Off-axis pumped Hermite-Gaussian mode solid-state laser

Abstract

To study the modes’ pattern and the modes’ competition behavior of an off-axis pumped solid-state laser, a small signal approximation method is derived, which simplifies the multiple-mode differential equations into liner algebraic equations. When the pump beam radius is small, the higher-order Hermite-Gaussian modes emerge successively with the off-axis displacement increasing, while the pattern evolution shows some complexity when the pump radius is larger. The percentage of the modes with a small pump power near the threshold, calculated with the small signal method, is close to that calculated at a higher pump power by directly solving the rate equations numerically. This indicates that we can estimate the modes’ pattern of an actual high power laser by using the small signal method. For a multiple Hermite-Gaussian modes off-axis pumped solid state laser, as the pump power increases, the photon number of the mode increases linearly as its net gain becomes positive, while that of the second mode with a smaller net gain does not increase immediately as it becomes positive successively. Larger pump power is required until the photon number begins to increase. The increasing slope of first mode decreases as the second mode begins to grow. The dynamics of the modes’ competition presents cross spiking and cross relaxation process before they become stable. Moreover, the outputs of the modes HG₀₀-HG₅₀ are experimentally demonstrated, and the spot evolution with the off-axis displacement agrees very well with the calculated result.