1 INTRODUCTION

The filamentation of femtosecond laser radiation in air is accompanied by the formation of broadband coherent radiation, i.e., supercontinuum [1, 2]. In the case of the filamentation of near infrared pulses, this supercontinuum extends from ultraviolet to mid-infrared [3, 4]. Such a broad spectrum and the possibility of its remote obtaining at a given distance from a source open prospects of the application of the femtosecond filaments in remote sensing problems [5]. In this context, the study of the frequency–angular structure of the radiation generated during filamentation on a long atmospheric path and the evolution of this structure in the process of propagation becomes important.

The main features of this evolution have been already studied experimentally and in numerical simulation. It was shown that, after the filamentation, a sequence of maxima is formed on the beam axis in the red wing of the spectrum due to the self-modulation at the instantaneous and delayed response of the medium [6, 7]. In the process of pulse propagation, these maxima are redshifted [8, 9], and the transformation of the red wing of the spectrum with an increase in the shift of maxima to the infrared region in collimated geometry continues up to distances of about 20 m behind the plasma region [10]. The supercontinuum in the blue wind of the spectrum has both the axial component and components propagating at nonzero angles to the filament axis and forming conical emission [7, 11]. Since the angular distribution of the supercontinuum generated during the filamentation depends on the wavelength, its spectral and angular characteristics should be studied jointly.

For such studies, a method was developed to measure frequency–angular spectra of radiation after the filamentation [12]. The frequency–angular spectrum is a two dimensional (θ, ω) or (θ, λ) distribution of the intensity, where θ is the radiation propagation angle with respect to the beam axis and ω and λ are the frequency and wavelength of the radiation, respectively. This method is an efficient tool for analysis of processes accompanying the filamentation because the spectral and spatial characteristics of the radiation are measured simultaneously. Frequency–angular spectra contain indirect information both on the temporal structure of a pulse during filamentation [12] and on the dispersion properties of the medium where the pulse propagates [13–15]. In particular, the frequency–angular spectrum has the X and O shapes at the normal and anomalous dispersion of the medium, respectively [13, 14]. The transition between these two characteristic shapes under the variation of the central wavelength of the laser pulse was experimentally demonstrated in condensed media in [14, 16]. An X‑shaped frequency–angular spectrum was observed in experiments in air [4, 17–20] (sometimes, with absent “branch” in the red wing, which is characteristic of nearly zero dispersion [16]).

The recent numerical simulation in [21] has shown the possibility of a smooth transition of the X-shaped frequency–angular spectrum to the O-shaped one at a fixed central wavelength of the laser pulse due to the variation of the composition of the gas mixture where the filamentation occurs. The calculation was performed for the mixture of nitrogen at a pressure of 40 bar and water vapor at a pressure up to 0.36 bar at a temperature of 85°C for the central wavelength of the laser pulse 1.3 μm. The region of negative dispersion necessary for the formation of the O-shaped structure of the frequency–angular spectrum appears because of the presence of the absorption band of water vapor near 1.3 μm.

In this work, we experimentally detect for the first time the O-shaped structure formed in the frequency–angular spectrum of the pulse after the filamentation in atmospheric air on a long path. In contrast to the conditions proposed in [21], we do not modify the medium to facilitate observation of this structure. We also did not choose the wavelength of the laser source in the absorption band: spectral components in this band are generated during filamentation. The wavelength range of 930–960 nm, where the O-shaped structure is observed in the frequency–angular spectrum, corresponds to the absorption of water vapor two orders of magnitude weaker compared to the 1.3‑μm absorption band. Due to the assembly of these factors, the result obtained is interesting not only fundamentally but also for the diagnostic of impurities in the atmosphere.

2 SCHEME OF THE EXPERIMENT

The sketch of the experiment is presented in Fig. 1. The radiation of a Ti:sapphire laser system generating 100-fs pulses with a central wavelength of 744 nm, an energy of 8.5 mJ, and a repetition frequency of 10 Hz was directed to the long path in a corridor. The 1/e beam diameter was 8 mm. Measurements could be carried out on the path with the length reaching 95 m. A filament was formed at a distance of \( \leqslant {\kern 1pt} 40\) m from the output of the laser system; after this point, the diameter of the central spot formed in the filament changed slightly during the propagation over a distance of about 40 m, which is characteristic of the post-filamentation regime [22] (see also [10, 20], where the evolution of the post-filamentation channel under close experimental conditions was considered in detail).

Fig. 1.
figure 1

(Color online) Sketch of the experiment: (W1, W2) quartz wedges; (D1, D2) adjusting diaphragms; (NF) neutral light filters; (M1, M2) aluminum-coated plane mirrors; and (SM) the aluminum-coated spherical mirror.

Full size image

To measure (θ, λ) spectra, we constructed a movable experimental installation, which allowed their single-pulse detection in a spectral window with a width of 250 nm. Adjusting the spectrometer in the wavelength by rotating the grating, we recorded frequency–angular spectra in the range from 650 to 1020 nm (in several pulses). To form the angular spectrum in the plane of the spectrometer input slit, we employed an aluminum-coated spherical mirror (SM in Fig. 1) instead of a lens usually applied for this purpose. This allowed us to exclude the effect of chromatic aberrations when tuning the wavelength in such a wide range. The nonlinear propagation of the pulse was interrupted by means of the quartz wedge W1. Further, the pulse energy was additionally reduced using the quartz wedge W2. These wedges and a pair of adjusting diaphragms D1 and D2 ensured a constant angle of incidence on the spectrometer when the installation was moved along the path. Calibrated neutral light filters NF were used for additional radiation attenuation. A pair of mirrors M1 and M2 allowed us to minimize the angle of incidence of the radiation on the spherical mirror SM and, correspondingly, in-troduced astigmatism. To detect spectra, we used a Solar M150i-III imaging spectrometer with a The-ImagingSource DMK 33GX249 CCD. The spectra were processed taking into account the quantum yield of the CCD as a function of the wavelength, the reflection curve of the diffraction grating of the spectrometer, and transmission curves of calibrated neutral light fi-lters.

3 EXPERIMENTAL RESULTS

Figure 2 presents the measured (θ, λ) spectra of (a) the initial pulse, (b) the pulse immediately after the filament at a distance of 40 m from the laser system, and (c) at a distance of 75 m from the laser system.

Fig. 2.
figure 2

(Color online) (θ, λ) spectra of the pulse (а) at the output of the laser system, (b) at a distance of 40 m from the laser system (~5 m behind the filament), and (c) at a distance of 75 m from the laser system (~40 m behind the filament) normalized to their individual maxima.

Full size image

If the initial laser pulse was collimated (divergence of about 0.1 mrad) and had a relatively narrow spectrum (a FWHM of about 10 nm), its spectral and angular characteristics change dramatically already at a distance of 40 m from the laser system. Conical emission is formed in the anti-Stokes region with a divergence of about 0.5 mrad with respect to the axis. It can indicate the appearance of the plasma (see [11]). A sequence of local maxima on the axis extended above 850 nm appears in the Stokes wing of the spectrum. The (θ, λ) spectrum at this distance already has all features appearing at the filamentation of the femtosecond laser pulse in air.

At a distance of 75 m, the intensities of all local maxima in the infrared region increase, whereas their angular widths decrease slightly due to the formation of a post-filament, and the most pronounced maximum is shifted by more than 850 nm (see Fig. 2b). Conical emission in the anti-Stokes part of the spectrum is no longer detected because it is beyond the apertures of the optical elements used to introduce the radiation in the spectrometer.

The measured (θ, λ) spectra are generally in good agreement with the data previously obtained for the case of the filamentation in air [17, 18, 20] and have the X shape corresponding to the normal dispersion of air in this spectral range.

We now consider the frequency–angular spectrum structure of the 780–1010-nm part of the spectrum (see Fig. 3). To measure it, we turned the grating of the spectrometer so that the intense radiation at the central wavelength did not reach the CCD, which made it possible to detect less intense spectral components.

Fig. 3.
figure 3

(Color online) (a, b) (θ, λ) spectra of the Stokes wing of the supercontinuum after the filamentation at distances of (a) 40 and (b) 75 m normalized to their individual maxima. The inset of panel (b) shows the region of the (θ, λ) spectrum in an increased scale where the O-shaped structure is observed (marked by dashed ellipses). (c) (Black line) Absorption spectrum of water vapor according to HITRAN data including the collisional broadening of spectral lines. (Red line, values are multiplied by a factor of 10) Same spectrum including the resolution of the spectrometer.

Full size image

Local maxima in the long-wavelength part of the (θ, λ) spectrum detected almost immediately after their appearance at a distance of 40 m from the laser system have a unimodal shape (see Fig. 3a). However, the shape of the infrared local maxima changes at a distance of 75 m from the laser system. The (θ, λ) spectrum in the range of 900–970 nm has the branches directed toward each other with the intensity minimum near 950 nm, i.e., has the O shape with an intensity dip near 950 nm (see Fig. 3b). This behavior is not observed at wavelengths below 900 nm.

The appearance of the region of negative dispersion near 950 nm necessary for the formation of the O-shaped structure of the (θ, λ) spectrum is possible in the presence of the absorption band near this region. The only component of atmospheric air having significant absorption near 950 nm is water vapor. Figure 3c shows its absorption spectrum in the range of 780–1010 nm calculated from HITRAN data [23]. The 930–960-nm absorption band corresponds to the center of the observed O-shaped structure in the (θ, λ) spectrum.

4 DISCUSSION OF THE RESULTS AND CONCLUSIONS

To summarize, we have experimentally detected for the first time the O-shaped structure in the (θ, λ) spectrum in the post-filament channel of the femtosecond laser pulse in air at a distance more than 50 m from the output of the laser system. This structure appears due to the anomalous dispersion region associated with the 930–960-nm absorption band of water. This result demonstrates the potential possibility of detecting impurities in atmospheric air by their effect on the dispersion characteristics of the medium. In contrast to absorption lines whose quantitative separation from modulations of the spectrum in the nonlinear medium can be difficult, the transformation of the frequency–angular spectrum is a qualitative change that can be easily identified against the background of these modulations. Measurements of the frequency–angular spectrum do not require the accurate tuning of the laser wavelength and allow the simultaneous detection of several lines/substances with a single laser pulse. We note that femtosecond laser systems of the mid-infrared region with a power sufficient for the formation of filaments in air developed in the last decade [24] open wide possibilities for detecting organic impurities having absorption bands in this region.