The Theoretic Modeling And Measurement Of Thermo-optical Coefficient For Germanium Near The The Absorption Edge

The refractive index and the thermo-optical coefficient are important parameters of materials. Germanium(Ge), as a frequently used infrared optical material, most research about optical properties are focused on the transparent region, while near the absorption edge(about 1550 nm, near-infrared region), has few research. In our paper, we made a careful analysis for the absorption process of Ge which occur in the regions near the absorption edge. It can be found that intrinsic absorption and exciton absorption have great influence on thermo-optical effect near the absorption edge. Based on the inner relationship between the absorption coefficient and refractive index, we can find the thermo-optical coefficient model of Ge near the absorption edge and measure the value by experiment.Specific ideas for theoretical modeling: the major absorption processes near the absorption edge are intrinsic absorption and excitonic absorption. The intrinsic absorption is caused by inter-band electronic transition, including direct and indirect inter-band transition. We ignored the influence of indirect inter-band transition in this model, and only consider the direct inter-band transition which have a higher transition probability. It can be described with the help of the classical harmonic oscillator model. Here, according to the contribution to the thermo-optical coefficient, the direct inter-band transition can be divided into the E0 transition and the rest direct transition. The E0 transition can be described with a simple parabolic energy band structure, and the influence of the rest direct transition on the thermo-optical coefficient is calculated by the model of refractive index in transparent area. Considering that we are interested in the area near the absorption edge, we focus on the effects of the thermo-optical coefficient caused by excitonic absorption and described by Wannier excitonic model. And try to find the relationship between variable and temperature in the Wannier model, then obtain the relationship between the refractive index and temperature. Finally, we combined with the harmonic oscillator model and Wannier excitonic model to describe the optical phenomenon of absorption edge. According to the theoretical calculation, there is an abnormal phenomenon about thermo-optical effect near the absorption edge—the thermo-optical coefficient of Ge increases with the temperature increasing, but we can find a sudden change near the absorption edge.To measure the thermo-optical coefficient of Ge accurately, we set up an experimental platform based on optical fiber sensor. The end face of the fiber is coated with a layer of Ge with vacuum evaporating as a sensing unit, thermostats produces adjustable temperature field. We can obtain the curves of the temperature changing with the reflectivity. Then we get the temperature dependence of the refractive index, also means the thermo-optical coefficient. The experimental results show that: such as the theoretical model predicts, the thermo-optical coefficient of germanium changes with temperature from positive to negative near the absorption edge. The experimental results are consistent with theoretical model.