Beam divergence and refractive power of directly coated solid state lasers

A relation between the far field divergence angle of a laser output beam and the elements of the laser resonator matrix is derived. This relation is applied to the resonator matrix of directly coated laser rods and yields an expression for the far field angle θ_m of the output beam in terms of the pump light induced refractive power D of the rod. By means of this expression D versus the average pumping power is calculated from the experimental values of θ_m for several laser rods and is found to be in good agreement with previously published values.