Relationships between different expressions of thermo-optic and photoelastic coefficients of YAG crystal

Using correct expressions for piezo-optic and elasto-optic effects, the analytical relations between thermal coefficients of the refractive index at zero stress and zero strain have been established for YAG-type cubic crystals. Using the plane strain and plane stress approximations, analytical expressions for thermal radial and tangential changes of the refractive index have been found. The relations between different expressions for photoelastic coefficients are established. Examples of the inconsistent usage of generalised thermo-optic coefficients are discussed. It is shown that their values are often significantly overestimated when the results of the plane stress approximation are applied to a laser rod with a length larger than its diameter.