# Transient Changes of Optical Properties in Semiconductors in Response to Femtosecond Laser Pulses
## 3 Results and Discussion  
### Diamond  
We begin with a study of transient optical parameters in irradiated diamond. The XTANT model treats only single-photon absorption. Thus, it is limited to photon energies above \(\sim\)30 eV and to low FEL fluences. For our simulations we will use photon energy of 50 eV, unless stated otherwise. Such photon energy has been frequently used for experiments at various FEL facilities, for instance, at FLASH [24; 25], or at FERMI [26]. We perform a set of simulations with FEL pulses of 50 eV photon energy, Gaussian temporal profile and duration of 90 fs FWHM for different absorbed doses: 0.6 eV/atom, 0.8 eV/atom, and 1.0 eV/atom. Figure 3: Optical refractive indices \(n\) (**left**) and \(k\) (**right**) of the equilibrium GaAs. The dots are experimental data [22]; the solid line shows TB model prediction with XTANT-2 (64 atoms in the simulation cell, 2197 (\(13\times 13\times 13\)) \(k\)-points). Figure 2: Optical refractive indices \(n\) (**left**) and \(k\) (**right**) of the equilibrium silicon. The dots are experimental data [22]; the solid line is TB model prediction with XTANT-2 (64 atoms in the simulation cell, 2197 (\(13\times 13\times 13\)) \(k\)-points). The damage threshold dose for diamond is \(\sim 0.7\) eV/atom as previously calculated [12]. For doses above the threshold dose a transition of diamond to graphite can be triggered [12; 27; 28]. In Figure 4 time-dependent reflectivity, transmission and absorption coefficients are shown for the three absorbed doses. In all cases a characteristic rise of absorption and drop of transmission are observed already during the pulse. In case of the below-threshold dose, the transmission does not decrease to zero, and the reflectivity slightly changes. For doses above the damage threshold, optical transmission decreases in two stages--first, to some intermediate value after \(\sim\)100 fs after the pulse maximum (located at 0 fs), and then to zero after additional 100 fs. The reflectivity rises up at those times, respectively. The transient transmission plateau \"shorten\", when the absorbed doses become closer to the damage threshold. If the dose is sufficiently high (above the damage threshold), transmission drops to zero rapidly after 100 fs, without any intermediate plateau, see Figure 4c. The following physical processes are responsible for the changes of optical properties. At the first stage, diamond absorbs energy from the laser pulse. Transmission coefficient then begins to decrease. This occurs mainly due to the excitation of electrons from the valence to the conduction band, whereas the electron band structure and atomic structure remain practically unaltered during the first \(\sim\)50 fs. Later, if the density of excited electrons overcomes a certain fraction of the total number of valence band electrons (\(\sim\)1.5% for diamond), the electronic band structure undergoes significant changes, with the most prominent effect of the band gap collapse [29]. For above-threshold doses, band gap collapse is clearly visible on the time scale of the transmission decrease. However, it can also occur before the final drop of the transmission to zero, because it takes some time for atoms to relax into a new equilibrium state of graphite [29]. That is reflected by an occurrence of a transient plateau in the transmission curve mentioned above. Band gap closure promotes even more electrons to the conduction band, leading to the rapid changes of the potential energy surface. If the change is significant, the sp\({}^{3}\) bonds in diamond begin  
Figure 4: XTANT-modeled optical coefficients of diamond at different radiation doses absorbed: (**a**) 0.6 eV/atom; (**b**) 0.8 eV/atom; and (**c**) 1.0 eV/atom. Solid lines depict reflectivity coefficients, the dashed lines are transmission coefficients, the dot-dashed lines show absorption coefficients. The simulations were performed with 216 atoms in the supercell. Pump pulse maximum is at \(t=0\) fs. The figures (**a**) and (**c**) are reproduced from [10]. to break.