# Germanium Single Crystals for Photonics
## 6 Nonlinear Absorption of Germanium in the Range of 3-5 \(\upmu\)m  
When using optical elements made of germanium in laser technology operating in the atmospheric window of 3-5 \(\upmu\)m, it should be taken into account that in the range of 2.6-5 \(\upmu\)m, in addition to the usual absorption, additional effects of two-photon and three-photon absorption are observed [84; 85]. In this case, the process of radiation absorption is nonlinear, and this fact must be taken into account.  
In work [86], nonlinear absorption of radiation from a high-power non-chain pulsed HF(DF) laser was investigated on Ge samples of different thickness and specific resistance. Depending on the composition of the active mixture (SF\({}_{6}\):C\({}_{2}\)H\({}_{6}\) or SF\({}_{6}\):C\({}_{6}\)D\({}_{12}\)), laser radiation was generated in the range of either 2.7-3 \(\upmu\)m (HF laser) or 3.7-4.1 \(\upmu\)m (DF laser). The HF laser generation spectrum was a set of 18 different lines in the range \(\uplambda\) = 2.6-3 \(\upmu\)m (average \(\upnu\) = 0.4397 eV, which corresponds to \(\uplambda\) = 2.82 \(\upmu\)m). The laser pulse duration at half-height was \(\sim\)150 ns; the maximum pulse energy was E \(\approx\) 5 J; the energy distribution was close to uniform.  
Even at low HF laser irradiation intensities (\(I\) = 0.3 MW/cm\({}^{2}\)) in the absence of visually visible damage to the samples, a significantly nonlinear nature of the passage of radiation through Ge is observed. Figure 8 shows the experimental dependences of the transmission of Ge with a thickness of h = 1 mm on the radiation power density of HF and DF lasers, respectively, and Figure 9 shows the dependence of the concentration of nonequilibrium free-charge carriers generated in the process of two-photon absorption by depth (the calculation was carried out for the time t \(\sim\) 200 ns). Nonlinear absorption of DF laser radiation in a germanium single crystal was observed at a significantly higher radiation intensity \(I>10\) MW/cm\({}^{2}\). The transmission of Ge in the nonlinearity region decreases significantly with increasing sample thickness and value of crystal resistivity. The power of the transmitted pulse is noticeably reduced; the pulse shape is strongly deformed, and at the same time, a noticeable shortening of the leading edge is observed. The coefficient of two-photon absorption of single-crystal germanium K\({}_{2}\) = 55 \(\pm\) 10 cm/GW was calculated.  
The influence of pulse parameters on the dynamics of the passage of an intense HF laser pulse through Ge samples of different thicknesses (h = 0.03-0.55 cm) is analyzed. The intensity distribution \(l(l)\) over the thickness of Ge changes noticeably during the duration of the laser pulse. The generated nonequilibrium carriers are concentrated in a thin layer near the input surface of the crystal (see Figure 8), i.e., the main processes of nonlinear absorption occur in the surface layer less than 50 \(\upmu\)m thick. A kind of nonlinear filter arises, as in the case observed when exposed to a CO\({}_{2}\) laser. It prevents the destruction of the material volume even when trying hard to focus the laser energy into the sample volume. This circumstance indicates a large influence of nonlinear absorption of intense laser radiation occurring in the surface layer of germanium. In this case, the value of  
Figure 8: Transmission coefficient of Ge (\(\rho\) = 20 Ohm\(\cdot\)cm) with thickness h = 1 mm depending on the incident energy density of HF and DF lasers.  
the recombination coefficient of free carriers on the surface can exceed the volume value by several orders of magnitude. Therefore, special doping of the surface layer makes it possible noticeably change the value of nonlinear transmission of the entire Ge sample.