confirms the same tendency for these molecules as for the atomic gases (see Table 1). The two noble gases with the highest IPs lead to the smallest slopes for Δω as a function of pressure, while R152a and ethylene, which have the lowest IPs, feature the highest slopes. From these slopes, we can conclude that the n2 of R152a is approximately 3 times higher than that of krypton, which is similar to the n2 ratio of xenon to krypton [20]. Noticeably, ethylene has the lowest IP but is not broadening more than R152a. This is attributed to the feature observed in Fig. 2(a) in which the broadening from the blue side appears to be suppressed in ethylene.
Although these measurements allow to sort the nonlinear response in different gases, there is no information concerning the effect of ionization, which may also contribute to the total broadening. Therefore, we have performed another set of measurements where we defined the onset of ionization and compared the total broadening obtained in each gas at this threshold. For each gas, the pressure was kept constant and the pulse energy was increased until we observed a 5% drop in transmission through the HCF due to ionization. We attribute the decrease in transmission to the ionization process. The photons are absorbed by atoms or molecules, generating charged species and free electrons, and this process results in a reduced transmission through the HCF. Given that the input of the fiber is kept under vacuum, the transmission drop cannot be attributed to fiber coupling issues such as self-focusing of the laser beam.
These measurements were performed with a fiber whose core diameter was 350 μm. The total broadening obtained at the critical ionization threshold for each gas is presented in Fig. 4(a), with the corresponding pulse energies. Two molecular gases, ethylene and R152a, show opposite behaviors compared to krypton. On the one hand, ethylene ionizes quickly before reaching appreciable spectral broadening. R152a, on the other hand, can undergo significant spectral broadening before ionizing when compared to the other gases. As for R134a and krypton, they have comparable bandwidth at this critical point. From this measurement, we conclude that R152a actually represents a valuable option to ensure maximal spectral broadening together with high overall throughput. Interestingly, in agreement with this result, it was previously reported that organic molecules can be more difficult to ionize than atoms for equivalent ionization potentials [33,34].
Fig. 4 (a) Spectral broadening at the ionization threshold (at indicated energies) for different gases at different pressures; (b) Measured spectra at a pressure of 500 Torr.
In Fig. 4(b), spectra measured at the critical ionization energy are shown. We observe that even under these conditions, the spectral shape for the refrigerant molecules remains highly similar to that of krypton, with the one of R134a actually being identical to the krypton one. The spectra for R152a are broader from both the blue and the red side. For ethylene, the broadening on the blue side is once again strongly suppressed.
It should be noted that fine dust deposition was observed when using ethylene for conditions of high nonlinearity. This is attributed to the polymerisation of hydrocarbon chains that leads to carbon deposition and permanent degradation of the fiber such as reported in the conclusion of the paper by Mansour et al. [20]. This detrimental effect was not observed when using hydrofluorocarbon gases under our present conditions and we assume that HFC fragments do not polymerise like hydrocarbon fragments. However, we do not exclude that hydrocarbon chains could be formed also for these gases in conditions of high excitation and/or ionization and therefore may represent in some cases a limiting factor for applications.
3. Pulse compression of the Ti:Sa laser pulses
Since broadened spectra from R152a and R134a are highly similar to the reference spectra of argon and krypton, positively chirped pulses generated in these molecular gases are expected to be compressible in the same way as it is routinely achieved for atomic gases. Indeed, we were able to compress the 800 nm Ti:Sa pulses in both gases, using chirped mirrors for dispersion compensation. To compensate the chirp induced by SPM, 5 pairs of chirped mirrors (UltraFast Innovations, Garching, Germany) with a group delay dispersion (GDD) of −25 fs2 per bounce were used, along with few millimeters of fused silica for GDD fine tuning, for a total compensation value of about −180 fs2. The pulses after compression were temporally characterized by second-harmonic generation frequency-resolved optical gating (SHG-FROG) [35].
As an example, the experimental SHG-FROG spectrogram measured for a 120 μJ input pulse in R152a at a pressure of 650 Torr is shown in Fig. 5(a). Figure 5(b) illustrates the numerically retrieved spectrogram. The corresponding intensity and phase of the reconstructed pulse and spectrum are depicted in Fig. 5(c) and 5(d) respectively. In this case, we were able to shorten the pulse duration from 40 fs down to 7.1 fs (FWHM). The retrieved spectrum is not strictly identical to the measured experimental one in Fig. 5(d) but essential features are however reproduced. The residual oscillations observable in the temporal trace in Fig. 5(c) are related to third order dispersion, which is not exactly compensated here. Based on the experimental spectrum in shaded grey in Fig. 5(d), the transform limited pulse duration is 5.6 fs.
Fig. 5 Result of dispersion compensation for R152a, E = 120 μJ, p = 650 Torr: (a) Experimental SHG-FROG trace; (b) Retrieved SHG-FROG trace; (c) Retrieved intensity and phase in the time domain; (d) Retrieved intensity and phase in the spectral domain. The experimental spectrum is shown in shaded grey.
4. Spectral broadening and pulse compression of the Yb-based laser pulses
Pulse compression was achieved also with a Yb:KGW laser source. The experiment is carried out with an R134a-filled HCF in order to demonstrate the potential of hydrofluorocarbons for relatively low pulse energy and high repetition rate applications, for which ytterbium-based lasers are typically used. The scheme is similar to Fig. 1, but this experiment is performed in parallel on a different setup described in [36]. It should be noted that a shorter fiber with a smaller diameter could have been chosen but for convenience we used this readily available setup. The ytterbium laser delivers 170-fs pulses centered at 1030 nm at a repetition rate of 1 kHz. The flexible hollow fiber has a length of 6 m and a core diameter of 500 μm. In this experiment, the fiber was filled with gas at a static pressure because a higher nonlinearity was required to broaden the narrow spectrum in comparison with the Ti:Sa system. This way, the higher pressure combined with the increased length of the fiber yields stronger SPM. The positive chirp induced by SPM is then compensated using one of the two following compression setups. (i) For E = 150 μJ, dispersion compensation is achieved by successive reflections on pairs of chirped mirrors, with a group velocity dispersion of −50 fs2 per reflection. The optimal compensation was obtained with 12 bounces, for a total GDD value of −600 fs2. (ii) For all the other energies (50 μJ and 200 μJ), a folded 4f stretcher/compressor was used to arbitrarily tune and optimize the amount of GDD. The 4f setup consists of a concave aluminium mirror (f = 200 mm), a 600 lines/mm grating, and a plane mirror reflecting back the spectral components through the same path, slightly offset, resulting in a total transmission of ∼50%. While grating compressors enable continuous control of the GDD, chirped mirrors offer optimal reflectivity. Overall, the throughput of the HCF itself remained above 65% for the experimental measurements.
Input pulses with 3 different energies, 50 μJ, 150 μJ, and 200 μJ, were compressed with our setup. The experimental SHG-FROG trace obtained after compression of the 200 μJ pulse in R134a at 2000 Torr is depicted in Fig. 6(a). The reconstructed spectrogram, presented in Fig. 6(b), is in good agreement with the experimental one in Fig. 6(a). The shortest pulse, a sub-five-cycle pulse at 1030 nm, was obtained after compression of the 200-μJ, 170-fs pulse to 15.6 fs (compression factor of about 11), as shown by the reconstructed pulse intensity and phase in the time domain in Fig. 6(c). The retrieved spectrum is also in very good agreement with the experimental one, as shown in Fig. 6(d), except for the peak at the fundamental frequency of 1030 nm. We believe that this peak in the experimental spectrum corresponds to a temporal background from the laser. The spectrometer is unable to distinguish a background signal with low intensity on a ps or ns timescale from the main pulse. Therefore, we assume that the poor temporal contrast of the laser system is accountable for the mismatch between both spectra at 1030 nm. This also implies that the pulse energies presented are overestimated, as they include the energy contained in the temporal background signal.
Fig. 6 Result of dispersion compensation for R134a, E = 200 μJ, p = 2000 Torr: (a) Experimental SHG-FROG trace; (b) Retrieved SHG-FROG trace; (c) Retrieved intensity and phase in the time domain; (d) Retrieved intensity and phase in the spectral domain. The experimental spectrum is shown in shaded grey.
The FWHM pulse durations obtained for the other input energies are listed in Table 2 with the corresponding spectral broadening. As expected, the spectral broadening increases with input energy, leading to potentially shorter pulses. An important broadening factor of 20 is observed for the shortest pulse compared to the initial spectral width of 0.016 PHz. The lowest energy pulse (50 μJ) is broadened by a factor of 8 with this setup.
Table 2. Pulse duration with the corresponding spectral width after compression for different input pulse energies in R134a at ∼2000 Torr.
5. Conclusion
In conclusion, we have demonstrated that molecular gases, more specifically hydrofluorocarbons like R152a (1,1-difluoroethane) and R134a (1,1,1,2-tetrafluoroethane), can be a valuable alternative to expensive noble gases for pulse compression using hollow core fibers. Molecular characteristics leading to a nonlinear response similar to atoms is not fully understood and has to be further investigated. However, the low ionization potentials which characterize these molecules are associated with higher nonlinear indices n2. Therefore, significant and cost efficient spectral broadening is possible with smaller pulse intensity, making this method ideal for high average power applications with pulse energy on the order of tens to hundreds of μJ. In R134a, we were able to broaden the spectra of 170-fs, 200-μJ Yb:KGW input pulse by a factor of 20 to achieve pulse compression down to 15.6 fs at a pressure of 2000 Torr. The pulse durations obtained are already sufficiently short for interesting applications, such as high harmonics generation in the range of hundreds of eV. For example, if we refer to the work of Boullet et al. [12], they were able to generate harmonics up to order 31 (approximately 40 eV) in argon with 100 μJ, 270 fs pulses at 100 kHz. In our experiment, we compressed pulses of similar energies to sub-20 fs duration. From this result, we expect the output pulses to constitute an efficient driver for a coherent XUV source with cut-off photon energies in the range of 200 to 250 eV [37].
Funding
Canada Foundation for Innovation (CFI), the Natural Sciences and Engineering Research Council of Canada (NSERC), and the Fonds de Recherche du Québec sur la Nature et les Technologies (FRQNT). R. Morandotti acknowledges additional support by the Government of the Russian Federation through the ITMO Fellowship and Professorship Program (grant 074-U 01) and by the 1000 Talents Sichuan Program in China. E. Haddad acknowledges financial support from NSERC and FRQNT M.Sc. scholarship programs.
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