Until recent years, filamentation of femtosecond mid-infrared (mid-IR) pulses in ambient air remained a long-standing challenge because of the lack of high-peak-power sources capable of exceeding the critical power of self-focusing which scales quadratically with the wavelength [1]. The critical power of self-focusing for femtosecond 800 nm driving pulses in ambient air, in dependence on the pulse duration, was evaluated to be $\sim 5–10\mathrm{GW}$ [2] which, when applying ${\lambda }^2$-scaling law, results in 125–250 GW for 3.9 μm pulses. Following a steady progress in the development of mid-IR optical parametric chirped pulse amplification (OPCPA) technology [3], the first successful demonstration of mid-IR filaments in ambient air was recently reported [4,5]. Recent numerical studies [6,7] reveal that substantially lower ionization rates cause significantly smaller electron plasma densities in mid-IR filaments as compared to the case of filaments generated by more common 800 and 1030 nm near-infrared (near-IR) drives. Next to lower plasma density, other factors, such as saturation of higher-order Kerr nonlinearity terms [8], shock driven walk-off of generated harmonics [7], anomalous dispersion [9], or thermal gas density gradients [10,11] might play a non-negligible role in filamentation of mid-IR pulses. Furthermore, through numerical simulations [6,12] it was demonstrated that, since a mid-IR spectral range contains numerous vibrational resonances, energy losses due to the absorption of the spectral components generated in a filament as a result of spectral broadening need to be considered next to ionization, rotational Raman excitation, and plasma absorption [13,14]. However, in Refs. [6,12], self-phase modulation (SPM) was considered as the main mechanism of spectral broadening, whereas stimulated Raman scattering (SRS) was not included in the models. Here, by means of extensive experimental studies of filamentation of 3.9 μm pulses in air, we identify that SRS is responsible for the enhancement of dynamic absorption by ${\mathrm{CO}}_2$ molecules and, therefore, plays a key role in governing energy losses during filamentation. In addition, as filamentation is usually assisted by external focusing, we show that the focusing strength strongly affects the plasma density inside a mid-IR filament and discuss its influence on the spectral dynamics and related energy losses.

Experiments were performed with a hybrid OPA/OPCPA system described in detail in Ref. [3]. In order to reach peak powers exceeding the critical power of self-focusing in mid-IR, the system was upgraded by installing an additional OPCPA stage non-collinearly pumped by 700 mJ, 70 ps pulses originating from a Nd:YAG amplifier [Fig. 1]. In this additional OPCPA stage, based on a potassium titanyl arsenate (KTA) nonlinear optical crystal, idler 3.9 μm pulses are amplified to an energy exceeding 45 mJ, which is reduced to 30 mJ during compression in a grating compressor with the transmission efficiency of 66%. As pulses are compressed to a duration of 90 fs, peak powers higher than 330 GW are achieved.

 

Fig. 1. Layout of the upgraded OPA/OPCPA system and the experimental arrangement with an open-ended gas tube; BD, beam dump; KTA, Brewster-angle cut potassium titanyl arsenate crystal; ${\mathrm{CM}}_1$, spherical mirror; ${\mathrm{C}}_1$, open-ended gas cell; ${\mathrm{W}}_1$, ${\mathrm{CaF}}_2$ wedge.

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Filaments in ambient air were generated by focusing 3.9 μm pulses with spherical mirrors having focal lengths ranging from 0.25 to 7 m. For the characterization of generated filaments, we monitored the energy transmitted through the filament, ionic plasma density, side plasma luminescence, spectra and temporal profiles of pulses, as well as a variation of the beam profile along the filament. The spectra were recorded using a scanning monochromator (Digikrom, CVI) and a liquid nitrogen cooled InSb photodetector. Temporal pulse profiles were determined by a second harmonic generation frequency-resolved optical gating (SHG-FROG) apparatus, and spatial beam profiles were detected with a pyroelectric beam profiling camera (Pyrocam III). Relative density of ionic plasma generated as a consequence of ionization during filamentation was measured with a plasma capacity probe [15], consisting of two flat $1\mathrm{cm}\times 1\mathrm{cm}$ copper electrodes separated by a distance of 1 cm and charged to 2 kV DC voltage. A signal governed by the current produced by ${\mathrm{O}}_2^{-}$ and ${\mathrm{O}}_2^{+}$ ions gives information about the plasma density on a microsecond time scale [16]. In addition, side plasma luminescence was recorded with a digital photo camera (Canon 350D). The luminescence is caused mainly by neutral (excited by an electron impact) and by ionized ${\mathrm{N}}_2$ molecules and takes place on a nanosecond time scale, i.e., before the plasma channel expands, which allows us to monitor both the diameter and the length of the filament.

Similar to the case of near-IR filamentation [17], plasma density, spectral, and structural transformations in mid-IR filaments were found to be strongly dependent on the focusing strength. When 30 mJ pulses are hard-focused with spherical mirrors of $f\le 0.75\mathrm{m}$, a donut-like beam profile is observed after the filament. In this case, the filament is evidenced by a bright plasma channel. Spectra recorded in the periphery of the donut-shaped beam feature strong plasma blueshift, with the blue wing of the spectrum reaching a wavelength of 2 μm [top panel of Fig. 2(a)]. In this case, around 30% of the energy is transferred into wavelengths below 3 μm, as determined by blocking the mid-IR radiation by a 1 cm thick BK7 substrate. The spectrum recorded in the central part of the beam [bottom panel of Fig. 2(a)] extends from 3.5 to 4.1 μm, i.e., it does not exhibit any substantial spectral broadening, which reveals that the donut-shaped beam profile is caused by plasma refraction. The steady spectrum in the center of the beam corresponds to the leading front of the pulse, wherein the intensity which is necessary for plasma generation, is not yet reached. By increasing the focal length ($0.75\mathrm{m}<f<2.5\mathrm{m}$) both ionic plasma manifestation and blue-sided spectral broadening become less pronounced, and the beam retains its spatial quality, even though the pulse energy is increased. In the case of loose focusing ($f=7\mathrm{m}$), when plasma luminescence is not detectable, the spectral dynamics is similar in the center and at the periphery of the beam and is dominated by a redshift of the spectrum [Fig. 2(b)], typical for the case of molecular gases and attributed to SRS [18].

 

Fig. 2. Spectra and beam profiles recorded at the distance of 0.33 and 8.5 m from the spherical mirrors of (a) $f=0.25\mathrm{m}$ and (b) $f=7\mathrm{m}$; the gray shaded area represents the original spectra; the spectra were recorded in the center and at the edge of the beam (indicated by the numbers); the red dashed line in the top panel (a) represents the transmission spectrum of a 1 cm thick BK7 window.

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In the case of loose focusing, a rather weak plasma generation, evidenced by vanishing electrical signal and the absence of visible luminescence, was observed. In order to confirm filamentation of the mid-IR pulses under these circumstances, we examined the evolution of the beam profile along the propagation [Figs. 3(a) and 3(b)]. The beam profile evolution in the vertical ($y$) and horizontal ($x$) directions was recorded for compressed pulses, filamentation takes place, and for attenuated long chirped pulses (stretched to $>3\mathrm{ps}$ pulse duration by detuning the OPCPA compressor), which corresponds to the case of linear propagation. In the case of stretched pulses, the measured beam radii correspond well to the calculated radii evolution of a Gaussian beam [Figs. 3(a) and 3(b)]. Note that the initial beam profile is slightly elliptical, and the beam is astigmatic, exhibiting different divergences in ($x$) and ($y$) directions. By contrast, when compressed pulses are focused by an $f=7\mathrm{m}$ mirror, beam radii rapidly shrink to sub-2 mm and remain at this level for several meters. In the case of compressed pulses, the minimum beam radius of $\sim 0.4\mathrm{mm}$ at the $1/{\mathrm{e}}^2$ level was measured along both transverse axes at the distance of $\sim 550\mathrm{cm}$ from the focusing mirror. As can be seen from Fig. 3(c), self-symmetrization of the beam profile takes place already at the position of the focusing mirror and is sustained for more than 5 m. At the distance of $\sim 6\mathrm{m}$, two distinct side-lobes emerge along the long axis of the ellipse representing the initial beam [right most profile in Fig. 3(e)]. In contrast to multiple filamentation caused by modulation instability, this beam profile evolution is reproducible from shot to shot and is presumably caused by the nucleation of low-intensity structure distributed around the filament core [19]. The observed beam self-symmetrization in the case of 30 mJ, 90 fs pulses reveals that an arrest of the intensity takes place, which is a robust feature of filamentation.

 

Fig. 3. (a), (b) Correspondingly, the evolution of the radii of the beam in y- and x- directions at $1/{\mathrm{e}}^2$ level and ellipticity along the propagation of compressed (open red dots) and stretched to $>3\mathrm{ps}$ (open black squares) pulses, the solid blue lines represent calculated beam diameter and ellipticity evolution in the case of linear focusing with an $f=7\mathrm{m}$ spherical mirror; (d), (e) beam profiles measured accordingly (from left to right) at the position of the focusing mirror, minimal beam-waist position, and at the distance of 8 m from the focusing mirror for (d) stretched and (e) compressed pulses.

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Capacity probe measurements [Fig. 4(a)] reveal that with the softening of focusing from $f=0.25\mathrm{m}$ to $f=7\mathrm{m}$, both the current between the electrodes, resulting in a voltage drop on a resistor, and both integrated (not shown) and peak plasma luminescence decrease by a factor of more than 20. Note that in the case of $f=7\mathrm{m}$ plasma luminescence was not detectable.

 

Fig. 4. (a) Dependence of the maximum signal on the electrodes of the plasma capacity probe (open circles) and luminescence intensity (solid circles) on the strength of focusing; (b) dependence of the energy losses on the strength of focusing; the shadowed area corresponds to the focusing range at which losses decrease with the softening of the focusing.

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By contrast, the energy losses during filamentation, with respect to the focusing behave quite differently [Fig. 4(b)]. As focusing softens from $f=0.25\mathrm{m}$ to $f=1.5\mathrm{m}$, the losses decrease from 17% to $<10\%$, which follows the trend of decreasing plasma signature. With further softening of the focusing toward $f=7\mathrm{m}$, in which case the plasma density is rather low, the losses surge to the level of $>35\%$.

To examine the losses in the case of 7 m focusing, we generated filaments in the main constituent parts of atmospheric air, and monitored spectra and ionic plasma signals. The compressor of our OPCPA system in each case was adjusted for the highest filamentation losses. In order to avoid additional nonlinear effects in the cell windows, the experiments were performed in a 4 m long tube with open ends (Fig. 1), as gases under investigation were flown through the tube with slight overpressure.

The spectral broadening in pure ${\mathrm{O}}_2$ and ${\mathrm{N}}_2$ was found to be more efficient than in ambient air and is dominated by a redshift due to SRS [18]. In Ar, spectral broadening in the mid-IR is more symmetric and is caused mainly by SPM, without any significant plasma blueshift which was reported in the case of focusing 12 mJ pulses with an $f=2\mathrm{m}$ spherical mirror into a gas cell with Ar at 4.5 bar [20].

As seen from Table 1, where the results are summarized, measurements with the capacity probe reveal weak ionic plasma generation in ${\mathrm{N}}_2$ ($\sim 10\mathrm{mV}$ signal) and four times higher in ${\mathrm{O}}_2$ ($\sim 42\mathrm{mV}$ signal), which is explainable by the lower $I_p$ of oxygen. In air, the signal of the plasma capacity probe is determined by an even more complex plasma chemistry than in the cases of pure ${\mathrm{N}}_2$ or ${\mathrm{O}}_2$. The signal in air is 17 mV, more similar in magnitude to ${\mathrm{N}}_2$. However, the energy losses, 8% in the case of ${\mathrm{N}}_2$ and 13% in the case of ${\mathrm{O}}_2$, are significantly lower than that in air ($>36\%$). The losses do not correlate with the maximum of the capacity probe signal, suggesting that they are not related to the generation of weak plasma. Furthermore, in Ar, which has an $I_p$ similar to that of ${\mathrm{N}}_2$, capacity probe measurements provide a more than 10 times larger signal as compared to the case of ${\mathrm{N}}_2$ (explainable by a substantially longer plasma lifetime in Ar [21]). At the same time, filamentation losses in the case of Ar are hardly detectable. Those observations suggest that neither plasma generation nor rotational Raman excitation of ${\mathrm{N}}_2$ and ${\mathrm{O}}_2$ [14] are responsible for the observed $>36\%$ losses during filamentation in air when filamentation is assisted by loose focusing.

Table 1. Ionization Potential ($I_p$), Concentration in Air (C), Ionic Plasma Signal (V), and Losses Measured After the Filaments Ignited in Atmospheric Gases^a

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In order to determine the origin of the losses we examined spectral, temporal, and spatial transformations of 3.9 μm pulses during filamentation (Fig. 5). The obtained data allow us to retrieve intensity evolution along the filament and to characterize filamentation dynamics in the case of loose focusing. Filamentation dynamics was found to be very sensitive to the chirp of propagating mid-IR pulses, which is subject to a separate investigation. For these particular measurements, the compressor of the OPCPA system was tuned to maximize the losses after the filament. As determined by SHG-FROG characterization, the optimal input pulses were slightly positively pre-chirped to the duration of 130 fs FWHM.

 

Fig. 5. Measured evolution of (a) the spectral shape, (b) the losses, and (c) the pulse duration and intensity during filamentation of 30 mJ pulses assisted by 7 m focusing; in (a), the distance from the focusing mirror is indicated in the panels; the area under the spectra are scaled to the pulse energy; the initial spectrum is shown by a black line in the lower panel; in the insets, the red part of the spectrum is zoomed with $\times 10$ magnification.

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As seen from Fig. 5(a), during propagation through the first 4 m of air the spectrum is only slightly transformed by a redistribution of the spectral content from the blue to the red wing [lower panel in Fig. 5(a)] which is a recognizable feature of SRS [18]. In addition, due to the anomalous dispersion of air in the spectral range of 3.6–4.2 μm [22], during this initial propagation, pulses are recompressed to 90 fs [Fig. 5(c)]. Small ($<3\%$) losses during the first four meters of propagation [Fig. 5(b)] might be caused both by the absorption of ${\mathrm{CO}}_2$ and rotational Raman excitation of ${\mathrm{N}}_2$ and ${\mathrm{O}}_2$ molecules [14].

With further propagation, the intensity sharply rises [Fig. 5(c)] which is a combined effect of pulse compression and reduction of the beam diameter [Figs. 3(a) and 3(b)]. The sharp rise of the intensity is followed by a pronounced redshift of the spectrum, which correlates with the sharp increase of the losses. The absorption coefficient of air at the wavelength of 4.26 μm, corresponding to the ${\mathrm{CO}}_2$ resonance is ${10}^{-2}{\mathrm{cm}}^{-1}$ [23], which means that nearly 2/3 of 4.26 μm light is absorbed after traveling 1 m of air. We observe intensity stabilization of the $40\mathrm{TW}/{\mathrm{cm}}^2$ level between 5 and 6 m of propagation, which is explained by a continued decrease of the beam diameter [Figs. 3(a) and 3(b)] and still growing losses. After propagation of 6 m from the focusing mirror, a noticeable spectral change takes place as the pulses undergo temporal splitting, which makes the evaluation of the intensity complicated.

As it follows from Fig. 5(a), the spectral broadening toward longer wavelengths from the ${\mathrm{CO}}_2$ absorption band is still observed for propagation distances over 5 m. We argue that SRS-driven continuous redshift cannot be the only mechanism responsible for this efficient spectral broadening. A different wave-mixing mechanism, such as SPM, must contribute to the generation of new spectral components in the red wing of the spectrum.

In conclusion, filamentation of mid-IR pulses in ambient air is strongly affected by focusing, but in a rather different way than it is known for near-IR filamentation. Experimental results suggest that the physical origin of losses and the mechanism of stabilization of the spatial collapse in mid-IR filaments strongly depend on the focusing conditions. In the case of strong focusing, the generated plasma plays a dominant role in determining spectral dynamics and losses during filamentation. In the case of loose focusing filamentation can be achieved with low plasma density. Under these conditions, although the concentration of ${\mathrm{CO}}_2$ in ambient air is in the order of 500 ppm, this atmospheric constituent plays a dominant role in determining losses during filamentation, as spectral amplitude, continuously red-shifted by rotational SRS, provides steady supply for resonant ${\mathrm{CO}}_2$ absorption. Consequently, the dynamic ${\mathrm{CO}}_2$ absorption plays an important role in filamentation of 3.9 μm pulses and, either by itself or in combination with other (nonlinear) processes, contributes to the arrest of the intensity and to the prevention of beam collapse.