## 1 Introduction  
Ultrashort optical pulses have been successfully used in a variety of fundamental studies related to ultrafast phenomena. The binding energy of an electron in an outer-shell orbital is several eV, and therefore, a femtosecond laser emitting in the deep-ultraviolet (DUV) region (200-300 nm) can be employed in chemical reactions such as photo dissociations. On the other hand, the ionization energy is ca. 10 eV for most organic molecules, suggesting the possibility of efficient two-photon ionization using a DUV femtosecond laser. In fact, such a laser has been used practically as an ionization source in the studies of multiphoton ionization mass spectrometry for numerous organic molecules, including toxic compounds such as dioxins and pesticides, explosives such as trinitrotoluene and triacetone triperoxide, and even nerve agent metabolites [1]. The molecular ion, which is useful for identifying the molecule and for determining molecular weight, can be observed in many cases when the pulse width of the DUV laser is decreased to several tens of femtoseconds [2]. As a result, a technique for generating an ultrashort DUV optical pulse has attracted the interest of many researchers, not only in fundamental studies, but also in practical applications.  
Several approaches have been reported for generating ultrashort optical pulses in the DUV region. One such approach is the use of self phase modulation of a Ti:sapphire laser to generate ca. 10-fs pulses [3; 4; 5; 6]. Four-wave mixing is another approach [7; 8; 9; 10], in which a negatively-chirped pulse can be generated in the DUV region, and even in the vacuum-ultraviolet (VUV) region, and is then compressed to 10-20 fs pulses by positive dispersion in the optical media--such as air--and a MgF\({}_{2}\) plate inserted into the beam path. The other approach is through direct frequency upconversion (harmonic generation) of a near-infrared few-cycle optical pulse to generate an ultrashort DUV pulse (2.8-3.7 fs) [11; 12].  
In order to generate shorter optical pulses, it is necessary to further expand the spectral domain. It is possible to generate a supercontinuum in a very wide spectral domain using a gas-filled photonic crystal fibers [13; 14]. Another approach is the generation of multiple sidebands based on four-wave Raman mixing [15]. In fact, the generation of a train of 1.6-fs optical pulses in a nanosecond envelope in the visible to near-infrared region was reported [16; 17]. In a recent study, a series of Raman sidebands was generated in the DUV region by a pump-probe technique, in which a two-color beam emitting at 800 and 1200 nm was utilized as the pump beam with a single-color beam emitting at 267 nm or 200 nm as the probe beam, to generate several Raman sidebands in the DUV and VUV regions [18; 19]. A hollow-core capillary was employed as a waveguide to improve the conversion efficiency by increasing the interaction distance between the laser and the Raman medium. However, the temporal shape and phase of such Raman sidebands have not yet been evaluated [18; 19].  
In this study, we used the pump-probe technique to generate Raman sidebands, and evaluated the temporal profile and the phase of the emissions using a self-diffraction (SD) frequency resolved optical gating (FROG) system [20; 21; 22]. From the fringe patterns observed in the FROG trace, we verified that the Raman sidebands were phase locked, and confirmed the generation of ultrashort optical pulses. This proof-of-principle experiment points to the potential advantage of four-wave Raman mixing to be used for the generation of an ultrashort optical pulse, and for applications to practical spectrometric studies [1].