# Characteristics of Coherent Optical Phonons in a Hexagonal \(\mathbf{YMnO_{3}}\) Thin Film
## 2 Generation Mechanisms of Coherent Phonons  
Phonon modes in hexagonal \(R\)MnO\({}_{3}\) compounds have investigated mainly by Raman spectroscopy [17; 19; 20; 28]. A Raman scattering signal is evaluated as a function of energy difference between incident and scattered lights. This means that Raman spectroscopy is one of spectroscopic methods in the frequency domain. When the time duration of ultrashort laser pulses is shorter than the oscillation period of a phonon mode, it can generate the population of the phonon with the same initial phase. This is a coherent phonon. The dynamics of the coherent phonon can be observed in the time domain by using an ultrafast spectroscopic technique as described in Section 3. Since the observed result includes the dynamical property of the phonon, it can bring out a different aspect of the phonon property to that evaluated by Raman spectroscopy. We briefly describe two typical generation mechanisms of coherent phonons below.  
Various models have proposed for the generation mechanism of coherent phonons. In the investigation of the generation mechanism, it is important clue that whether the target material is transparent or opaque to the excitation laser. In the case that an opaque range is excited, the photoexcitation of electrons occurs. The ultrashort laser excitation instantaneously creates dense excited electrons, which can change the equilibrium position of atoms. Atoms does not instantaneously respond to the change of the potential in accordance with the Franck Condon principle. After the completion of the excitation of electrons, atoms start moving and then oscillate around the new equilibrium position. This generation process is referred to as the displacive excitation of coherent phonons (DECP) mechanism [29].  
Impulsive stimulated Raman scattering (ISRS) mechanism is a potential candidate under the excitation condition that the target material is transparent to the excitation photon energy [30; 31]. First, we describe a Raman scattering process with a monochromatic laser. When the laser with the frequency of \(\omega_{1}\) is incident to the material, electrons are instantaneously excited from a ground state to virtual intermediate state. Then, phonons with the frequency of \(\Omega\) and scattered light with \(\omega_{2}=\omega_{1}-\Omega\) are spontaneously emitted from the intermediate state. An ultrashort laser pulse inherently has a broad spectral component \(\Delta\omega\). If \(\Delta\omega\) is wider than \(\Omega\), the light pulse can include the \(\omega_{1}\) and \(\omega_{2}\) components. Accordingly, the \(\omega_{2}\) light can be emitted from the intermediate state by the stimulated emission process. This process generates coherent phonons with \(\Omega\). It is referred to as the ISRS mechanism. In contrast to the DECP mechanism, the ISRS mechanism can contribute in both the opaque and transparent ranges [32]. One of the effective method to investigate the generation mechanism is to measure the pump photon energy dependence of the coherent phonon around the absorption edge in the target material. Other approach to distinguish the generation mechanisms is to observe the phase of the coherent phonon oscillation. In DECP, atoms start moving from the former to new equilibrium positions and then oscillate around the new one. Therefore, the signal shows a cosine shape. On the other hand, the signal with ISRS shows a sine shape because atoms oscillate around their fundamental equilibrium position. For the precise determination of the phase, on the other hand, a pulsed light source that is much shorter time duration than the oscillation period of the coherent phonon is required.