# Transient Changes of Optical Properties in Semiconductors in Response to Femtosecond Laser Pulses
## 3 Results and Discussion
### Diamond
We can follow the dynamics of the system by looking at the snapshots of atomic positions at different time steps (Figure 5). One can see there when the cubic structure and the sp\({}^{3}\) bonds in diamond are breaking, and when the sp\({}^{2}\) bonds and individual parallel planes of graphite are forming. Comparison of these figures and the corresponding timescales in Figure 4 shows that the atomic rearrangement plays a major role in inducing changes of optical coefficients. We can theoretically study the connection between phase transition and changes of optical coefficients by artificial decoupling of electron excitation and atomic dynamics within the model. For this illustrative example, we \"switched off\" the transient atomic dynamics, \"freezing\" the atoms in their equilibrium positions and allowing only the electrons to be excited by an FEL pulse. This modeling scheme tests the correctness of an often-used assumption that the evolution of optical properties can be traced, if only accounting for electron kinetics, while keeping band structure and atomic structure unaffected. In this \"artificial\" case, even for an above-threshold dose of 1.0 eV/atom, the optical coefficients remain unchanged after the pulse and the completed electron cascading (Figure 6). This unambiguously shows that the abrupt changes of optical coefficients are the direct outcome of a structural transformation, while the electronic excitation plays there a less important role. Thus, atomic dynamics must be included in models describing the evolution of optical properties in materials under femtosecond X-ray irradiation at doses close or above their damage threshold. Figure 5: Snapshots of atomic positions in the diamond supercell at different time instances: \(-100\) fs (**left panel**), 150 fs (**middle panel**), 400 fs (**right panel**). Absorbed dose is 1.0 eV/atom, \(\hbar w=50\) eV, pulse duration \(\tau=90\) fs. Pump pulse maximum is at \(t=0\) fs. The simulations were performed with 216 atoms in the supercell. The figure is reproduced from [10]. Figure 6: Optical coefficients of diamond in case of “frozen atoms” (see text) irradiated with the dose of 1.0 eV/atom. Pump pulse maximum is at \(t=0\) fs. The simulations were performed with 216 atoms in the supercell. The simulations using supercell with periodic boundary conditions are affected by finite size effects which decrease with increasing number of atoms within the supercell. The oscillations of optical parameters were observed for the case of diamond irradiation at the near-threshold absorbed dose of 0.8 eV/atom. These simulations were performed with 216 atoms in the supercell. In order to check the potential influence of the finite size effect, we performed test calculations with 512 atoms. In this case the amplitude of the oscillations significantly decreased. This would indicate that the finite size effect is responsible for the oscillations. We cannot entirely exclude the possibility of some coherent atomic motion during the system relaxation, however, we cannot resolve it with the current tool and data available. Our simulation results can be compared with the available experimental data. So far, experiments on graphitization have been performed with optical pumping. In the work by [PERSON] et al. [30] transient reflectivity of diamond was measured. Optical pump and probe pulses had the same wavelength of 630 nm and duration of 90 fs, and the absorbed dose was 9 times higher than the threshold dose. As it was mentioned in Section 3, XTANT code is not able to model optical pumping directly. However, it can use instead soft X-ray pulses. They induce fast cascading of electrons and their fast relaxation. Electronic dynamics in the system becomes then similar to the optical case shortly after the pulse. A good agreement between the measured reflectivity coefficients and our predictions can be seen in Figure 7. A small discrepancy between predictions and the data during the pulse can be expected due to the reasons presented above.