## 3 Spectra  
Spectra of the fundamental and SH used for MIR generation are shown in Figure 2. The fundamental spectrum showed significant ionization-induced blue shift, whereas the SH spectrum was also blue shifted and strongly broadened to low frequency region by cross-phase modulation, which fact was also observed in previous experiments [18, 22]. The fundamental pulse was self-compressed down to 15 fs, which was characterized with cross-correlation frequency-resolved optical gating. Figure 1: **(a)** Schematic of the system. Shaded region was purged with nitrogen at around atmospheric pressure. BBO: \(\beta\)-BaB\({}_{2}\)O\({}_{4}\) crystal (Type 1, \(\theta=29^{\circ}\), \(t=100\)\(\mu\)m), DL: delay plate (calcite crystal, \(t=1.7\) mm), DWP: dual wave plate (\(\lambda\) at 400 nm, \(\lambda/2\) at 800 nm), CM1: \(r=1\) m concave mirror, CM2: \(r=0.5\) m concave mirror, MH: aluminium-coated mirror with a hole (\(\phi=7\) mm); **(b)** Schematic of the system for electro-optic sampling. OP: aluminium-coated off-axis parabolic mirror, BF: bandpass filter for 400 nm (10 nm FWHM, FB400-10, Thorlabs), P: calcite polarizer, PMT: photomultiplier tube (H10721-210, Hamamatsu); **(c)** Schematic of the system for cross-correlation frequency-resolved optical gating. BF: bandpass filter for 335–610 nm (FGB37, Thorlabs), OMA: spectrometer for ultraviolet region (USB2000+, OceanOptics); **(d)** Schematic of the system for carrier-envelope phase measurement. BBO: \(\beta\)-BaB\({}_{2}\)O\({}_{4}\) crystal (Type I, \(\theta=29^{\circ}\), \(t=50\)\(\mu\)m) on a fused silica substrate (\(t=2\) mm), BF: bandpass filter for 335–610 nm (FGB37, Thorlabs), P: calcite polarizer, OMA: spectrometer for ultraviolet region (USB2000+, OceanOptics). The spectrum of the MIR pulse filtered through ZnSe (\(t=1\) mm), Ge (\(t=0.5\) mm), and two Si (\(t=0.5\) mm) plates was measured with a home-built Fourier transform spectrometer. The Michelson-type interferometer consisted of a Ge coated KBr beam splitter optimized for 3-20 \(\mu\)m, silver mirrors, and a feedback-loop piezo electric translation stage (PX400 SG, Jena). The beam from the interferometer was focused into a TGS (triglycine sulfate) pyroelectric detector by an aluminium-coated  
Figure 3: **(a)** Typical spectra of the MIR pulse generated through filamentation in nitrogen. Some sharp structure around 1000 cm\({}^{-1}\) is due to absorption of Si wafer; **(b)** The FWM spectra calculated with the measured fundamental and the SH spectra after the filament (shown in Figure 2). The optical path difference between the fundamental and SH are 0 nm (red), 50 nm (green), and 100 nm (blue), respectively. Figure 2: **(a)** Fundamental spectra measured before and after the filament (solid and filled curves, respectively). The spectrum did not change when the delay time between the fundamental and the SH pulses was adjusted; **(b)** SH spectra when the delay time between the fundamental and the SH pulses was not adjusted (solid curve) and was adjusted (filled curve). parabolic mirror (\(f\) = 150 mm). The measured spectrum is shown as a filled curve in Figure 3(a). The broadband spectrum spread over the whole MIR region (400-5500 cm\({}^{-1}\) at tenth maximum), which was due to the weak dispersion of the medium. While straightforward convolution of the fundamental and SH spectra should yield the MIR spectrum, the experimental MIR spectrum was reproduced only with the spectra after the filament. This means that the blue shift and broadening of the input spectra in the filament are the key processes to generate wavelength shorter than THz. The slight detuning of the input SH wavelength did not significantly contribute to the shift of the generated wavelength from THz to MIR since the detuning frequency was about 7.5 THz (250 cm\({}^{-1}\)), which is far from the MIR frequencies. The MIR generation technique, FWM of the fundamental and SH of Ti:sapphire amplifier output, is essentially identical to those used for THz generation [23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36].