RESUMO
Temperature profiles in pumped solid-state laser disks are generally calculated numerically by using finite-element programs to solve the heat conduction equation in the disk and the heat spreader. Analytical expressions exist for the longitudinal temperature profile in the case of an infinitely thick heat spreader or in the limit of zero thickness of the disk. We are presenting a simplified, semi-analytical method to calculate the three-dimensional temperature profiles for any disk or heat spreader dimensions by solving the heat conduction equation using Hankel transforms. This method allows for straightforward optimization of the cooling properties of heat-sink-mounted solid-state and semiconductor disk lasers.
RESUMO
The main challenge in disk laser design is the realization of efficient heat removal from the pumped area by optimizing the heat spreader design and the water impingement cooling. This generally requires the calculation of the temperature distribution in the disk by numerically solving the heat conduction equation using finite element algorithms. We have developed a simple method to calculate disk temperature profiles that is based on analytically solving the heat conduction equation in Hankel transform space. This method can be applied to disks that are mounted on multi-layered, water-cooled heat spreaders, which may include glue or solder layers and dielectric coating layers. The temperature and heat fluxes at the interfaces of the layers are connected via a heat transfer matrix, which allows for straightforward incorporation of additional heat sink layers or an undoped cap into the model. This generalized model allows for the parametric optimization of the heat distribution in pumped solid-state laser and semiconductor laser disks.