## 3 Results and Discussion
### Phase Control of the Raman Sidebands  
FROG traces calculated under different relative phases are shown in Figure 7. These data suggest that the relative phases can be evaluated from the fringe patterns observed in the FROG trace. In fact, a train of pulses with a spacing of 8 fs can be generated (see Figure 7A), as is shown in Figure 5A, which is in contrast to the generation of a train of pulses with a spacing of 4 fs (see Figure 7C), as is shown in Figure 5B. The dependence of the angle of the CaF\({}_{2}\) plate inserted into the 267-nm beam on phase change was calculated, and the result is shown in Figure 8. These data suggest that the phase can be changed by more than 2\(\pi\) by changing the angle of the CaF\({}_{2}\) plate from 0 to 3.7\({}^{\circ}\). The fringe patterns observed for the components at 300 and 240 nm are shown in Figure 9. The observed data indicate that the emission lines are in phase, and produce a train of pulses, as shown in Figure 5A. An attempt was made to retrieve the FROG trace, but the 267-nm pulse was attenuated by ca. 10 fold. As a result, the SD FROG signal was reduced by ca. 1000 fold, thus preventing the FROG trace from being measured accurately. In addition, the spatial and temporal adjustments of the three beams emitting at 240, 257, and 300 nm became more difficult due to a small SD signal, which increased the FROG error. One of the approaches to solve this problem would be the use of a more sensitive transient grating (or cross-correlation) FROG system [24]. This approach was, however, not pursued in this study because of the complexity of the FROG system.  
Figure 6: Calculated FROG trace.  
Figure 7: FROG traces calculated under different relative phase. (**A**) 0, 0, 0 (**B**) \(\pi\)/2, 0, 0 (**C**) \(\pi\), 0, 0 (**D**) \(3\pi\)/2, 0, 0.  
Note that the total number of fringes in the trace is much larger than the value predicted from calculations (see Figure 6), which can be attributed to the pulse width (ca. 170 fs) being expanded by the optics, such as the dichroic mirrors, and also by the air in the beam path of the Raman emissions. In order to generate a single optical pulse, it would be necessary to expand the spectral domain for the probe beam, e.g., the use of a <8-fs pulse with a negative chirp for pulse compression by the optical components and the air in the beam path. This approach would be applied for generating sub-femtosecond, or even attosecond pulses, with energy higher than 10 eV (<120 nm). Since it is difficult to generate a negatively-chirped pulse in the DUV region (e.g., no such chirp mirror is available), a positively-chirped probe pulse was prepared by passing the beam through the SiO\({}_{2}\) plate, and the effect of chirping on the generation of Raman sidebands was examined. When the pulse width was increased to 50-220 fs, the efficiency for the generation of Raman sidebands was decreased by 25%, some (or most) of which can be attributed to a slight beam walk-off in the alignment of the laser beam. Thus, this type of approach using a (negatively) chirp pulse would be useful for pulse compression in the DUV region. It should be noted that the electric field of the optical pulse can be controlled by changing the carrier envelope phase of the fundamental laser, thus providing optimal performance in the applications such as high-order harmonic generation.  
Figure 8: Dependence of the angle of CaF\({}_{2}\) plate on the phase change.  
Figure 9: Expanded views of the FROG trace in (**A**) Stokes (**B**) anti-Stokes regions shown in Figure 3A. The interference fringe patterns are more clearly seen by expansion of the picture. A sapphire plate (0.1 mm) was used as the SD material. White lines are drawn to indicate a spacing of 8 fs. A periodic structure suggests a sufficient stability of the relative phases of the Raman sidebands.