Highly efficient nonlinear compression of mJ pulses at 2 μm wavelength to 20 fs in a gas-filled multi-pass cell

Within this work we demonstrate the highly efficient nonlinear spectral broadening and subsequent temporal compression of 1.49 mJ pulses at 101 kHz repetition rate from an ultrafast thulium-doped fiber laser system employing a gas-filled multi-pass cell (MPC). To achieve spectral broadening, we use a krypton and helium-filled Herriott-type MPC with highly reflective broadband dielectric mirrors. The spectrally broadened pulses are subsequently compressed using fused-silica plates, resulting in a pulse duration of 20 fs and an overall excellent transmission of 96%. Furthermore, the beam quality is preserved up to the maximum output power of 144 W. It provides, to the best of our knowledge, the highest average power with few-cycle pulses at 2 µm wavelength with almost 10 times more pulse energy and 3 times more average power than previous 2 µm MPCs, enabling future secondary source experiments.


Introduction
In recent years, the field of ultrafast lasers in the short-wavelength infrared (SWIR, 1.4 µm-3 µm) region has experienced significant growth and has emerged as a topic of extensive study due to its numerous applications.Such SWIR driving sources are a promising route for secondary source experiments.The investigation of frequency conversion techniques to generate mid-infrared [1] or terahertz radiation [2], along with the exploration of photoionization regimes [3], hold significant scientific interest.In particular, high-harmonic generation (HHG) is of high interest to address the soft x-ray region, especially the 'water window' regime [4].Compared to the techniques established in the 1 µm wavelength range, the longer wavelengths of SWIR offer fundamental advantages for nonlinear frequency conversion processes, such as an increased phase-matching cutoff energy in the case of HHG [5].However, as shorter pulse durations are linked to an increased conversion efficiency, few-cycle pulses are advantageous [6,7].Exceeding the threshold of required photon flux for experiments in the desired wavelength range poses a substantial hurdle, as the reduced efficiency of long-wavelength driven HHG requires a high input average power in addition to the short pulse duration.A prevalent approach to address short pulse durations in the SWIR region is optical parametric chirped pulse amplification (OPCPA).It has been shown to be capable of sub-20 fs pulses [8,9] or more than 100 W average power [10].The latter case, where conversion efficiencies reach a maximum of 16%, distinctly illustrates the drawback in efficiency resulting from the pumping mechanism typically initiated from 1 µm wavelength.Besides OPCPA systems, a promising solution for achieving high average power ultra-short pulses around 2 µm is to use active gain media such as holmium-or thulium-doped materials in chirped-pulse amplification systems [11,12].However, the bandwidth of these gain media does not support the desired pulse durations directly.To achieve further pulse shortening, pulse post-compression is essential.State-of-the-art nonlinear pulse compression in the SWIR spectral region is realized employing thin plates or waveguide based approaches, such as normal dispersion fibers or noble-gas-filled hollow-core fibers or capillaries [13,14].However, multi-pass cells (MPCs) with a nonlinear element or gas have recently been proven as an alternative approach for nonlinear post-compression, providing high throughput efficiency, excellent beam quality preservation, spatially homogenized spectral broadening as well as being insensitive to beam-pointing and beam-profile variations [15][16][17][18][19]. Just recently, the first MPCs operating in the 2 µm regime with subsequent pulse compression have been demonstrated [20,21].

Method
The most commonly used geometry for MPC is a Herriott cell comprising two concave mirrors with identical radius of curvature R, separated by a distance L that satisfies the stability condition L < 2R [22].The off-axis propagation in the Herriott cell leads to a circular spot pattern on the mirrors.2R−L .To avoid both damaging the mirrors as well as ionization in the focal plane, the spot sizes have to be large enough, therefore the ratio of the corresponding beam diameters is crucial.Moreover, for a constant L/R, the eigenmode area at every point in a Herriott-cell can be enlarged by increasing the factor of λ • L. Hence, the mode volume and pulse energy can be scaled proportionally with distance and wavelength [20] maintaining conditions for spectral broadening, ionization and laser-induced damage threshold (LIDT) limits.The latter one also benefits from a longer wavelength λ as the LIDT typically increases with λ, provided the damage mechanism remains unchanged within the evaluated spectral range [23].An additional benefit of longer wavelengths arises from the elevated ionization threshold resulting from reduced photon energy, which renders effects like absorption or beam deterioration less probable [24].The spectral broadening factor in the dispersion-free and absorption-free case is primarily dependent on the nonlinear phase ϕ nl ∝ n 2 P/λ 2 ∝ P/P crit with the peak power P and the critical power for self-focusing P crit of the nonlinear gas [15].As the nonlinear refractive index n 2 exhibits only small wavelength dependence between 1 µm and 2 µm [23], doubling the wavelength necessitates a fourfold increase in n 2 to maintain the spectral broadening factor.This can be accomplished by either increasing the gas pressure or adopting an alternative nonlinear medium.

Results
In this work, we report on the first experimental combination of a thulium-doped fiber chirped-pulse amplification system (Tm:FCPA) with an all-dielectric mirror, gas-filled MPC demonstrating the first table-top 20 fs laser system with >150 W of average power in the SWIR regime.The driving laser system is described in detail in [12].It utilizes four coherently combined Tm-doped fiber amplifiers, delivering output pulses with pulse energies up to 1.76 mJ at a repetition rate of 101 kHz (178 W average power) and a pulse duration as low as 80 fs.The spectrum is centered at 1930 nm and has a bandwidth of 120 nm at −20 dB.The laser beam is mode-matched to the eigenmode of a gas filled Herriott-cell composed of two curved broadband mirrors with a radius of curvature of 750 mm and |group delay dispersion (GDD) (1675-2125 nm)| <25 fs 2 separated by 1443 mm.All mirrors in the setup are dielectric mirrors suitable for high average power scaling.Due to the short input pulse duration of the laser, a moderate number of 15 passes (beam waists) in between the cavity mirrors is sufficient for spectral broadening.In the absence of the Kerr-lensing effect, the beam diameters of the Gaussian eigenmode on the cavity mirrors and in the waist are 3.03 mm and 0.59 mm, respectively.The setup is enclosed in a vacuum tight vessel made of standard vacuum components (figure 1) and is designed to operate at pressures below 1 bar to simplify the design.The chamber is filled with krypton as the primary gas to collect sufficient nonlinearity while remaining below the ionization limit.Helium was added to increase heat dissipation and prevent potential thermally induced drifts.Prior to filling, it is necessary to evacuate the chamber to remove residual water vapor, that can lead to absorption at certain spectral proportions severely degrading the temporal and spatial properties of the propagating pulses [25].The laser beam is directed in and out the roundtrips between the two cavity mirrors with the help of two scraper mirrors.The mode-matching to the eigenmode of the Herriott-cell is achieved using a combination of three focusing/defocusing antireflective-coated lenses, while the output is collimated by a curved mirror with a radius of 4500 mm before exiting the pressure vessel through a 5 mm thick anti-reflection (AR) coated fused silica window.Afterwards, the beam gets sampled by an optical wedged fused silica plate, whose first wedge reflection passes through a 1 mm thick fused silica window before reaching the diagnostics, while the main part of the beam again passes through a 5 mm AR-coated fused silica window before reaching the thermal power sensor.Fused silica exhibits negative dispersion over the used wavelength range, with a group velocity dispersion of −86.3 fs 2 mm −1 at 1930 nm [26].This results in a GDD of −518 fs 2 at 1930 nm for 6 mm of fused silica in front of the diagnostics, which finally compresses the spectrally broadened pulses.

Experiment with reduced gas pressure
In the first experiment the Tm:FCPA delivers an average power of 178 W and a pulse energy of 1.76 mJ.The pulse duration and delivered peak power is estimated to 86 fs and 15 GW respectively by means of a previous second-harmonic frequency-resolved optical gating (SHG-FROG) measurement, which is comparable to the value stated in [12].This beam is then passed through the MPC filled with 350 mbar helium and 200 mbar krypton, corresponding to P/P crit = 0.2, before being compressed by the fused silica.The power at the MPC output was measured to be 165 W, resulting in a transmission efficiency of 93%.The dispersion per pass of the 350 mbar helium amounts to 0.2 fs 2 [27], while 4.6 fs 2 are estimated for 200 mbar krypton based on the extrapolation of the Sellmeier formula taken from [28].The GDD of the above mentioned coating is designed to oscillate around 0 fs 2 rendering the dispersion impact minimal.Thus, the propagation is considered dispersion free, as confirmed by simulation.The broadened spectrum was measured using an optical spectrum analyzer and shows the characteristic signature of self-phase modulation (figure 2).The −20 dB bandwidth of 341 nm supports a Fourier-transform limit (FTL) FWHM pulse duration of 30 fs.To evaluate the compressed pulse shape and duration a commercial TIPTOE device (sourceLAB) [29] is employed.The reconstruction algorithm converged with a RMSE of 3.8 • 10 −5 between the measurement and the reconstruction to a FWHM pulse duration of 30 fs (figure 3).This aligns well with the FTL of the measured spectrum within the respective measurement accuracies.With these results, the spectral broadening factor comparing the spectral bandwidths at −20 dB was measured to be ∆ω out /∆ω in = 2.8 and the temporal compression factor concerning the FWHM was determined to be τ in /τ out = 2.8.The resulting peak power enhancement of 2.5 is determined by comparative analysis between the FWHM obtained from the TIPTOE measurement and the prior SHG-FROG measurement, assuming an equivalent transmission-corrected integrated area of the pulses in the same time interval.The estimated peak power after compression is approximately 37 GW.Additionally, a 2D numerical simulation of the nonlinear compression stage was conducted using the measurement from the SHG-FROG as input.The simulation is based on solving the nonlinear Schrödinger equation, including dispersion and self-steepening with a total nonlinear phase of 1.2 π rad.The pulse compression is modeled by applying a phase equivalent to 6 mm fused silica based on Sellmeier formula [26].To assess the effect of the spectral broadening and temporal compression on the beam quality, a M 2 -measurement was conducted.The beam quality M 2 was measured and evaluated in accordance with the ISO 11146-1:2021 utilizing an indium-antimonide chip-based camera to M 2 x = 1.3 and M 2 y = 1.1.The minor deterioration in beam quality in x-axis is attributed to beam clipping within the cell (figure 4).Given that the setup is intended for future secondary source experiments, the power and pulse-to-pulse stability are crucial.The relative intensity noise was measured to be 1.17%, using a 12-bit oscilloscope and an InGaAs photodiode over a time interval of 100 ms.The signal was sampled with 2.5 GS s −1 and filtered with a 50 Ω and 48 kHz low-pass filter to eliminate the noise above half of the repetition rate of the laser.The variation of the pulse peaks was Fourier transformed and integrated in a frequency range from 20 Hz to 50 kHz.Finally, the long-term stability after compression was evaluated by tracking the system's output power over more than 2 h using a thermal sensor with a sampling rate of 1 Hz (figure 5).The laser system and pulse compression have a high stability with a mean value of 164.3 W with 0.25% rms variation over the given measurement period.

Experiment with increased gas pressure
In a second experiment, the pressure of krypton was raised to 550 mbar, while keeping the pressure of helium at 350 mbar.In this non-contiguous measurement campaign, the laser system delivered an input power of 150 W corresponding to a pulse energy of 1.49 mJ with a pulse duration of 97 fs, resulting in P/P crit = 0.41.The output power was measured to be 144 W, equivalent to a transmission efficiency of 96%.Employing the same measuring devices as above and the same 6 mm fused silica as a compressor, the reconstructed pulse duration of TIPTOE was measured to be 20 fs (figure 7) with an RMSE of 9.4•10 −5 , which corresponds to a temporal compression factor of 4.9.The −20 dB bandwidth of the spectrum was 536 nm (figure 6), supporting a Fourier-limited pulse duration of 20 fs, corroborating the retrieved pulse duration considering the respective measurement accuracies.The presence of steep slopes on the outer part of the spectrum can be seen, which were induced by the limited bandwidth supported by the dielectric coating (figure 6).The gas dispersion per pass was calculated to be 12.8 fs 2 , which in combination with the mirror GDD is still small enough to be considered as dispersion-free propagation.Using the same methodology as described earlier, the peak power enhancement is determined to be 4.6, with an estimated resulting peak power of 49 GW.The same numerical simulation as described above was carried out with a total nonlinear phase of 2.1 π rad and 4 mm of fused silica as compressor.The beam quality M 2 is measured to be M 2 x = M 2 y = 1.1.The improved beam quality and transmission are assigned to the elimination of clipping within the cell.

Discussion
Further pulse compression is constrained by the supported high-reflectivity and low-dispersion bandwidth of the coatings, resulting in reduced transmission of the MPC as the spectrum is further broadened.To address this issue, either a broader coating design at the potential expense of reduced LIDT or an alternative mirror approach such as enhanced metallic mirrors [18] or dielectric mirror pairs [30] should be pursued.The chosen compressor in terms of fused silica turns out to be an excellent compression scheme in this wavelength regime due to its ease of implementation and adjustment.A recent publication of Wang et al demonstrated that this compression approach allows compression (in combination with waveguide based spectral broadening) down to 10 fs [14].However, the potential for further pulse compression might be limited by the higher-order dispersion exhibited by fused silica.In order to accommodate higher pulse energies, the layout in terms of mirror distance should be adjusted to allow for larger beam sizes on the mirror as the fluence has already reached 70% of the safe value of 0.1 J cm −2 specified by the manufacturer.At the waist, 80% of the theoretical ionization value derived from the model in [24] was reached.This constraint can be addressed by opting for a nonlinear medium with a higher ionization threshold at an adapted pressure, such as argon or increasing the length of the MPC.Moreover, it is anticipated that scaling the average power should be feasible, as no thermal effects were observed during the experiment.

Conclusion
In summary, we demonstrate the first high average power pulse compression to 20 fs at 2 µm in a gas-filled MPC, with over 144 W of average power and more than 1.43 mJ of pulse energy.This represents a significant advancement compared to previous 2 µm MPC configurations, delivering a nine-fold increase in compressed pulse energy while achieving substantially shorter pulse durations.We achieved excellent long-term power stability, while preserving an almost diffraction-limited beam quality.Moreover, our setup can be easily integrated with other ultrafast 2 µm laser source, and the absence of thermal effects indicates the potential for further scaling of average power in the future.We believe these results are laying the foundation for forthcoming secondary source experiments.

2RL − 1 ,
Approaching the stability limit L = 2R the focal spot radius w 0 decreases w 2 0 = λL 2π √ while the spot radius w m on the mirror increases w 2 m = w 2 0 2R

Figure 2 .
Figure 2. Retrieved TIPTOE and measured spectrometer data for 350 mbar helium and 200 mbar krypton with an input pulse energy of 1.76 mJ.Measured input and output spectrum, retrieved output spectrum, simulated output spectrum and corresponding retrieved and simulated spectral phase.

Figure 3 .
Figure 3. Area-normalized retrieved and simulated pulse as well as the Fourier limit of the measured spectrum for 350 mbar helium and 200 mbar krypton with an input pulse energy of 1.76 mJ.

Figure 4 .
Figure 4. M 2 -measurement of the MPC output in accordance with ISO 11146-1:2021 with a gas pressure of 350 mbar helium and 200 mbar krypton with an input pulse energy of 1.76 mJ.The insets show the beam profile at different z-positions.

Figure 5 .
Figure 5.Long-term power stability measurement over 2 h utilizing a thermal power sensor with a sampling rate of 1 s.

Figure 6 .
Figure 6.Retrieved TIPTOE and measured spectrometer data for 350 mbar helium and 550 mbar krypton with an input pulse energy of 1.496 mJ.Measured input and output spectrum, retrieved output spectrum, simulated output spectrum and corresponding retrieved simulated spectral phase.

Figure 7 .
Figure 7. Area-normalized retrieved and simulated pulse as well as the Fourier limit of the measured spectrum for 350 mbar helium and 550 mbar krypton with an input pulse energy of 1.49 mJ.