Thermal effects of the refractive index caused by the electron-phonon interaction

The refractive index for crystals or small disordered materials has been derived by using a semiclassical method. The influence of the electron-phonon interaction on the thermal effects of the refractive index has been studied. The temperature coefficient of the refractive index is a constant at high temperature and is proportional to $T^3$ at low temperature. The zero-dispersion wavelength increases with a temperature rise. The temperature coefficients of NaCl, ZnSe, and several other materials have been calculated. Theoretical results are compared with experimental data, and they are consistent with each other.