## 3 Results and Discussion  
### Generation of the Multicolor Emission in the Gas Cell and the Gas-Filled Hollow Fiber  
When we used a hydrogen-filled gas cell, the FWM efficiently occurred in the vicinity of the foci at which the input beams have high intensities. The confocal parameter (2\(\pi{W_{0}}^{2}\)/\(\lambda\)) is a measure of the interaction length, where \(W_{0}\) and \(\lambda\) are the beam waist radius and the wavelength of the laser beam,  
Figure 1: The experimental setup. GM, gold mirror; SM, silver mirror; DM, dichroic mirror; PM, off-axis parabolic mirror; BS, beam splitter; DMM, dielectric multi-layer mirror; VND, variable neutral density filter. respectively. From the measured focal beam diameters of P1 and P2--300 \(\upmu\)m and 200 \(\upmu\)m--the confocal parameters of the beams were calculated. The value for P2 was 80 mm, which was shorter than that of P1 (120 mm). The interaction length for the gas cell was, therefore, estimated to be approximately 80 mm, which was shorter than that of the hydrogen-filled hollow fiber. The energies of the input and output pulses measured in front of the evacuated gas cell and hollow fiber chamber are listed in Table 1. From these values, the transmittance of the gas cell was calculated to be 90% for both P1 and P2. This value is in good agreement with the value calculated from Fresnel losses on the surfaces of the fused-silica windows of the gas cell. On the other hand, the throughput for the hollow fiber chamber was calculated to be 50% and 67% for P1 and P2, respectively. The smaller throughput for the hollow fiber may be due to coupling losses at the entrance of the hollow fiber and the linear propagation losses inside the fiber. For propagation of the EH\({}_{11}\) mode inside the hollow fiber, the linear propagation loss through the hollow fiber is calculated to be 9% at 1200 nm and 4% at 800 nm [27]. By assuming a coupling into the EH\({}_{11}\) mode and propagation of the mode inside the hollow fiber, the efficiency of coupling at the entrance of the hollow fiber is calculated to be 61% and 78% for P1 and P2, respectively. The smaller coupling efficiency for P1 than P2 arises from the too large beam diameter of P1 (300 \(\upmu\)m) to be perfectly coupled into the hollow fiber. The pulse durations of the input pulses were measured based on cross-correlation frequency-resolved optical gating, which allows for the characterization of the two unknown pulses simultaneously [28]. The pulse durations obtained were 50-60 fs. The spectra of the output beams measured at different pressures for both the gas cell and the hollow fiber chamber are shown in Figure 2. The efficiency in the generation of the anti-Stokes emission increased with increasing gas pressure for both cases. The spectral width of the emission increased because of SPM and XPM induced by the intense input pump pulses [9, 10, 12, 14]. In the case of the gas cell, the anti-Stokes emission lines were well separated from each other in the spectrum at pressures ranging up to 2 atm, while the spectrum became continuous above 1 atm in the case of the hollow fiber. The difference could be explained by the longer interaction length in the hollow fiber than in the gas cell. The spectrum of the output beam from the hollow fiber became a continuum at 2 atm, as shown in Figure 3. Even at a pressure of 0.8 atm, the influence of the phase modulation was appreciable in the case of the hollow fiber. An image of the output beam from the hollow fiber is shown in Figure 4, which was taken after passing the beam through a fused-silica prism and projecting the separated beam on a white screen. The spots are not separated from each other because of the broad bandwidth of the emission induced by the phase modulations. The spectral width of the anti-Stokes emission generated in the hollow fiber supported a sub-10 fs pulse duration, even at a pressure of 1 atm; no spectral overlap between adjacent anti-Stokes emission features was observed.