1. Introduction

Rapid development in ultrashort pulse laser techniques has facilitated numerous applications in innovative research in science and industry [1–3]. There is, however, still a vast demand to improve laser sources to enhance the performance of applications that require high peak power to enable the exploration of recently discovered phenomena; particularly, strong field interaction in solids [4], high harmonics generation [5–10], the modification of physical properties using light [11–16], and the generation and manipulation of electric currents [17–21]. In this regard, in order to boost intensities, a well-known approach is to shorten the pulse duration. Because of limited gain bandwidth of optical amplifiers, which imposes the limitation in shortest pulse duration from the laser, an external pulse compression is often employed to increase the spectral bandwidth, consequently shortening the pulse duration [22,23]. The most common technique to broaden a spectrum is the implementation of a gas-filled hollow core fiber (HCF) in which the pulses undergo self-phase modulation (SPM) inducing a positive chirp that is compensated by chirped mirrors. Other possible compression methods include thin bulk plates [24,25], conventional step-index solid glass fibers [26], and multi-pass cells [27,28]. While these methods can be successfully applied to low energy pulses, they are individually designed for a specified energy range whose ceiling is set by the damage threshold of the material and the lower bound by insufficient nonlinearity to achieve spectral broadening [27,28]. This is in contrast to the gas-filled HCF, which offers the essential advantage that one experimental setup is capable of handling a wide range of input pulse energies.

Although gas-filled HCF have been successful for the generation of few-cycle pulses at the millijoule (mJ) energy level [29,30], downscaling the energy to the microjoule (µJ) level with sufficient spectral broadening has been challenging. For noble gases with rather high ionization potential (IP), such as argon, it is impossible to induce a sufficient nonlinear effect with energies below the hundred µJ level. In the µJ energy level, inducing enough nonlinear phase to an optical pulse requires either to increase the nonlinear parameter ${n_2}$ or a tighter focal diameter. In the search for an optimal nonlinear medium, low IP noble gases, like xenon, have been tested at high pressure in a regular HCF in order to compress laser pulses with only a few µJ of energy [31–34]. To address the addition of the geometry parameter, Kagomé hollow-core photonic crystal fibers were recently used with low IP noble gases, like krypton and xenon, in order to compress low energy pulses to below 10 fs pulses [35–37]. However, these fibers are complicated to fabricate, which limits their accessibility, and there are also physical difficulties which accompany their use [38,39].

Recently, we have demonstrated pulse compression of Titanium:Sapphire (Ti:Sa) pulses to few-cycles duration, at the hundred µJ level, using hydrofluorocarbon molecular gases near 1 bar pressure with a conventional 1 m long HCF [40]. In this paper we further downscale this approach to the few µJ level and study the mechanisms underlying the spectral broadening in an HCF setup filled with 1-1 difluoroethane (C₂H₄F₂), also known as R152a. Unlike other molecular gases which exhibit a delayed nonlinear response, such as the excitation of rotational or vibrational modes [41,42], R152a behaves as a low-cost alternative to expensive noble gases like krypton and xenon. Here, we attain sufficient spectral broadening to generate <10 fs pulses, starting from 16 µJ, 45 fs pulses at 800 nm using only 3 bar of R152a. This result indeed indicates the capability of this gas to compress low energy laser pulses at the 10 µJ level. In addition, substantial impact of the group velocity dispersion (GVD) of the gas on the spectral broadening is observed at higher pressure, which has not been reported in previous literature. To highlight this effect, numerical simulations have been performed to estimate the pressure dependency of second order dispersion, ${\beta _2}$, and nonlinear refractive index, ${n_2}$.

2. Spectral broadening

The experimental setup is shown in Fig. 1, including the HCF. In this experiment, the output from a Ti:Sa amplifier, which delivers 45 fs-FWHM pulses at a rate of 2.5 kHz with 800 nm central wavelength, is attenuated to 16 µJ. With an f = +60 cm convex lens, the beam is focused and coupled into the HCF, which is 2 meters long with an inner diameter of 250 microns. The two vacuum tubes attached to the fiber holders are enclosed by 3 mm thick UV fused silica windows. In order to reduce unwanted nonlinear effects resulting from the intense beam interacting with a dense gaseous medium at the entrance, the gas is injected on the exit side while the entrance side is constantly pumped to build up a pressure gradient along the fiber. The employment of a differential pressure configuration suppresses the ionization, self-focusing and dispersive broadening, which contributes to a higher reliability in fiber coupling. An aperture is positioned after the lens to control the focal size. Here, the opening of the aperture is adjusted to optimize the focal diameter for transmission. The highest transmission of 53% is achieved when the 1/e² focal diameter is 150 microns, about 60% of the fiber diameter, which is close to the theoretical value of 64% for optimal mode coupling to the fundamental mode [43]. An f = +75 cm silver-coated spherical concave mirror is placed after the exit to collimate the diverging output beam. Afterwards, the pulses are reflected between chirped mirrors (Ultrafast Innovations GmbH, PC70). As each pair of bounces, at the 5 and 19-degree incidence angle, induces -50 fs² group delay dispersion (GDD), we employ seven pairs according to the required resultant GDD. A pair of wedges is used to provide continuous and precise tunability of the GDD. A series of reflections on pairs of chirped mirrors and uncoated wedge surfaces lead to an energy loss of ∼25%. Eventually, the temporal profile of the compressed pulses is measured by second harmonic generation frequency resolved optical gating (SHG-FROG).

 

Fig. 1. Experimental setup for the compression of low energy pulse.

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First, the spectral broadening under propagation in the HCF is investigated. Figure 2(a) describes the spectra for varying gas pressure for an input pulse energy of 16 µJ. The pressure is spanned from vacuum till 4 bar, being kept well below the vapor pressure of R152a, ∼5.1 bar at 20 ˚C [44], to avoid condensation. The fiber transmission remains almost constant for this pressure interval with the given pulse energy, indicating no sign of ionization. Increasing the pressure results in extension of the spectral edge towards both the blue and the red side, dominated by SPM. The degree of spectral broadening is quantified by defining ${\Delta }\omega $ as the width of the spectrum in angular frequency within which 50% of the spectral intensity is encompassed. ${\Delta }\omega $ with respect to the pressure is plotted as red symbols in Fig. 2(b). The transform-limited pulse duration, ${\tau _{\textrm{TL}}}$, corresponding to each spectrum are calculated and overlaid in Fig. 2(b) as black squares, exhibiting a strong inverse correlation with ${\Delta }\omega $. By increasing pressure, ${\tau _{\textrm{TL}}}$ decreases noticeably till 2.5 bar, then the pace of the decrease is slowed down at higher pressure. We conjecture that this is due to the hindrance of spectral broadening attributed to the temporal broadening of laser pulses in the dispersive gas. The influence of the GVD of R152a is discussed later in the context of Fig. 4. The estimation of ${\tau _{\textrm{TL}}}$ suggests the feasibility of compressing a ∼45 fs pulse to <10 fs with well-controlled dispersion.

 

Fig. 2. (a) spectra for different pressures of R152a at 16 µJ input energy. All spectra are normalized to unity and dispersed vertically for discernibility. (b) Transform-limited pulse duration ${\tau _{\textrm{TL}}}$ (black, left axis) and the spectral bandwidth ${\Delta }\omega $ (red, right axis) versus pressure obtained from the measured (black squares) and simulated (red squares) spectra for varying pressure.

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3. Pulse compression

To verify the compressibility, the broadened pulses are compressed with chirped mirrors. Since the spectral broadening encounters the obstruction at 2.5 bar as depicted in Fig. 2(b), increasing the pressure beyond this does not result in noticeably shorter pulses. Hence, the pressure of 3.0 bar is chosen, compromising between spectral width and consequent GDD which needs to be compensated. Equipped with chirped mirrors and a wedge pair, we have characterized the compressed pulses using SHG-FROG (Fig. 3). The measured spectrogram (Fig. 3(a)) and the iteratively retrieved one (Fig. 3(b)) bear fair semblance to each other, confirming the validity of the characterization. The reconstructed temporal profile reveals that the pulse is as short as ∼9 fs FWHM (Fig. 3(c)), in line with the calculated ${\tau _{\textrm{TL}}}$. In the spectral domain, the agreement of measured versus retrieved spectra is also confirmed (Fig. 3(d)). This leads to the compression of low energy laser pulses by a factor of ∼5 using R152a molecular gas with HCF. The energy of the compressed pulse is about 6 µJ.

 

Fig. 3. Characterization of dispersion-compensated pulses using SHG-FROG. Input energy is 16 µJ and the HCF is filled with R152a at 3.0 bar. (a) Measured and (b) reconstructed spectrogram; Retrieved intensity and phase in the (c) time and (d) spectral domain.

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4. Group velocity dispersion effect

To address the effect of GVD through the propagation, the spectral evolution during the guided propagation in the fiber is simulated by solving the generalized nonlinear Schrödinger equation using the fourth-order Runge-Kutta in the interaction picture method (RK4IP) and considering the effect of GVD [45]. We use 45 fs input pulse duration and 8 µJ energy in the simulations. This pulse energy is what we have measured at the output of the fiber. Our simulations are based on i) the fact that a significant fraction of the loss occurs at the coupling into the fiber, and ii) the valuable assumption that neglecting the losses accumulated in the fiber during propagation does not change the physical insights gained from the simulations. The pressure distribution in the fiber is modeled by the formula $P\; \, = \; \,{P_0}\sqrt {z/L} $, where ${P_0}$ is the applied pressure at the fiber output and L the propagation length in the fiber [46]. At each propagation step, the contribution of second order dispersion is calculated in the frequency domain, while both the nonlinear term and the self-steepening are computed in the time domain. As it was revealed in our latest publication, R152a possesses an ${n_2}$ comparable to that of xenon [40], therefore the ${n_2}$ of xenon is adopted as that of R152a in our simulations. Since the ${n_2}$ of xenon widely varies in the literature, we choose to rely on the mean value of the ${n_2}$’s presented in [47] which is ${n_{2}} = 6.0\times 10^{-23}\; {\textrm{m}^2}/\textrm{W}$. The second order dispersion ${\beta _2}$ is adjusted to show the best agreement with experiment which is found at ${\beta _2} = 64\; {\textrm{fs}^2}/\textrm{m}$ at 1 bar pressure. This value is slightly lower than the one reported for Xenon (${\beta _2}\, = {87}\;{\textrm{fs}^2}/\textrm{m}$) [48].

The simulations confirm the experiments in two independent cases; the transform-limited pulse duration, ${\tau _{\textrm{TL}}}$, and the pulse duration of the direct HCF output without chirped mirrors, ${\tau _{\textrm{chirped}}}$. To identify the contribution of GVD, the calculation is repeated with the second order dispersions being neglected, i.e., ${\beta _2} = 0$. The simulations with and without consideration of the GVD are superimposed with the measurements as shown in Fig. 4(a). The lower half below the break of the vertical axis corresponds to ${\tau _{\textrm{TL}}}$. Without the effect of GVD, one should have attained a much broader spectrum to support <5 fs pulses at higher pressures (filled blue diamonds). However, experimentally (filled black squares, the same as in Fig. 3(b)), the ${\tau _{\textrm{TL}}}$ reaches ∼10 fs, as do the simulations including GVD (filled red circles). The consideration of GVD leads to much better agreement with experiment, highlighting the role of dispersion in limiting the spectral broadening in the HCF. The upper half of the axis in Fig. 4(a) denotes ${\tau _{\textrm{chirped}}}$, the pulse duration of the direct HCF output without chirped mirrors. It is measured by intensity autocorrelation (black hollow squares). As the pressure is applied, the GVD of the gas interplaying with the broadened spectrum significantly elongates the pulse duration. The corresponding calculation considering GVD (red hollow circles) show a decent fidelity with the experiment, while calculations without GVD (blue hollow diamonds) predict a relatively insignificant increase of the pulse duration. This finding shows that pulse broadening during the propagation in the fiber indeed occurs due to GVD and is responsible for the impeded spectral broadening with rising pressure.

 

Fig. 4. (a) The transform-limited pulse duration ${\tau _{\textrm{TL}}}$ (solid symbols, axis below the break) and pulse duration before dispersion compensation ${\tau _{\textrm{chirped}}}$ (hollow symbols, axis above the break) derived from the experiment (black squares), simulated with dispersion being considered (red circles) and simulations with dispersion being disregarded (blue diamonds) as a function of pressure and (b) numerical simulations of the temporal and spectral evolution along the propagation in the fiber of an input pulse at 4.0 bar. Black thick solid lines depict 1/e² of the temporal and spectral profile with respect to the propagation length.

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With increasing pressure, we anticipate an interplay between two effects: 1) the spectral broadening is promoted by a denser gas medium leading to higher nonlinearity; 2) spectral broadening is hampered by the lower intensity resulting from the elongated pulse duration. The competition of these two counteracting effects sets a constraint for the spectral broadening. The influence of an elongated pulse duration is studied by numerically tracing the evolution of pulses in the temporal and the spectral domain (Fig. 4(b)). Assuming a high pressure of 4.0 bar, under which temporal broadening owing to GVD seems significantly probable, the suppression of spectral broadening is observed after propagation of ∼1 m as black lines shown in the right panel of Fig. 4(b). This coincides with the point where the temporal broadening begins as shown in the left panel. Thus, the GVD of the molecular gas restricts the spectral broadening.

5. Conclusion

In conclusion, we have illustrated that R152a is a suitable gas for pulse compression using hollow core fibers in the low energy pulse regime. This particular gas possesses a relatively low IP of ∼11.9 eV [49] compared to noble gases, and simultaneously a large ${n_2}$. Thanks to its relatively low price, it can also be used in a differential pressure scheme, which is the preferred method to avoid disruptive nonlinear effects at the fiber entrance. In this paper, 45 fs, 16 µJ pulses are compressed to 9.2 fs with an energy of ∼6 µJ; the pulse duration is reduced by a factor of 5. The overall energy efficiency amounts to ∼ 40%, including the fiber transmission of ∼53% and reflectance of chirped mirrors of ∼75%. Such promising results show that R152a gas can be an excellent candidate to compress low energy laser pulses in a conventional HCF setup, a substitute for the expensive noble gas xenon. In the future, we will further push this method to compress high repetition rate Ytterbium (Yb) laser systems, such as commercially available 100 W sub-300 fs Yb laser systems operating at hundreds of kHz.

In addition, the effect of GVD of the gas on spectral broadening is examined. GVD, which induces dispersive broadening of pulses, inherently leads to a strong reduction in intensity – which in turn restrains the spectral broadening during further propagation. This is verified by numerical simulations which take the second order dispersion into account. It is also confirmed that there is a trade-off between shorter pulse duration and lower input energy. For instance, in the case of 12 µJ input energy and at 3.0 bar gas pressure, the shortest compressed pulse duration obtained is 12 fs, showing the robustness of the HCF scheme. It can be further down-scaled, implying that even lower energy pulses can be compressed using this molecular gas at the expense of compression factor, as long as the pressure does not reach the condensation point (∼5 bar).