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.

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Analytical and numerical studies of the thermal characteristics of conventional and composite laser rods in laser-diode endpumped geometry are reported in detail using Nd : YAG rods as an example. It has been shown that taking into account the temperature dependence of the heat conductivity, the change of the temperature in the active element can be significantly higher compared to the data for the temperature-independent heat conductivity coefficient. It has been found that the dependence of heat conductivity on temperature causes the non-parabolic heat distribution even in the region inside the pump beam with the top hat intensity distribution. It has also been shown by direct numerical simulations that the undoped entrance section of the composite rod significantly reduces the peak temperature rise inside the crystal.

Temperature dependences of the thermal conductivity and thermo-optic coefficient are often neglected when thermal lensing in laser crystals is investigated, though their influence is very significant. In this paper, the general solution of heat transfer equation with temperature dependent thermal conductivity is found in an integral form, which is very convenient for analytical and numerical analysis. Using this solution, the possibility to eliminate spherical aberration by a proper choice of the pump parabolicity parameter is investigated in detail. The inaccuracies in the definition of optical path differences used in a few previous works for the case of temperature dependent thermo-optic coefficient are explained. It is shown that the use of a correct definition increases the value of the parabolic coefficient at which the elimination of spherical aberrations may be realized as compared with the original work of Hodgson and Weber. It is also found that nearly the same shapes of pumping are required for elimination of spherical aberrations for both radial and tangential polarization.

Correct use of the photoelastic effect for the description of thermally induced refractive index change is discussed and the analytical relations between thermo-optic coefficients at zero stresses and zero strains are found for all classes of cubic crystals. These relations may be useful for the investigation of thermal effects in very promising sesquioxide class m3 laser crystals. An accepted set of elasto-optical coefficients of the YAG crystal and an alternative one found in the literature were used in numerical simulations. Significant differences in the calculated thermo-optic coefficients and induced birefringence are found using different sets of these coefficients. Misunderstandings related with the so-called photoelastic coefficients are resolved and new expressions for these coefficients are found. It is shown that the incorrect use of these coefficients for different pump beam distributions can lead to significant discrepancies for thermally induced birefringence. It is also shown that common use of the generalized thermo-optic coefficients significantly overestimates the values of optical power of thermal lenses when they are applied to the laser rods with lengths several times longer than their diameter.