1. INTRODUCTION
Since the discovery of chirped pulse amplification [1], Ti:Sapphire technology has been the workhorse of ultrafast optics, producing high peak powers, alas with limited average powers. Most, if not all, optical applications will benefit from higher duty cycles, which translates to higher repetition rates. For strong field science, this means achieving both high peak and average powers. Recently, the development and wide adoption of Ytterbium (Yb)-based lasers over Ti:Sapphire have made the 100 W ultrafast regime accessible [2]. However, Yb’s narrow gain bandwidth produces long 1 ps–250 fs pulses [3]. Therefore, to be used in ultrafast science, these pulses must be broadened and compressed to drive many of the desired high-intensity applications of ultrafast optics [4–17]. The most common methods of spectral broadening at high peak and average powers are noble gas-filled multi-pass cells (MPCs) or hollow core fibers (HCFs) using self-phase modulation (SPM) [18–22].
There is a growing interest in molecular gases as a broadening medium, since many molecules exhibit a strong nonlinear refractive index n2 [23] responsible for SPM-induced spectral broadening: NLδω(t)=−δ?NLδt=−n2P0ω0LeffcAeffδIδt [24]. Additionally, two effects of molecular structure have demonstrated multi-octave generation in HCFs and MPCs [25–29]. One effect is stimulated Raman scattering (SRS), in which photons interact with ro-vibrational states. Since molecular transitions are predominant in SRS, asymmetric red shifting is observed in the broadening [30,31]. SRS has historically been used to extend the frequency tunability of laser systems [32] and is still an active area of research with results such as enhanced Raman response via multidimensional solitary states [25].
The second effect is molecular alignment. As an ensemble of molecules interacts with moderately intense pulses, their polarizability axis aligns to the electric field’s polarization, dramatically enhancing nonlinearity [27,33,34]. The goal of high-power molecular broadening has, until now, been focused on Raman red shifting. However, previous experiments strongly suggest that molecular gases are not suitable for high-power applications, since rotational heating suppresses broadening and transmission [23,35]. Techniques to mitigate this heating have been implemented, such as differential pressure schemes [25,35–37] that have allowed functional molecular broadening up to 25 W [36].
Fig. 1. Optimization of N2 HCF pressure allows broadening and compression of ps pulses to ≈120fs across a wide range of high pulse energies at high average power. N2 pressure is optimized for maximum broadening without transmission loss. Dispersion was optimized for pulse compression at each repetition rate.
Fig. 2. (a) High average and peak power broadening in N2 for different repetition rates and pulse energies demonstrating ≈120fs pulses at 218 W of input power with >70% transmission efficiency and a constant pressure of 1.5 bar. At repetition rates between 25 and 75 kHz temporal breakdown limits the maximum average power and occurs at 3 mJ of energy per pulse (red dotted line). Inset: SHG-FROG trace for 218 W, 200 kHz at 2.5 bar N2 starting from 1.06 ps (τIn) to 126 fs (τRet) FWHM of the intensity. (b) HCF transmission at 25, 50, and 100 kHz repetition rates as a function of input power limited by temporal breakdown or maximum energy reached. (c) Spectral broadening comparison of 218 W input power at 100 kHz in N2, Argon (Ar) with 1.5 bar, and Krypton (Kr) at 1.7 bar.
In this paper, a molecular nitrogen (N2)-filled HCF broadening and compression scheme is implemented. For the first time, average input powers up to 250 W were realized with repetition rates ranging from 25 to 200 kHz (corresponding to 12–1.5 mJ per pulse). Pulse compression from 1.3 ps to 120 fs was achieved in this manner. This denotes an order of magnitude average power scaling compared to previous reports in molecular-gas-filled HCFs or MPCs. N2 demonstrates 80% fiber transmission, spectral broadening similar to and even slightly greater than Krypton (Kr), and good pulse compression while preserving high spatial quality with M2=1.2. To understand this previously thought unreachable regime, the effect of high average power on molecular transmission and broadening is tested in N2, molecular Oxygen (O2), and Nitrous oxide (N2O) at up to 250 W. An explanation of transmission loss from bandwidth-driven cascaded SRS heating is developed on the basis of these experimental findings and supported via molecular state calculations. The limitations of broadening in molecular gases in our experiments are shown to be a function of primarily pulse energy and result in a pulse breakdown. The quality of the pulse after broadening in N2 with 218 W, 200 kHz is demonstrated by high-harmonic generation in Ar.
2. RESULTS
Experiments were conducted with an Amphos 3000 Yb amplifier system that delivers a maximum of 300 W of average power. The pulses are broadened in a 750 µm diameter, 4.45 m long gas-filled HCF (few-cycle Inc). The versatile setup accepts input energies varying from 2 mJ (200 kHz) up to 12 mJ (25 kHz) at constant average power. Active beam pointing (TEM-Messtechnik) is used to guarantee stable coupling to the fiber. Fiber output is compressed by a series of chirped mirrors (few-cycle Inc). Full details of the experiment are shown in Fig. S1.
First, a study of pulse quality after N2 broadening was carried out by optimizing the gas pressure in the HCF for maximum pulse compression in the 185–250 W regime across 25–200 kHz, as summarized in Fig. 1. Almost identical SHG-FROG traces and power stability measurements of these compressed pulses can be found in Figs. S2 and S3. This HCF filled with N2 displays high-power stability with 0.19% RMS power fluctuations over 2 h of 3.92 mJ pulses at 196 W input power and 80% fiber transmission and continuously runs in the lab on a daily basis without degradation.
A second set of experiments was carried out in N2 with a constant pressure of 1.5 bar and results are given in Fig. 2. The goal is to investigate the effects of molecular heating on fiber performance at high average power. Thus, we measured the repetition rate dependence of pulse breakdown, and the average power dependence of transmission, while demonstrating significant spectral broadening at 218 W. Output pulse breakdown was detected through SHG-FROG measurements as spectral and temporal instabilities within a FROG trace (see Supplement 1 for details). Temporal breakdown typically distorts the temporal and spatial properties of a pulse [38] in unison. Surprisingly, as seen in Fig. 2(a), the breakdown occurs at 3 mJ of energy regardless of the repetition rate. Furthermore, Fig. 2(b) shows that a constant transmission of ≈70% was sustained before the onset of temporal breakdown, contrary to the findings of previous work in N2 that molecular heating dramatically reduces transmission and bandwidth at higher average powers [35]. Transmission grows gradually with average power due to thermal lensing altering fiber coupling as discussed further in Supplement 1. The bandwidth achieved in N2 is shown in Fig. 2(c) and it is 1.3× wider at 1/e than that of Kr at 1.7 bar. However, we observed that Kr can operate at a higher fiber pressure than N2, 2.4 and 1.5 bar, respectively, without temporal breakdown of the output pulse at 250 W. Results with 1.5 bar of Ar are shown as a reference. Simulations of nonlinear pulse propagation through Kr and N2 in a HCF using Luna.jl software produce bandwidths with strong agreement with our measurements, as seen in Fig. S5 [39].
Fig. 3. Comparison transmission efficiency and pulse broadening in gasses N2, O2, and N2O for 100 kHz, 200 kHz, and 1 MHz repetition rates. (a) Transmission as a function of input power. (b) Transmission vs log of pulse energy. Legend is on the top right. (c) Symmetric spectra from N2 at 136 W and 245 W. Largest symmetric and asymmetric spectra generated in O2 at 81 W, 136 W and in N2O at 27 W, 54 W, respectively, with light/dark spectra for high/low power. Black spectra are that of the input pulse.
Our findings are in contrast to previous studies that generated broad red-shifted SRS spectra but could not overcome an average input power beyond 25 W (N2O) for any molecular gas [36]. To understand our results and their relation to other works, we performed a further transmission and broadening study of N2 with two other molecular gases, O2 and N2O, as illustrated in Fig. 3. O2 and N2O are useful comparisons, having similar ionization potentials but very distinct nonlinear indices and ro-vibrational state densities [23,40].
At these high average powers for a given repetition rate, O2 undergoes transmission loss and mode breakdown sooner than N2. Figure 3(b) is the same data as in Fig. 3(a), but plotted in energy per pulse rather than average power. As seen in Fig. 3(b), O2 withstands over twice the pulse energy of N2O without undergoing transmission loss. This shows that strong field ionization is not the primary cause of transmission loss because O2 has a slightly lower ionization energy at 12.07 eV than N2O with 12.89 eV. On logarithmic scale, it can be clearly seen that N2O, O2, and N2 are capped in the amount of broadening at three very different ranges of energy per pulse. Figure 3(c) shows the broadened spectra compared to the input spectrum for the three molecules at two powers indicated in each panel. Although the N2 spectra remain symmetric, the broadened spectra for O2 and N2O are largely asymmetric, favoring red wavelengths. This is indicative of SRS-induced broadening, instead of SPM [29]. N2 is then free of significant SRS heating and, therefore, experiences transmission loss from pulse energy like a noble gas. On the other hand, molecules undergoing Stokes Raman transitions in ro-vibrational manifolds lead to excitation. If such excitations are long-lived, the molecule does not return back to the ground state in the time between pulses, leading to residual heat being deposited. This repetition-rate-dependent heating explains the loss in transmission to pulse energy experienced by N2O. A plausible explanation for transmission loss is thermal lensing at the fiber entrance, which results in unreliable coupling [25,36,41].
We propose an explanation of our results based on cascaded SRS molecular heating that reveals previously unidentified high-power capabilities of molecules. The amount of SRS a molecule undergoes is directly influenced by the density of states in the vibrational manifold and the bandwidth of the laser. Stokes SRS processes couple two energy levels with two different photons from within the bandwidth of a single pulse. One photon is absorbed, exciting a virtual state, while the second photon drives stimulated emission. As seen in Fig. 4(a) N2O has an exceptionally dense manifold of ro-vibrational states in comparison to N2 and O2 in addition to a substantially lower first vibrational level. An explanation of state density calculations is given in Supplement 1 [42,43]. The dependence of SRS transitions on ro-vibrational state density and pulse bandwidth is shown in Fig. 4 and reveals how the density of states determines the maximum amount of bandwidth that can be generated before laser-induced ro-vibrational coupling occurs.
Fig. 4. (a) Rotational-vibrational energy levels for molecular gasses N2O, O2, and N2. First 20 odd number molecular rotational states (colored horizontal lines) superimposed on vibrational states (wider black lines). Only odd rotational states are plotted as Raman selection rules for linear molecules require ΔJ=±2. The population distribution of each gas at room temperature (300 K) is displayed vertically on the left of every gas’s density of states. Energy from 1/2 peak population at room temperature to first vibrational state is given. (b) Bandwidth edges at 1/10 max intensity of pulses broadened HCF with 1.5 bar of N2 (red), O2 (yellow), and N2O (blue) are shown as a function of power. Spectra corresponding to the largest ro-vibrational energy transition gap Δ? in each molecule are displayed as the power at Δ? bandwidth is reached.
We argue that molecular state density is relevant when the bandwidth is large enough to cover the spacing between the first excited vibrational level and the next-lower-lying rotational states, as denoted by Δ? in Fig. 4. For gasses N2O, O2, and N2 this SRS limits the ro-vibrational transition Δ?=3.8meV, 11.8 meV, and 16.6 meV, respectively, following rotational Raman transitions for linear molecules ΔJ=±2 [44]. Therefore, Δ? acts as an intuitive benchmark for the minimum bandwidth needed to drive cascaded SRS. Once this climbing process starts and rotational excitation reaches the first excited vibrational state, internal conversion couples the rotational states to the vibrational manifold [45–47]. This process can be repeated to reach higher vibrational states. For higher pulse repetition, the molecule remains in the vibrational states before it can relax and heat ensues. Therefore, as pulse bandwidth exceeds Δ?, cascaded SRS heating becomes unbounded, capable of exciting vibrational states.
To further make this point, the progression of spectral broadening in each gas as a function of input power is displayed in Fig. 4(b) and corresponds to the transmission data of Fig. 3. This allows a qualitative measurement of the prevalence of SRS in each gas at a given power through the degree to which a spectrum is red-shifted. SPM broadening is symmetric for a pulse with temporal symmetry. On the other hand, self-steepening deforms a pulse as the center peak moves slower through most media [48,49] yielding blue-shifted broadening. We thus can determine the relative prevalence of self-steepening, SPM, and SRS in a spectrum by considering the direction of shifts in center wavelength. It is also of note that molecular alignment occurs due to Raman transitions between rotational levels, but the degree of alignment is diminished for vibrationally excited states. In addition, increasing the temperature of all linear molecules has been shown to increase the threshold intensity needed for alignment [50,51].
Figure 4(b) clearly shows the predominance of red shifting in spectral broadening and how it differs greatly for each gas. To illuminate this, the Δ? of each molecule is given in bandwidth and displayed as a spectrum at the average power where the Δ? bandwidth is reached for each gas. N2 just reaches the Δ?N2 bandwidth at 250 W, which we accredit to the reason why the N2 spectra lack noticeable SRS red shifting, and the broadening of N2 with a greater bandwidth at similar pulse energies is known to create extreme red shifting [29]. While N2O has such a small Δ? that the input pulse is already broad enough to drive SRS transitions beyond the first excited vibrational level, losses occur soon after. O2 reaches Δ?O2 of bandwidth near 50 W and is therefore able to accommodate greater powers than N2O. Therefore, we submit that broadening in molecule-filled HCF occurs through both Kerr and SRS processes, but for bandwidth <Δ? heating is limited as SRS transitions to the first vibrational state are suppressed. With this in mind, one can explain why we are able to couple hundreds of watts in average power compared to previous studies since our starting pulses are of ps in duration vs 100–300 fs.
One of the most direct demonstrations of pulse quality is through a very high nonlinear process such as high-harmonic generation (HHG). In Fig. 5, 52 W of a total of 160 W output power, broadened in N2, and compressed to 136 fs at 200 kHz, were used to drive HHG in Ar. This leaves 108 W of additional compressed power for use in parallel experiments. As harmonics get sharper in energy with consecutive periodic sources, our 35 optical cycle long pulses produce XUV pulses with bandwidth <90meV and we believe they are ideal for photoelectron spectroscopy experiments.
Fig. 5. High-harmonic-generation spectra from 200 kHz pulses shown in the FROG trace of Fig. 2(a).
3. CONCLUSION
We have demonstrated pulse broadening and compression in a molecule-filled HCF at 10 times the previously recorded power for any molecular gas, reaching output powers of 218 W at 200 kHz. Input 1.3 ps pulses are compressed to 126 fs with 80% hollow core fiber transmission with high pulse quality, demonstrated through HHG with only 52 W of power at 200 kHz. A comparison is made between the gases N2, O2, and N2O. This study yielded a framework for the interplay between bandwidth and ro-vibrational coupling as a limiting factor for broadening in molecular gases. More precisely, in the absence of SRS or when SRS is limited, molecules behave as atoms in terms of broadening. That is, broadening is limited by the input energy per pulse. For SRS-dominated broadening, the level spacing between the rotational levels of the ground vibrational manifold and the first excited vibrational state seems to be the limit in bandwidth that can be reached at high repetition rates, due to heat deposition in the molecule and consequent loss in transmission. This fact explains why it is possible to couple and broaden >250W of average power in a molecule-filled HCF with ps-long pulses and still achieve a factor of 10 in compression and high transmission efficiency.
Our findings can have strong implications for intense, high-repetition-rate, pulsed ps laser propagation in the atmosphere where the dominant species are N2 and O2. Therefore, we believe our findings will guide future directed-energy laser atmospheric propagation studies and design.
