Optimization of intracavity doubled passively Q-switched solid-state lasers

Passively Q-switched lasers can be optimized by the choice of two factors: 1) reflectivity of the output coupler and 2) transmission of an unsaturated absorber. When intracavity frequency doubling is adopted, the nonlinear crystal behaves as a nonlinear output coupler. In this paper, we generalize the optimization theory for intracavity frequency-doubled passively Q-switched lasers, By introducing a nonlinear loss term caused by the frequency doubler into the coupled rate equations describing the operation of saturable absorber passively Q-switched lasers, we can express the harmonic pulse characteristics such as peak power, pulse energy, pulsewidth, and a factor describing pulse symmetry. Using the Lagrange multiplier technique to maximize the peak power of the second harmonic for a given pump level, we obtain an additional constraint equation describing the relation of a frequency-doubling factor to a normalized intermediate variable, which can be solved quickly to determine the characteristics of the pulse. The frequency-doubling factor, which is a normalized key parameter, is found to depend not only on the commonly used coefficient of the nonlinear frequency doubler and the emission cross section of the laser medium, but also on the laser cavity optical length. We plot design curves indicating the key parameter and the pulse characteristics via two normalized variables, one representing the pump level, and the other representing the laser emission medium and the absorber medium. Using these curves and expressions, one can design an optimal passively Q-switched intracavity frequency-doubled miniature laser and predict the pulse characteristics without relying on computer calculation.