Small signal approximation method to determine output patterns of off-axis pumped solid-state lasers

To determine the output patterns of off-axis pumped solid-state lasers, we develop a small signal approximation method to obtain the relative modal weightings of Hermite Gaussian modes. The advantage of the method is that the differential rate equations are simplified to linear algebraic equations, which can be easily solved. In order to prove the validity of the method, we experimentally demonstrated an off-axis pumped laser, and measured its relative modal weightings. The experimental results are in high concordance with the calculated results. Moreover, the characteristics of the modes near the threshold are investigated. The modes exhibit the competition effect at the beginning, and then the photon number of each mode turns into linear increasing with the pump power growing. Due to this linearity, we can calculate the relative modal weightings for an actual laser by the small signal method, although it always operates far above threshold. •A method to calculate the modal weightings of off-axis pumped lasers is presented.•We can predict the modal weightings for an actual laser by the method porposed.•A Hermite Gaussian mode laser is experimentally demonstrated.