## 3 Results and Discussion  
Figure 2 shows the measured THz waveforms (upper row) and the spectra of THz radiation reconstructed from these waveforms (dots, middle row). Panels (a)-(c) in Figure 2 correspond to \(\omega+DC\), \(\omega+2\omega\) and \(\omega+2\omega+DC\) schemes of THz generation, respectively. The simulated THz spectra are shown in Figure 2 (middle and lower row) by solid curves. In reasonable agreement between the numerical and experimental results, the spectrum of THz radiation generated from a DC-biased single-color (\(\omega+DC\)) filament is localized at \(\upsilon\lesssim 1\) THz (Figure 2a). In the experiment, strongly divergent low-frequency (\(\upsilon\approx 0.1\) THz) spectral components escape the Teflon lenses and do not enter the TDS detector. Owing to this effect, the maximum of the experimental spectrum was achieved at \(\upsilon\approx 0.4\) THz, while the simulations predicted the spectral maximum at much lower frequencies. In the case of the \(\omega+2\omega\) filament, the experimentally obtained and simulated spectra are much broader than in the \(\omega+DC\) one (cf. Figure 2a,b). The spectrum reconstructed from the measured THz waveform is limited by the ZnTe phonon band at \(\upsilon\gtrsim 3\) THz [40]. The simulated spectrum goes down very slowly and has a width of about the inverse pulse duration in agreement with the previous studies [41]. The low-frequency part of the experimentally obtained THz spectrum qualitatively agrees with the simulated one (Figure 2b). The spectrum of THz radiation generated in a DC-biased two-color filament (\(\omega+2\omega+DC\), see Figure 2c) combines the characteristics of \(\omega+DC\) and \(\omega+2\omega\) spectra considered above. This is clearly pronounced in the higher-frequency range \(\upsilon\gtrsim 1.5\) THz. The spectrum of THz radiation generated according to the \(\omega+2\omega+DC\) scheme extends up to 3 THz and the spectral intensity at 2 THz constitutes \(10^{-2}\) of the spectrum maximum (Figure 2c). Without the second harmonic field, the spectral intensity at 2 THz is of the order of \(10^{-3}\) of the spectrum maximum (Figure 2a). This wide high-frequency wing in Figure 2c originates due to the 800-nm pump pulse mixing with the second harmonic pulse as seen from the \(\omega+2\omega\) spectrum in Figure 2b. However, the direct intensity summation of the THz spectra in the \(\omega+DC\) and \(\omega+2\omega\) schemes does not exactly reproduce the THz spectrum corresponding to the \(\omega+2\omega+DC\) scheme. We suggest that superposition of THz waves should be considered in the temporal domain. Therefore, we will study the partial contributions of the THz waveforms from the \(\omega+DC\) and \(\omega+2\omega\) sources into the overall THz emission from the \(\omega+2\omega+DC\) filament. As all the experimentally obtained waveforms were measured in the same conditions, they have the same scale and can be quantitatively compared with each other, see Figure 3a. The simulated on-axis waveforms processed by the bandpass filter 0.2 THz \(<\
u<\) 3 THz, which roughly reproduces the spectral sensitivity of TDS, are plotted in Figure 3b. The rectangular filter cannot fully reproduce the TDS transfer function and spatial convolution with the probe beam, so the simulated waveforms in Figure 3b reproduce the measured ones in Figure 3a qualitatively. This reproduction includes the main physical characteristics of the waveforms, such as the correct relation between the amplitudes, the frequency content and the temporal shape of waveforms obtained from the \(\omega+DC\), \(\omega+2\omega\) and \(\omega+2\omega+DC\) sources (Figure 3a,b, cf. the curves with the same colors). Note, in particular, the shorter period of THz field oscillations as the \(2\omega\) pulse is added to the filament (cf. red and blue curves in Figure 3a,b).