# Transient Changes of Optical Properties in Semiconductors in Response to Femtosecond Laser Pulses
## 2 Model
Optical refractive indices \(n(\omega)\) and \(k(\omega)\) represent the real and the imaginary part of the complex refractive index, \(\bar{n}(\omega)=n(\omega)+ik(\omega)=\sqrt{\epsilon(\omega)}\), where only the diagonal matrix elements of the CDF tensor are used [10]. They can be evaluated for many materials with XTANT. Below we use 125 \(k\)-points calculations of the CDF sampled according to the Monkhorst-Pack scheme [21]. The \(n(\omega)\) and \(k(\omega)\) as functions of photon energy were calculated with XTANT for equilibrium diamond. They are shown in Figure 1. Comparison with the available experimental [22] and DFT data [23] shows discrepancies, e.g., the main peak is missing in the XTANT simulation. This is due to the limited accuracy of the (nearest-neighbour) tight-binding method which we apply here. In particular, it does not describe properly high-lying states in the conduction band and possible resonances. However, the agreement at energies below \(\sim 5\) eV is reasonably good. As we will see later, it is sufficient for the description of pump-probe experiments with optical probe pulses. The same comparison was made for silicon, and the same sort of discrepancy was found (Figure 2). As band gap in silicon is narrower than in diamond, the limiting energy, under which the agreement of data and our simulations is achieved, is at \(<\)2 eV. As the later comparison with experimental data will show, this is still sufficient for calculations of optical properties in the optical wavelength regime. Although the accuracy of tight-binding parametrization for a material in a fixed state or phase can, in principle, be improved by incorporating contribution of neighbours up to the third nearest neighbour (shown by [PERSON] et al. in [20]), such extension is not available for transferable tight-binding scheme applied in XTANT. Final comparison was made for GaAs (Figure 3). The agreement between theory and experiment is worse than in the previous cases due to the complexity of the GaAs band structure. Figure 1: Optical refractive indices \(n\) (**left**) and \(k\) (**right**)of the equilibrium diamond. The dots are experimental data [22]; the solid line is tight-binding (TB) model prediction with X-ray induced Thermal And Non-thermal Transitions (XTANT)-2 (64 atoms in the simulation cell, 2197 (\(13\times 13\times 13\)) \(k\)-points). Finally, let us emphasize that although different transferable TB parameterizations can be found in the literature, we did not explore (and compare) the effect of each specific parametrization on the simulations. This is not straightforward as each parameterization is functionally different and would require a dedicated implementation into the code. The various TB parametrizations arise from the underlying density functional theory (DFT) or Hartree-Fock (HF) calculations, to which the TB parameters are fitted. Consequently, they may produce slightly different cohesive energies or band structures. Thus, one would expect to see an effect of the specific parametrization on the results. However, we are unable to quantify this statement at present; it deserves a separate investigation.