# Transient Changes of Optical Properties in Semiconductors in Response to Femtosecond Laser Pulses
## 1 Introduction  
Modern experiments with free-electron-lasers (FELs) using pump-probe schemes achieve a few-femtosecond time resolution in monitoring transient material properties [(1; 2; 3)]. With a pump X-ray pulse different transitions inside the material can be triggered, such as structural transformations or phase transitions [(4; 5)]. By applying optical probe pulse on the sample after a certain time delay, their temporal evolution can be probed. Optical cross-correlation scheme proved to be especially successful, giving access to the time-resolved electron kinetics in single-shot experiments [(1; 6)]. Post-mortem time-sorting scheme extracts jitter-free data, enabling a robust few-femtosecond time resolution in such experiments [(2; 7)].  
Optical properties of solids have been measured experimentally, see, e.g., [(8; 9)]. The measurements include reflectivity, transmission or absorption which can be converted into the complex dielectric function or an optical conductivity.  
In this review paper we summarize the results of our theoretical studies on transient optical properties of semiconductors irradiated by ultrafast X-ray pulses [(10)]. Such pulses can trigger thermal and non-thermal transitions. Thermal phase transitions occur on ps timescale. They are triggeredby electron-atom kinetic energy exchange, which, through electron-phonon coupling, leads to the subsequent lattice heating.  
In contrast, non-thermal transitions occur due to a free-electron-induced change of interatomic potential. If radiation dose absorbed by the material is high enough to excite a sufficient number of electrons into the antibonding states of the conduction band, the potential energy surface rapidly changes. The solid is driven out of equilibrium. This leads to breaking of chemical bonds and atomic rearrangement, until a new atomic structure stabilizes. Thus, the presence of highly excited electrons leads to destabilization of the atomic structure [11]. Such phase transitions may occur on the timescale of a few hundreds fs which is much faster than a ps-long timescale of thermal phase transition [12].  
Below we will show examples of thermal and nonthermal phase transformations in diamond, silicon and gallium arsenide. These three semiconductors differ by the electronic properties, such as their band gap. This influences radiation-induced transformations in these materials, specifically, the contributing processes and their timescales. In particular, we will demonstrate that a non-thermal phase transition of diamond into graphite, which occurs within \(\sim\)200 fs after X-ray irradiation, is accurately reflected in the transient optical properties. The resulting closure of the band gap induces a strong decrease of material transmission. A similar effect can be observed in silicon during its nonthermal melting on 300-500 fs timescales, and during its thermal melting on a few-picosecond timescale. The effect of lattice heating is clearly visible in the reflectivity measurements of GaAs. This allows to extract the electron-lattice thermalization time from these data.