With the rapid development of aerospace technology, high-effective turbine engines are increasingly required. How to accurately measure the pressure in the turbine under a harsh environment becomes the key issue. The traditional piezoresistive sensor is greatly affected by electromagnetic interference, while the application temperature of the quartz optical fiber sensor is relatively low, which makes it no longer applicable. The sapphire optical fiber pressure sensor has high-temperature resistance, anti-electromagnetic interference, and other excellent characteristics, which make it an ideal device for monitoring pressures at temperature above 1000 ℃. There are few studies on the high-temperature refractive index of sapphire, and the highest temperature of refractive index measurement is only 700 ℃. In this study, an experimental device for measuring the refractive index anisotropy of crystals is designed based on the Huygens principle. As temperature ranges from room temperature to 1200 ℃, the ordinary refractive index n_o and the extraordinary refractive index n_e of sapphire at wavelength of 445 nm are measured by the laser displacement method. In addition, optical parameters such as the refractive index of sapphire in this temperature range are calculated by the first-principles method. Finally, the experimental and calculated results are compared to verify the reliability of the measured data.

In this study, the high-temperature refractive index of sapphire is studied by experimental tests and computational verification. Firstly, we build an experimental device that can indirectly measure the high-temperature refractive index of sapphire. This device can adjust the temperature from room temperature to 1200 ℃ and guide the laser to pass through the sapphire crystal at a certain angle, and then make it received by the position-sensitive sensor. Besides, we install a polarizer on the optical path to measure the anisotropic refractive index of the crystal. Based on this device, we propose the laser displacement method to measure the refractive index of a single sapphire crystal under different temperatures. When the polarization direction of the laser is perpendicular to the optical axis of the crystal, the measured refractive index is n_o. When the polarization direction is parallel to the optical axis of the crystal, the measured refractive index is n_e. Subsequently, we perform error analysis and thermal expansion correction on the experimental results. In addition, we measure unit cell parameters of sapphire at high temperatures by variable temperature X-ray diffraction (XRD). According to the first-principles thinking, we calculate the band structure and optical properties of sapphire under different temperatures. The reliability of the laser displacement method is verified by experimental results, and the increase in the refractive index is explained in terms of lattice expansion.

The practicability and credibility of the experimental device (Fig. 2) and laser displacement method (Fig. 3) are verified in this study. The ordinary refractive index n_o and the extraordinary refractive index n_e (Fig. 6) measured by the laser displacement method increase linearly with the increase in temperature. To improve the accuracy and reliability of the data, we analyze the horizontal error of laser translation and the pixel size of the complementary metal oxide semiconductor (CMOS) camera. Besides, we have corrected the error caused by the thermal expansion. The final thermo-optical coefficients of the sapphire are 1.5793×10^-4 K^-1 (o-ray) and 1.5517×10^-4 K^-1 (e-ray), respectively. The lattice parameters a and c [Fig. 4(a)] of sapphire measured by XRD increase linearly with the increase in temperature. To further verify the reliability of experimental data, we use the first-principles calculation to obtain the relationship between the refractive index of sapphire and temperature (Fig. 8 and Fig. 9). The results show that the changing trend of the calculated data is the same as that of the experimental data, and the reason why calculation results are smaller is analyzed. In addition, we calculate the relationship between the band gap and temperature (Fig. 10) , and explain why the refractive index of sapphire becomes larger under high temperatures.

Sapphire is an ideal structural material for high-temperature pressure sensors at a temperature above 1000 ℃. The dearth of refractive index under high temperatures restricts the development of these sensors. In this paper, an experimental device for measuring the refractive index anisotropy of crystals is designed based on the Huygens principle. As temperature ranges from room temperature to 1200 ℃, the ordinary refractive index n_o and the extraordinary refractive index n_e of sapphire at wavelength of 445 nm are measured by the laser displacement method. The final calculated thermo-optical coefficients are 1.5793×10^-4 K^-1 (o-ray) and 1.5517×10^-4 K^-1 (e-ray), respectively. In addition, optical parameters such as the refractive index of sapphire in this temperature range are calculated by the first-principles method. The results show a similar variation of refractive index with temperature. The experiment and simulation results are in good agreement and verify the reliability of high-temperature refractive index data. Besides, we find that lattice expansion is the cause of a smaller band gap and a larger refractive index. The data provides an effective reference for the development and application of sapphire materials and the performance optimization design of related devices.