Geometrical optimization of longitudinally lasers

End pumped or longitudinally pumped solid-state lasers have proven to be very efficient sources. They differ from side pumped lasers, regardless of the nature of the pump, by the fact that the gain is concentrated in a very well defined region. Furthermore the gain exhibits a transverse profile directly related to the pump beam profile which induces new requirements on the relative sizes of the pump beam and cavity mode. For example when an amplifying medium is pumped by a gaussian beam the unsaturated gain is higher on axis than on the edges of the gain profile. The average gain seen by a beam sent through this amplifier becomes a function of the beam size: the smaller the beam, the higher the small signal gain but also, the higher the saturation. There is then a trade-off between large small signal gain (i.e. small beam) and little saturation (i.e. large beam). Modeling of longitudinally pumped lasers has been extensively worked out [ l-61. The optimization of the different parameters influencing the efficiency of those lasers has been studied. In general it leads to complicated relations between these parameters which are difficult of use. We used a simplified analysis of gain saturation including transverse profiles of both pump and laser beams in order to find a simple rule of thumb giving the optimum ratio of the pump and laser beams sizes. This rule is found to work with gaussian and super-gaussian pump beams. We consider a laser medium of length 1 pumped by a beam which transverse profile isf( r). Only beams with cylindrical symmetry are considered in the fol-