1 Introduction

Harmonic generation of ultrashort laser pulses is one of the main processes of laser frequency conversion and has facilitated a broad variety of applications. Solid media are commonly used with high conversion efficiency, although they are limited by their size, damage threshold and absorption edge. Direct TH generation has been shown in rare gases [1], and with upcoming of high-power laser systems, HH generation became an available XUV source [2, 3]. However, TH and HH generation in gases suffer from the short interaction length. Filamentation as a dynamic self-guiding mechanism balances nonlinear effects including Kerr self-focusing, plasma defocussing and nonlinear absorption to establish an interaction length significantly larger than in linear focal geometries [4–6]. TH generation from filamentation has been demonstrated in [7–12], revealing that 95% of the energy is emitted off-center in a conical ring. On-axis emission can be considerably enhanced by disturbing the dynamics of the filament with a plasma string or a thin metal fiber perpendicular to the filament [13–15]. We recently introduced another approach by truncation of the filament with a pinhole and a steep pressure gradient, which leads to a clean on-axis beam profile of the TH and 28 dB enhancement in conversion efficiency compared to the undisturbed filament [16]. This method allows for the extraction of radiation at any position along the filament [17]. It reveals that the complex dynamics leads to intensity spikes, exceeding the limit of intensity clamping with local intensities high enough to produce HH radiation [18, 19].

Here, we present a systematic study of the spectral evolution of the fundamental, UV, and XUV spectra along the propagation axis inside a filament in air. The filament is truncated by a laser-drilled pinhole, producing a steep transition, to vacuum and removing the nonlinear medium. This stops the nonlinear interaction and forms a pressure gradient, prospering phase-matching conditions for TH generation with a clean on-axis beam profile [16]. By varying the distance between the curved mirror and the pinhole, the interaction length is systematically changed, allowing for tracking the pulse evolution and the UV/XUV generation along the filament (see also [19]).

2 Experimental set-up

Figure 1 depicts the experimental set-up. A chirped-pulse amplification system (Dragon, KM-Labs Inc.) delivers pulses with a FWHM duration of 30 fs and a pulse energy of 1.3 mJ centered at 780 nm. A variable aperture after the amplifier system trims the beam to a diameter between 5.5 mm and 7.0 mm. The laser beam is then focused by a concave silver mirror with focal length of 200 cm. Depending on the input aperture diameter, the confocal parameter is 8 to 10 mm. The focus lies within a semi-infinite gas cell (SIGC) of 90 cm length filled with 1 bar of air. Its entrance is formed by a 1-mm-thick CaF2 window far apart from the focus to avoid nonlinear interaction in the material. Inside the SIGC the peak power is about 21 GW (for an input aperture of 6.5 mm), which is well above the critical power P cr=3.2 GW necessary to start the filamentation process [20]. The end of the SIGC is formed by a laser-drilled pinhole (diameter ∼800 μm) and a transition to a rough vacuum at <10−1 mbar. A delay line is placed between the focusing mirror and the SIGC, so that the position of the geometrical focus can be shifted along the propagation axis. In this way, the length of the filament can be varied by changing the position of its onset while keeping the position of its termination fixed. This defines the position axis by the distance L between the curved mirror (CM in Fig. 1) and the pinhole.

Fig. 1
figure 1

Experimental set-up. Laser pulses from a chirped-pulse amplifier system are focused by a curved mirror (CM) into a semi-infinite gas cell (SIGC). Inside the air filled cell, a filament is formed and truncated by a laser-drilled exit pinhole. The generated radiation propagates in vacuum (<10−1 mbar) behind the pinhole. For recording XUV radiation, a second pinhole is used to realize a pressure below 5×10−4 mbar. After 1 m of propagation in vacuum, different spectrometers are used to detect the VIS, UV and XUV radiation (see text for details)

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For VIS and UV measurement, an output window (CaF2, 2 mm thickness) is placed at a distance of 1 m behind the pinhole to avoid nonlinear effects or damage. The visible part of the spectrum containing the fundamental driver pulse is recorded using a spectrometer (AvaSpec, Avantes based on 300 Lines/mm grating and 10 μm slit). Three dielectric mirrors with high transmission for the infrared and VIS spectral region reflect the UV part of the spectrum into a UV spectrometer (AvaSpec, Avantes with 1200 Lines/mm grating, 10 μm slit). In both cases, only the central part of the beam is used for spectral analysis due to the input slit size of the spectrometers.

To record XUV radiation generated inside the filament, propagation in high vacuum is necessary. Therefore, a second laser-drilled pinhole (diameter ∼500 μm) is placed approximately 10 mm behind the first one (see inset in Fig. 1). Using turbo-molecular pumps, we impose a pressure gradient behind the second pinhole down to 5×10−4 mbar, so that absorption and nonlinear propagation can be neglected. In this case, the output window is replaced by our XUV spectrometer (McPherson, 300 lines/mm grating, CCD DH420A-F0, ANDOR Technology) at a distance of 1 m behind the pinholes. Fundamental radiation is blocked by a 200-nm-thick aluminum filter before entering the XUV spectrometer.

3 Results and discussion

Figure 2 shows the generated radiation in the VIS, UV and XUV spectral range in dependence of the propagation distance L. All spectra are recorded with an input aperture behind the laser of 6.5 mm diameter. The VIS (Fig. 2a) as well as the UV spectrum (Fig. 2b) encounter a continuous broadening with increasing interaction length. The spectral gap in the UV at a wavelength around 255 nm is found independent of the distance L. Beyond L=225 cm, the spectrum extends below 240 nm and a second gap appears. In Fig. 2c, the corresponding XUV spectra are shown with harmonic orders beginning at HH 11 and the cut-off at HH 25. No HH signal was detected at propagation distances longer than 232 cm.

Fig. 2
figure 2

Spectra of (a) the VIS, (b) UV and (c) XUV radiation, recorded as function of the distance between the focusing mirror and the pinhole. The color/brightness encodes the spectral power density in arbitrary units

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The normalized integrated pulse energies extracted from the spectra are shown in Fig. 3. At a propagation distance of 221 cm, the energy of the visible and UV radiation reaches its maximum. Both decrease slowly to 50% and 20%, respectively, at a distance of 243 cm. In the XUV range, the peak energy integrated over all harmonic orders is found at 217 cm. From there it undergoes a steep decrease, reaching zero beyond L=232 cm.

Fig. 3
figure 3

Pulse energy after integration of recorded VIS (), UV () and XUV () spectra. The curves represent boxcar averages (boxcar width: 3 cm) and the data are normalized to the peak value of the average curves

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The Fourier-limited pulse durations evaluated from the spectra in Fig. 2 are shown in Fig. 4. For the VIS spectral range, the Fourier limit decreases monotonically from 25 fs down to 7 fs at a distance of 243 cm. The TH Fourier limit starts at 14 fs and decreases to 5 fs at L=227 cm. However, it remains constant for propagation distances L>227 cm.

Fig. 4
figure 4

Fourier-limited pulse durations calculated from recorded spectra for VIS () and UV () for a fixed input aperture of 6.5 mm. The red solid and blue dashed curves represent corresponding boxcar average values (boxcar width: 3 cm). The orange solid curve is the VIS Fourier limit divided by \(\sqrt{3}\)

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3.1 Discussion

Figure 3 reveals the position of the maximum pulse energy in each spectral range. The normalized energies do not include off-axis radiation, as it is cut away by the pinhole(s) and the spectrometer input aperture. Behind the maximum, the VIS pulse energy (solid red curve) decreases due to plasma absorption and multiphoton absorption [5], eventually limiting the length of an undisturbed filament.

XUV radiation is quickly absorbed in the high pressure environment of the filament. In the explored spectral range, the transmission is below 1% after 100 μm of propagation [21]. Thus, HH generation acts as a probe for the local intensity inside the filament core. The XUV pulse energy curve (dotted green) indicates the formation of an on-axis intensity spike of the driving field located at L≈217 cm—a short sub-pulse with a peak well beyond the clamping intensity formed by a spatio-temporal refocusing cycle of the filament (see [18, 19] for a detailed explanation).

The UV pulse energy (dashed blue curve) follows qualitatively the visible pulse energy curve, while slopes are steeper due to the third-order nonlinear dependence on the VIS pulse energy. The main part of TH is generated in the vicinity of the pinhole due to the pressure gradient inside the pinhole, which significantly enhances phase-matching conditions for TH generation [16]. As a consequence, the UV pulse inherits the pulse energy evolution as well as the spectral bandwidth from the generating VIS pulse. Figure 4 shows the decrease of the VIS Fourier limit due to spectral broadening during nonlinear propagation inside the filament (solid red curve) and the UV Fourier limit (dashed blue curve). For comparison, the perturbative estimation (orange solid curve) is calculated by dividing the VIS Fourier-limited pulse duration by \(\sqrt{3}\). The UV Fourier limit follows the perturbative estimation quite well, confirming that the source of the broad UV spectrum is the already large bandwidth of the generating VIS spectrum. Note that a small deviation between the UV Fourier limit and the perturbative estimation exists. It is most pronounced at the position of the on-axis spike in fundamental intensity. The net energy contained in the spike is too small to observe its Fourier limit in Fig. 4. Nevertheless, due to the high spike intensity, the TH Fourier limit is below the perturbative estimation of the main VIS pulse. In contrast to the XUV spectral range, UV radiation is not absorbed and propagates further in the high pressure region. As a result, the Fourier-limited pulse duration saturates at distances behind the on-axis intensity spike.

3.2 Variation of the input aperture

Changing the diameter of the input aperture behind the laser affects the input pulse energy, the focusing conditions, and the phase-matching in harmonic generation. We recorded the positions of the pulse energy maxima from Fig. 3 for four different input apertures from 5.5 to 7.0 mm, depicted in Fig. 5. For all spectral regions, the maxima shift toward larger propagation distances with increasing aperture diameter. We attribute this behavior to the earlier onset of plasma defocussing due to higher input pulse energy.

Fig. 5
figure 5

Position of the pulse energy maximum after integration of recorded VIS (), UV () and XUV () spectra in dependence of the input aperture diameter

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4 Conclusion

In conclusion, we have shown that a simple and low-cost set-up for femtosecond filamentation in atmospheric air yields broadband visible and broadband UV emission as well as HH generation under identical conditions. We have identified optimum parameters for broadband UV generation by systematic variation of the propagation distance and input aperture diameter. The UV Fourier-limited pulse duration saturates at <5 fs centered at 264 nm. XUV radiation is emitted by means of HH generation up to the 25th order. Terminating the filament at different lengths reveals an on-axis intensity spike in the filament core. In presence of this spike, the UV spectrum encounters broadening beyond the perturbative estimation.