Limiting thermal regimes of active disk elements under steady-state pumping and two-dimensional temperature distribution inside the disk

An analytic expression describing the stationary two-dimensional axially symmetric temperature distribution in a disk active element (AE) is derived upon pumping the entire disk whose thickness is 0.01 cm ≤ h ≤ 0.3 cm and the diameter-to-thickness ratio is 1 ≤ d/h ≤ 100. Thermomechanical stresses are calculated. It is shown that from the point of view of the disk damage, the tangential stress on the disk side face constitutes the major threat. For different scaling parameters x =d/h, the limiting lasing powers P_las are estimated in multimode approximation, which can be obtained using a disk AE in the case of end and side cooling for different heat exchange coefficients a (by the example of an Nd : YAG crystal). It is found that the side cooling can decrease P_las in some situations. The priority regions are established in the space of the parameters h, x, and a which, while increasing the pump intensity, are accompanied by one of the three events violating the normal operation of the laser: deterioration of spectral and luminescent AE parameters due to heating, malfunctioning of the cooling regime, or thermomechanical damage of the disk. It is shown that an increase in the scaling parameter x smoothes the radial temperature profile and the thermoelastic stress distribution profile.