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Abstract
A conventional hollow core fiber (HCF) scheme is implemented to investigate spectral broadening of Titanium:Sapphire (Ti-Sa) femtosecond laser pulses in saturated hydrocarbon molecules compared to unsaturated ones. While the saturated molecules exhibit a spectral broadening similar to noble gases, for the unsaturated ones with π bonds, broadening towards blue is restrained. Numerical simulations underpin that it is a combination of group velocity dispersion (GVD) and Raman scattering which limits the spectral broadening for the unsaturated molecules. Compression of low energy ∼40fs pulses to ∼8fs using saturated hydrocarbons is demonstrated, suggesting the feasibility of this media for high repetition rate laser pulse compression.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The development of ultrafast laser technologies has allowed to discover unprecedented physical phenomena in light-matter interaction [1–4]. By reaching higher power levels as well as shorter pulse duration, it has been possible to explore dynamics down to the attosecond duration [5–11] and in strong intensity regimes [12–18]. In the last decades of the 20th century, the advent of Ti-Sa gain medium [19] has disseminated femtosecond lasers. Kerr lens mode-locking [20] in combination with chirped pulse amplification [21] has expedited access to high focal intensity comparable or even higher to the Coulomb field in atoms to reach the relativistic regime [22,23]. As the gain narrowing of the amplification medium limits the spectral width, an additional stage for spectral broadening and compression is necessary to further shorten the pulse duration of Ti-Sa lasers to few optical cycles. Most popularly, expanding the spectral bandwidth by means of self-phase modulation in noble gases in a HCF and subsequent dispersion compensation [24] have demonstrated compression down to the single-cycle regime [25]. Nowadays, the concept of HCF is well established and widely used in the community due to its versatility and robustness [26–29]. Compression of low energy pulses using various gaseous molecules (apart from noble gases) in HCF has recently been investigated [30–32]. This provides the perspective of applying the HCF method to compress Ytterbium-based lasers [33,34], which lately receives attention as a prospective femtosecond laser source, e.g. to drive high flux high harmonics generation (HHG) thanks to its high average power and high repetition rate [35–38].
In the present study, several hydrocarbons are tested as nonlinear medium for pulse compression using HCF. It is observed that methane (CH4) and ethane (C2H6), referred to as saturated hydrocarbons, function like well-known noble gases for spectral broadening and compression; pulse compression down to sub-10fs with CH4 is demonstrated. On the other hand, for the unsaturated molecules ethylene (C2H4) and acetylene (C2H2), a lack of blue shift at the output of the HCF is observed. This behavior results in a narrower spectral bandwidth, making them less suitable for pulse compression. Through numerical simulations, we highlight that an interplay between GVD and Raman response is responsible for this distinct spectral aspect between saturated and unsaturated molecules.
2. Experimental condition
The experiments have been performed at the Advanced Laser Light Source infrastructure located at INRS-EMT. The experimental setup is described in Fig. 1(a). A Ti-Sa multipass amplifier is used which generates 40fs pulses with an adjustable pulse energy up to a few mJ at a repetition rate of 2.5kHz. The output is focused and coupled to a 2-meter-long HCF with an inner diameter of 250 microns (few-cycle Inc.). The 1/e2 focal spot size amounts to 150 microns, which approximately coincides with an optimal ratio against the core diameter, ensuring a decent transmission efficiency of 55%. The HCF assembly is equipped with a vacuum pump connected to the laser input side and a gas supply tube attached to the laser output side. This configuration enables one to build a pressure gradient in the HCF; low at the laser entrance and high at the exit. It is intended to avoid undesired interaction between the focusing laser beam and the gas media before being coupled into the fiber [26].
Fig. 1. (a) Schematic drawing for the experimental setup (b) exemplary input (gray shaded) and output (black line) spectra with the descriptions for blue and red edges (c) typical transmission drop with respect to increasing input pulse energy, observed in acetylene gas, from which the ionization threshold ${E_{th}}$ is derived. The transmission begins to drop around 60% of ${E_{th}}$.
The output spectra from the HCF filled with different hydrocarbon molecules are recorded for varying input energies. In addition, the same measurements are repeated with krypton as a reference. The pressure of each gas is controlled to 1 bar in order to keep the number of molecules participating in the interaction constant. It also complies with the regulation imposed by material safety data sheets (MSDS), staying below the limit pressure of 1.5 bar for acetylene.
3. Experimental findings
Example spectra for an input pulse and a broadened output pulse are presented in Fig. 1(b). For analysis, the red (or blue) edge of a spectrum is defined as the wavelength above (or below) which 6.77% ($= 1/2{e^2}$) of spectral intensity is encompassed. Therefore, 86.5% ($= 1 - 1/{e^2}$) of spectral intensity is contained between the blue and the red edge, namely, within the spectral width. With growing input energy, all gases undergo a drop of transmission which is an indication of ionization of the molecules. We define the threshold of ionization ${E_{th}}$ as the input pulse energy at which the HCF transmission reduces to 45% (see Fig. 1(c)). The input energies in the following context are normalized with respect to the ${E_{th}}$ of each gas, which are displayed in Table 1.
Table 1. Ionization threshold of gases tested in the present study.
The evolution of blue and red edges with increasing energy is depicted as filled symbols in Fig. 2(a). The complete set of raw spectra is presented in Fig. 5 in the appendix. All gases exhibit a similar spectral extension towards the red, i.e., the deviation among different media is insignificant as presented in Fig. 2(a). On the contrary, for the blue shift, ethylene and acetylene behave in a well-distinguishable manner compared to the rest. Ethylene and acetylene broaden with the magnitude of the descending slope of the blue edge being comparable to that of the ascending slope of the red edge. For the other gases, the slope for the blue shift is greater than the red one by about ∼2.5 times due to the combination of self-phase modulation and self-steepening. This leads to approximately half the spectral width for unsaturated hydrocarbons compared to the saturated ones (Fig. 2(b)).
Fig. 2. (a) spectral broadening after the propagation in a HCF filled with 1 bar of various gases for varying input energy. The shape of symbols denotes the blue edge (triangles) and the red edge (square) of the spectra. The colors represent the species of gas as shown in the legend. Open symbols stand for calculated spectra (ethane and ethylene only). Vertical dashed line stands for the intensity at which the drop of HCF transmission is first perceived, indicating the occurrence of ionization. (b) the spectral width derived from (a).
4. Numerical simulations
In parallel to the experiment, pulse propagation in a gas-filled HCF is simulated by numerically solving the nonlinear Schrödinger equation [39,40].
Ethane and ethylene are chosen to represent saturated and unsaturated hydrocarbons. The fundamental vibrational modes, C-C and C-H stretch, are taken into account. Relevant parameters are given from our measurements (laser pulse energy, pulse duration at input, central wavelength and focal diameter, the dimension of the HCF and pressure in it) as well as from literature (nonlinear refractive indices [43,44], dispersion coefficients [45], vibrational frequencies and their bandwidths with corresponding Raman cross sections [46–49]).
5. Comparison between the experiment versus the simulation
At a half of ${E_{th}}$ input energy, simulated spectra for both gases are overlapped on the measured ones (gray shaded area) as shown in Fig. 3. The red and blue edges and positions of some peaks and valleys are well reproduced in the simulation considering GVD and Raman effect (solid black line). In order to identify the contribution of each effect, we repeated simulation with either GVD or Raman effect being ignored (dashed red and dotted blue lines in Fig. 3, respectively). 1) The neglect of GVD, putting ${\beta _2} = 0$ in Eq. (1), assumes a constant pulse duration during the propagation, which is not the case in reality; GVD of gases elongates the pulse duration to effectively reduce the intensity. Therefore, consideration of GVD tends to correct the overestimated spectral broadening. 2) The Raman can be neglected by putting ${f_R} = 0$ in Eq. (2) thus $R(t )= \delta (t )$ which signifies domination of instantaneous responses. The consideration of Raman tends to induce spectral shift toward red. Lower energy photons generated by inelastic scattering are amplified by Raman gain, being pumped by the blue part of the same pulse. The process continues along the fiber, continuously transferring energy from blue components to red. Such an energy transfer appears as a red shift of the spectrum, with shift increasing with propagation length.
Fig. 3. measured (area filled with gray) and simulated (solid black with both GVD and Raman being taken into account, dashed red without GVD and dotted blue without Raman) spectra for ethane (lower panel) and ethylene (upper panel) at a given input energy of 50% of the ${E_{th}}$. The insets are spectral phases conjugated to the simulated spectra with both GVD and Raman components being taken into account.
In the case of ethylene, a neglect of either GVD or Raman worsens the agreement with the measured spectrum. It denotes that both GVD and Raman contribute substantially to the spectral shape in ethylene. On the other hand, for ethane, disregard of GVD induced noticeable divorce from the measured spectrum whereas that of Raman exerts little influence; decent agreement with the experiment is revealed by considering solely GVD. Relatively weak Raman contribution in ethane is accounted for the smaller ${f_R}$ for the C-C stretch mode compared to ethylene. It implies that the π-bond between two carbon atoms in ethylene (C = C) is responsible for larger Raman cross section than ethane (C-C). It makes the Raman contribution of ethylene nonnegligible while the electronic contribution dominates in ethane. Eventually it results in a dissimilar spectral shape in ethane and ethylene. In ethane, noble gas-like spectral broadening takes place via SPM whereas ethylene renders the spectrum redshifted by Raman, leading to relative frustration of blue.
In the calculations on spectral broadening with respect to increasing input pulse energy, which are superimposed onto Fig. 2(a) and Fig. 2(b) (hollow symbols), a comparable red shift and a stronger blue shift for the saturated molecules is predicted, in agreement with our experimental observations. The agreement is noticeably better for lower energies. This is because the ionization, recognized by a decrease in transmission, onsets around ∼60% of ${E_{th}}$ (Fig. 1(c)) and the numerical simulations do not take the contribution of an ionized medium into account. Especially for the saturated hydrocarbons, as well as for krypton, the ionization is also manifested by an intensified blue shift (see spectral modulation in the blue in Figs. 5(a), 5(b) and 5(e)); the measured blue edges for higher input energies tend to be overestimated. It elucidates the discrepancy between measurement and simulation at the blue edge for higher energy regimes near ${E_{th}}$.
6. Pulse compression using saturated hydrocarbons
As the saturated hydrocarbons exhibit spectra about two times broader than the unsaturated ones as shown in Fig. 2(b), they are deemed proper nonlinear media for pulse compression. An input pulse energy well below ${E_{th}}$ (∼16µJ) in conjunction with a higher pressure (∼6.5 bar in absolute pressure) facilitates a sufficient spectral width to support sub-10fs pulses. The employment of pressure gradient minimizes unwanted nonlinear effects like self-focusing and filamentation at the input of the hollow core fiber [26]. The spectrally broadened pulses are compressed by chirped mirrors installed downstream, and characterized by second harmonic generation frequency resolved optical gating (SHG-FROG), demonstrating ∼8fs pulse as displayed in Fig. 4. Unsaturated hydrocarbons, in contrast, cannot compress below 15fs. This is also consistent with the simulations. The calculated spectral phase of ethane is nearly parabolic, thus compressible to the transform-limit by compensating the group delay dispersion (GDD). On the other hand, ethylene is subjected to a stronger high order spectral phase, which allows considerable residual phase in spite of the cancellation of GDD (insets of Fig. 3).
Fig. 4. Compressed pulses characterized by means of SHG-FROG. The 40fs, 16µJ input pulses are guided through a HCF filled with methane at 6.5bar then compressed using chirped mirrors. (a) measured and (b) reconstructed spectrogram and corresponding (c) temporal and (d) spectral intensity profiles and phases
Moreover, the unsaturated hydrocarbons gradually degrade in transmission over time, which makes them unsuitable for practical use, while the saturated ones maintain the performance over time. This is tested with input pulses with an excessive energy of about two to three times the ${E_{th}}$, in order to expedite the response. For the unsaturated molecules, an exposure to such high energy pulses leads to a steady drop of the HCF transmission (see Fig. 6 in the appendix). A visible deterioration of the HCF is recognized after a prolonged irradiation, as its inner wall near the laser entrance gets coated with black dust. This is because C2H4 and C2H2 are highly reactive when ionized as the carbons are not saturated and new chemical bonds can be created resulting in the formation of larger molecules, namely, polymerization.
7. Conclusion
To summarize, spectral broadening of femtosecond laser pulses using HCF is compared for single- and multiple-bonded hydrocarbons under controlled conditions. The spectral widths from saturated hydrocarbons are roughly twice broader than those from the unsaturated ones, and similar to the reference noble gas, krypton. This is mainly because of the suppressed blue shift for the unsaturated carbon bonds due to a larger Raman cross section originating from their π-bonds. The compressibility of wider spectra from the saturated molecules is confirmed by characterizing ∼8fs pulses after optimizing the GDD. This works suggests the feasibility of saturated hydrocarbons as an inexpensive compression media for low energy, high repetition rate laser sources.
8. Appendix
Fig. 5. Measured spectra of hollow core fiber output filled with 1 bar of (a) methane, (b) ethane, (c) ethylene, (d) acetylene and (e) krypton for varying input pulse energy up to ${E_{th}}$ of each gas. All spectra are corrected by multiplying the response curve of the spectrometer and the amplitudes are normalized to one. The spectra are vertically fanned out with the spacing of 0.5 unit for clearer visualization.
Funding
Canada Foundation for Innovation; Natural Sciences and Engineering Research Council of Canada; Fonds de Recherche du Québec - Nature et Technologies.
Acknowledgements
R. Safaei acknowledges financial support from the FRQNT Ph.D. scholarship program. The authors thank Xinhua Xie, Paul-Scherrer Institute, for stimulating discussions.
Disclosures
The authors declare no conflicts of interest.
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