## 1 Introduction  
Many papers report attosecond pulse generation via high-order harmonic generation (HHG) for use in the studies of ultrafast phenomena related to electrons in an inner-shell orbital of an atom and molecule [1]. On the other hand, an ultrashort optical pulse approaching 1 fs, the spectrum of which is extended from the ultraviolet (UV) to the visible (VIS) region, would be useful for studies of ultrafast phenomena related to electrons in an outer-shell orbital, which are directly concerned with chemical bond/reaction and are more important in chemistry. For example, a molecular ion in mass spectrometry can be strongly enhanced by decreasing the optical pulse width in the femtosecond regime, which is then useful for more reliable identification of the explosive substances [2]. Several methods have been developed for generating an extremely-short optical pulse. For example, numerous emission lines have been generated in the entire VIS region, based on non-resonant four-wave mixing in a thin fused silica plate. This technique has been utilized to generate 2.2-fs optical pulses [3]. On the other hand, coherent supercontinua have been generated from the UV to near-infrared (NIR) by focusing the beam in a hollow-core fiber filled with neon gas, and a three-channel optical field synthesizer has been utilized to generate 2.1-fs pulse [1]. As recognized from the uncertainty principle, a wider spectral domain is essential for the generation of a 1-fs optical pulse. The generation of high-order Raman sidebands extending from the deep-UV (DUV) to the NIR region was first reported in a few decays ago [4]. To date, an extremely wide spectral region extending from 183 to 1203 nm has been covered, based on resonant vibrational four-wave Raman mixing in molecular hydrogen, suggesting that the generation of a 1-fs optical pulse by a phase control of the emission lines is possible [5]. A variety of techniques, including autocorrelation (AC) and frequency-resolved optical gating (FROG), have been developed to measure optical pulse widths [6]. In these techniques, a nonlinear optical effect such as second harmonic generation (SHG), self-diffraction (SD), and others have been utilized. To measure a 1-fs optical pulse, it is necessary to use a nonlinear optical effect that is usable in a wide frequency domain in the UV-VIS region. A GaN diode with a nature of two-photon absorption in the VIS region (at round 400 nm) has been employed as a detector in a fringe-resolved autocorrelator (FRAC) [7]. In a previous study, we reported on the development of an FRAC, in which a mass spectrometer was employed as a two-photon-response device in the DUV region (at around 267 nm) [8]. However, the frequency domain of these techniques is limited to one octave [9]. As a result, it is difficult to measure optical pulse widths less than 1 fs in the UV-VIS region. In order to overcome this problem, the use of a nonlinear optical effect that can be used in the spectral region wider than one octave would be necessary. One of the approaches would be the use of a third harmonic generation (THG) as a nonlinear optical effect, since it has a frequency domain of twice one octave [10]. A surface-sensitive THG has been successfully used for the autocorrelation measurement [11,12]. Moreover, several papers have reported on the FROG system based on THG (THG-FROG), including the THG on the surface of a glass plate [13], in organic films [14], and in a glass coverslip used in multiphoton microscopy [15]. The use of a solid material is simple and easy-to-use. It is, however, difficult to transmit the THG beam generated in the vacuum-UV (VUV) region and to reduce dispersion to negligible levels, especially in the DUV region. On the other hand, a gas such as helium or argon is transparent, even in the VUV region, and the dispersion sufficiently small to be negligible. Thus, the THG in a gaseous medium would be useful for measuring a pulse width in a wide frequencydomain.