Subterawatt Few-Cycle Mid-Infrared Pulses from a Single Filament

1Russian Quantum Center, Skolkovo, Moscow Region, Russia 2Physics Department, International Laser Center, M.V. Lomonosov Moscow State University, Moscow, Russia 3National Research Center "Kurchatov Institute", Moscow, Russia 4Institute on Laser and Information Technologies of the Russian Academy of Sciencies, Federal Scientific Research Center «Crystallography and Photonics»of Russian Academy of Sciences, Shatura, Moscow Region, Russia 5Photonics Institute, TU Wien, Vienna, Austria 6Center for Physical Sciences & Technology, Vilnius, Lithuania 7Department of Physics and Astronomy, Texas A&M University, College Station, TX, USA Contact Email: dima-sidorov@mail.ru

Motivated and driven by numerous applications and long-standing challenges in strong-field physics [1,2], molecular spectroscopy [3,4], semiconductor electronics [5], and standoff detection [6], ultrafast optical science is rapidly expanding toward longer wavelengths in quest for technologies enabling the generation of highpeak-power ultrashort pulses in the mid-infrared (mid-IR) range.Optical parametric chirped pulse amplification (OPCPA) has been shown to open new horizons in ultrafast optics in the mid-IR, providing a method whereby sub-100 fs pulses with energies at the level of at least tens of millijoules can be delivered at a central wavelength of about 4 μm as an output of a robust, solid-state compact light source [7].Such OPCPA-based mid-IR systems offer unique opportunities for highly efficient coherent [8] and incoherent [9] x-ray generation, enable mid-IR laser filamentation in the atmosphere [10], help achieve lasing in filaments [6] and create high-power light bullets [11], provide a bright source of multioctave high-energy supercontinua [12][13][14], and reveal unique regimes of laser-matter interactions [15] along with unexpected optical properties of materials in the mid-IR [16].
Because the parametric gain band is inevitably limited, mid-IR OPCPA sources can generate remarkably short, yet multicycle, mid-IR pulses.To satisfy the demand for few-cycle field waveforms in the mid-IR, needed to confront some of the long-standing fundamental challenges at the forefront of ultrafast optical science, the OPCPA output has to be compressed to a few-cycle pulse width with an appropriate pulse compression technology, which should be solid enough to deal with high peak powers.In the near-IR range, laser-induced filamentation is known to provide suitable scenarios of nonlinear field dynamics that enable pulse compression at high levels of peak power [17][18][19].However, since laser filamentation occurs as a result of a complicated interplay between strongly coupled ionization-assisted spatial and temporal nonlinear-optical processes [20,21], which all scale in very different ways with the wavelength [20][21][22], extending the filamentation-based pulse compression technique to the mid-IR range is not trivial.Moreover, because of the strong enhancement of plasma refraction in the mid-IR range, which has a significant influence on the properties of filaments in this spectral range [10], the answer to the question as to whether mid-IR pulses can be compressed in the regime of single filaments, i.e., without losing the spatial coherence of the mid-IR beam through multiple filamentation, is not obvious at all, remaining the focus of comprehensive theoretical studies [23,24], which shed new light on the fundamental physical aspects of filamentation.
Here, we show that the filamentation-assisted pulse compression technology can be extended to the mid-IR range, enabling the generation of subterawatt few-cycle pulses in the mid-IR.A diagram of our experiment, performed using the Russian Quantum Center source of ultrashort high-power mid-IR pulses [10], is sketched in Fig. 1.Mid-IR pulses were delivered by a laser system [10] consisting of a solid-state ytterbium laser with an amplifier, a three-stage optical parametric amplifier (OPA), a grism stretcher, a Nd:YAG pump laser, a three-stage OPCPA system, and a grating compressor for mid-IR pulses (Fig. 1).The 1 kHz, 200 fs, 1 mJ, 1030 nm regeneratively amplified output of the Yb:CaF 2 laser system is used as a pump for the three-stage OPA, which generates sub-200 fs, 1460 nm pulses at its output.These 1460 nm pulses are then stretched with a grism stretcher and used as a seed in a three-stage OPCPA, consisting of three type-II KTA crystals, pumped by 100 ps Nd:YAG-laser pulses with energies of 50, 250, and 700 mJ.The idler-wave stretched-pulse output of the OPCPA system has a central wavelength of 3.9 μm and energy above 50 mJ.After a grating compressor, the mid-IR pulses have a pulse width of about 100 fs and energy up to 35 mJ.The 3.9 μm OPCPA output is focused into a 215 cm long gas cell using a CaF 2 lens (Fig. 1), which has a thickness of 5 mm and a focal length f of 1.5-2 m, and is placed at a distance of 35 cm from the entrance window of the variable-pressure gas cell.Since water vapor can give rise to strong absorption lines within the spectral range of interest and can modify gas dispersion, the content of water vapor inside the gas cell was monitored by absorption measurements within water vapor absorption lines and was kept below 0.001%.The grating compressor of the OPCPA is adjusted in such a way as to provide the minimum pulse width behind the focusing CaF 2 lens and a 3 mm thick CaF 2 entrance window of the gas cell.A 3 mm thick BaF 2 plate is used as the exit window of the gas cell.The thickness and material of the exit window are chosen in such a way as to provide at least partial compensation of the nonlinear phase acquired by the mid-IR pulse in the gas cell.The mid-IR beam at the output of the gas cell is collimated by a spherical mirror with a focal length of 2 m.Spectral measurements in the mid-IR range are performed with a scanning monochromator and a HgCdTe detector, which is cooled with liquid nitrogen and connected to a battery power supply in order to reduce dark-current noise.For the spectral measurements in the ultraviolet, visible, and near-IR ranges, OceanOptics HR4000 and NIRQuest spectrometers are employed.
The temporal envelopes and phases of mid-IR pulses are characterized using frequency-resolved optical gating (FROG) based on second-harmonic generation (SHG).The FROG characterization of the mid-IR pulses in front of and behind the gas cell is performed on low-energy fractions of the mid-IR beam, split off from the main mid-IR beam by CaF 2 wedges inserted into the beam, respectively, in front of and behind the gas cell (Fig. 1).Inside the FROG apparatus, two identical replicas of this low-energy mid-IR beam were produced using a thin-film beam splitter to deliver FROG traces through frequency-resolved SHG in a 0.3 mm thick AgGaS 2 crystal (Fig. 1).Typical SHG FROG traces of the mid-IR pulses at the input and output of the gas cell along with the pulse envelopes, spectra, and phase profiles retrieved from these traces are shown in Figs.2(

a)-2(c).
A mid-IR driver pulse with peak power of P above the selffocusing threshold, P cr ≈ 100p 0 ∕p GW for N 2 , p being the gas pressure in the cell in bars and p 0 1 bar, induces an extended filament when loosely focused in the N 2 -filled gas cell.The filamentation of the mid-IR pulse is accompanied by a dramatic spectral broadening, giving rise to supercontinuum radiation [Figs.2(c) and 2(d)].An accurate spectral analysis of this radiation using a scanning monochromator and a liquid-nitrogen-cooled HgCdTe detector shows that, with appropriate experimental conditions, the mid-IR part of the spectrum of this filamentationinduced supercontinuum may stretch from approximately 2.6 to 5.5 μm at the level of 10 −3 of its maximum [Fig.2(d)].
To analyze the spatiotemporal field dynamics in the mid-IR filament, we use a (3 1)-dimensional model based on the field  evolution equation in the form of Eqs.(45a) and (45b) in Ref. [21] and solve this equation jointly with the equation for electron density, where the photoionization rate is calculated using the Popov-Perelomov-Terentyev version of the Keldysh formalism [20,21].Numerical simulations were performed using a message passing interface parallel programming interface and a CUDA graphic parallel architecture on the Lomonosov supercomputer cluster of Moscow State University.
To model the beam shape delivered by the mid-IR OPCPA, we assume the input beam to have a small ellipticity, with an 8∶7 ratio of the principal axes.The ionization potential for N 2 is taken to be equal to 15.6 eV.Dispersion is included through the Sellmeier equation with a standard set of constants for N 2 [25].The Raman response is modeled with a damped oscillator model [20,21] with time constants of 62.5 and 120 fs.The fraction of Raman nonlinearity in the overall nonlinear response is 0.35.As the nonlinear constants in the mid-IR are yet to be understood [1,15] and there is no good reference for such constants in the mid-IR, the nonlinear refractive index coefficients were varied in our simulations to simultaneously fit the experimental data for the spectra, pulse envelopes, and beam profiles of the mid-IR field, as well as the length and location of the filament along the propagation axis.The best fit was achieved with n 2 210 −19 p∕p 0 cm 2 ∕W and n 4 −1 10 −33 p∕p 0 cm 4 ∕W 2 [Figs.2(c), 2(e), and 3(a)-3(f )].This value of n 2 agrees well with the available data for both near-and mid-IR ranges [14,26,27].Although the n 4 value used in this work is consistent with the earlier results for n 4 in sign and order of magnitude [26,27], this parameter could not be estimated with a high accuracy in the regime studied here, as the omission of the n 4 term from the model does not lead to significant changes in the spectra, pulse shapes, and beam profiles of the mid-IR field behind the filament, affecting only the length and position of the filament.
Due to the ω p ∕ω 2 scaling of the ionization-induced change in the refractive index with radiation frequency ω (ω p being the plasma frequency), the plasma refraction of mid-IR radiation is greatly enhanced compared with that in the near-IR range.As a dramatic manifestation of this scaling, within a broad range of field intensities of mid-IR pulses, gas densities, and beam focusing lengths, a transient spatial profile of electron density induced by the leading edge of the pulse can give rise to a strong scattering of its trailing edge [Figs.4(d)-4(f )].In this regime, it is difficult to provide a uniform spectral broadening across the beam and along the pulse, needed for efficient pulse compression.Such a scenario of spatiotemporal field dynamics can be avoided, as our simulations [Figs.3(b) and 4(a)-4(c)] and experiments [Figs.3(a) and 3(e)] show, with an appropriate choice of the focusing geometry and gas pressure, helping to reduce excessive ionization-induced scattering of the trailing edge of the pulse.For our experimental conditions, this requirement dictates long focusing lengths and gas pressures below 4 bar [Figs.3(a)-3(f )].Notably, for a much tighter beam focusing, e.g., for f 0.5 m, when the mid-IR driver induces much higher electron densities near the beam focus region, plasma dispersion can give rise to pulse self-compression, similar to that observed by Reiter et al. [28].The pulsecompression ratios in this regime are, however, lower than those achieved in the filamentation regime studied here.
A typical filamentation dynamics that provides efficient and reasonably uniform spectral broadening of a mid-IR pulse along the filament and across the beam is illustrated in Figs.5(a)-5(d).The length of the ionized region inside the filament is about 75 cm.The broadening of the mid-IR part of the spectrum in this regime [Fig.5(a)] is primarily due to self-phase modulation and, to a lesser extent, ionization-induced blue shifting.The pulse self-compression observed within a small central part of the beam [Fig.5(c)] has almost no effect on the temporal profile of the pulse when integrated over the beam [Fig.5(d)].
The parameter space of filamentation-assisted pulse compression is further limited by spatial modulation instability (MI) [29], which tends to break a high-peak-power beam into multiple filaments.However, due to the λ 2 scaling of the critical power of self-focusing with radiation wavelength λ, the energies and peak powers of ultrashort pulses that can be compressed using filamentation in the mid-IR range are much higher than they are in the near-IR range.In our experiments, laser pulses with energies up to 20 mJ could be compressed in a truly single-filament regime without the beam developing signatures of higher order spatial modes [Figs.above P cr , the output beam started to develop clear signatures of mode degradation, indicative of the buildup of MIs.These signatures are clearly visible in the time-resolved beam dynamics presented in Figs.4(g)-4(i), where a beam breakup into multiple filaments is especially well pronounced toward the back of the driver pulse.Unlike plasma-induced scattering, which, in the absence of MIs, gives rise to distorted, but axially symmetric, beam profiles [e.g., Fig. 3(d)], the MIs, seeded by random fluctuations of beam intensity or refractive index, translate into beam profiles with randomly distributed hot spots.While the angular spectrum of the mid-IR filament output for the chosen filamentation parameters is close to that of a diffraction-limited beam [Fig.5(e)], MIs, building up across beams with higher P∕P cr , induce energy transfer to higher order spatial modes, leading to an irreversible degradation of beam quality and focusability [Fig.5(f )].
The shortest pulse widths and the highest pulse compression ratios were observed with P ≈ 150 GW ≈ 4P cr in experiments on molecular nitrogen at p ≈ 3 bar.Following partial chirp compensation across the supercontinuum spectrum by a 3 mm BaF 2 exit window of the gas cell, the FWHM pulse width of this mid-IR output retrieved from the SHG FROG trace of the supercontinuum pulse behind the gas cell [Fig.2(b)] is about 35 fs [Fig.2(e)].A residual chirp, primarily in the long-wavelength part of the spectrum [Fig.2(c)], translates into a pedestal, which may carry up to 30% of the total energy of the mid-IR output.An ideal compensation of this residual chirp, shown by the dashed line in Fig. 2(e), would yield a transform-limited pulse width of about 30 fs [shown by shading in Fig. 2(f)].An almost transform-limited pulse width could also be achieved by compensating the residual phase of the mid-IR supercontinuum output with the phase induced by the dispersion of 1 mm of BaF 2 [solid line in Fig. 2(f)].
The output beam profile of the compressed pulse in experiments performed with a gas cell filled with 3 bar of N 2 has a very smooth shape, displaying no signatures of beam breakup, with field intensity reaching its maximum at the center of the beam and monotonically falling off toward the beam periphery [Figs.3(a), 3(b), and 3(e)].Pulse compression is uniform across the output beam.For an input mid-IR pulse with energy of about 15 mJ and a pulse width of about 100 fs, the total energy in the compressed mid-IR output is about 13 mJ.The central, 35 fs, peak of this pulse contains about 70% of the total output energy, which corresponds to 2.7 field cycles at a central wavelength of 3.9 μm and peak power of about 260 GW.

Fig. 2 .
Fig. 2. (a), (b) FROG traces of the mid-IR pulse at (a) the input and (b) the output of the gas cell filled with N 2 .(c) The spectrum (solid line) and spectral phase (dashed line) retrieved from the FROG trace of the mid-IR pulse at the output of the gas cell and the results of numerical simulations (dashed-dotted line).The input spectrum is shown by shading.(d) The spectrum of the mid-IR supercontinuum output measured with a scanning monochromator and a liquid-nitrogen-cooled HgCdTe detector.The input spectrum of the mid-IR driver is shown by shading.(e) Temporal envelope (solid line) and phase (dashed line) retrieved from the FROG trace of the mid-IR pulse at the output of the gas cell and the results of numerical simulations (dashed-dotted line).Temporal envelope of the input mid-IR pulse is shown by shading.(f ) Temporal envelope (solid line) and phase (dashed line) obtained by partially compensating the residual phase of the mid-IR pulse at the output of the gas cell with the phase induced by the dispersion of 1 mm of BaF 2 .The transform-limited pulse supported by the entire spectrum of the mid-IR filament output is shown by shading.The 15 mJ, 100 fs mid-IR driver is focused into a gas cell filled with N 2 at [(a)-(c), (e), and (f)] p ≈ 3 bar and (d) p ≈ 2.2 bar by a lens with [(a)-(c), (e), and (f )] f 2 m and (d) f 1.5 m.

Fig. 3 .
Fig. 3. (a)-(d) Beam profiles for the mid-IR pulse at the output of the gas cell filled with N 2 at (a), (b) p 3 bar and (c), (d) p 4 bar: (a), (c) experimental results and (b), (d) (3 1)-dimensional simulations.(e), (f ) One-dimensional cuts of the experimental (solid lines) and simulated (dashed lines) beam profiles of the mid-IR pulse at the output of the gas cell filled with N 2 at (e) p 3 bar and (f ) p 4 bar.The mid-IR beam is focused by a lens with f 2 m.

Fig. 5 .
Fig. 5. Simulated dynamics of the mid-IR field in a filament induced in a gas cell filled with N 2 : (a) the spectrum of the mid-IR pulse integrated over the beam, (b) the beam profile of the mid-IR field integrated over the pulse, (c) the temporal profile of the mid-IR pulse on the beam axis, (d) the temporal profile of the mid-IR pulse integrated over the beam, and (e, f ) the angular spectrum of the collimated mid-IR beam behind the filament (solid line) versus the angular spectrum of a diffraction-limited beam (shading) for [(a)-(e)] P 150 GW and p 3 bar and (f) P 680 GW and p 4 bar.