Simple analytical method to calculate the radial energy deposition profile in an isotropic diode-pumped solid-state laser rod.

We provide an approximate but simple analytical solution to the radial distribution of deposited energy in a diode-array-pumped laser rod, subject to some assumptions that are naturally fulfilled for most applications of practical interest. The solution is useful to survey quickly irradiance distributions for a wide variety of pumping geometries and to find the radially most uniform energy deposition. We find that the radial deposition profile, as well as the pump light absorption efficiency, is largely controlled by just two dimensionless parameters: the number of absorption depths and the ratio of the width of the unabsorbed pump beam at the rod center divided by the rod radius. A side-by-side comparison with a numerical model is given. Results describing the best achievable trade-off between absorption efficiency and pumping uniformity are presented in the form of a recipe that can be followed without studying our research in detail. Finally, the model equations are applied to a practical side-pumped geometry.