# Characteristics of Coherent Optical Phonons in a Hexagonal \(\mathbf{YMnO_{3}}\) Thin Film
## 3 Experimental Procedure of Time-Resolved Pump-Probe Spectroscopy  
Time-resolved pump-probe spectroscopy is widely used to study electron and phonon dynamics [1]. Here, the laser pulse used for the generation of excited states is called pump pulse and that for detecting a change in physical quantities due to the excited states is called probe pulse. The pump and probe pulses are irradiated to the same position of a target material, while the arriving times of the pump and probe pulses are independently controlled. The change in reflectance or transmittance is recoded as a function of the delay of the arriving time of the probe pulse relative to the pump pulse. Because the oscillation of coherent phonons modulates the dielectric function in the target material, it induces a periodical change in reflectance or transmittance with the phonon frequency.  
Figure 1 shows the schematic diagram of the setup for time-resolved reflection-type pump-probe spectroscopy used in our study. A light source was a mode-locked Ti:sapphire laser with a pulse duration of about 80 fs with a repetition rate of 76 MHz. The tuneable wavelength range was from about 710 to 830 nm, where the full width at half maximum (FWHM) of the spectrum was about 10 nm. The spectrum was evaluated in all pump-probe measurements by using a spectrometer with a resolution of 0.2 nm. The laser pulse passed through a dispersion compensating prism pair was split to the pump and probe pulses by a beam splitter (BS). The time delay \(\tau\) between the pump and probe pulses was periodically scanned by a retroreflector attached to a shaker with a frequency of ~70 Hz. The full time window in the present system was ~5 ps. The polarization directions of the pump and probe pulses were orthogonal each other by using pairs of half-wave plate (HWP) and polarizing beam splitter (PBS). The pump and probe pulses were irradiated to the same position of the sample surface with a lens, where the incident angle of probe pulses was ~4\({}^{\circ}\) with respect to the surface normal. The change in intensity of the reflected probe pulse was detected by a balanced photodetector simultaneously measuring the intensity of reference pulses. A polarizer (P) was placed in the reflected beam pass to cut the reflection of the pump light from the sample. The detector output was recorded as a function of the time delay by a high-resolution recorder (12 bits) synchronized with the shaker. This time-resolved measurement technique is called fast-scan method [33]. The recorded signal was divided by the original reflected probe intensity to convert the time-resolved reflectivity change (\(\Delta R/R_{0}\)). The discernible signal level of \(\Delta R/R_{0}\) was ~1 \(\times\) 10\({}^{-6}\) with 40,000 times of signal averaging. Because the fast-scan method can measure the time-domain signal in a few picoseconds range with a high S/N ratio, it is a powerful tool for studying sub-picosecond (terahertz) range coherent oscillations [34].  
In measurements of the dependence of the pump photon energy, we tuned the light source; the photon energies of pump and probe pulses are simultaneously changed.