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Theory of intracavity-frequency-doubled solid-state four-level lasers

The spatial distributions of the pumping, the population inversion density, and the intracavity photon densities of the fundamental and the second harmonic are taken into account in the rate equations of the intracavity-frequency-doubled cw lasers. By normalizing the related parameters, it is shown that the general solution of these space-dependent rate equations is dependent upon three dimensionless paramenters: the pump to laser-mode size ratio, the normalized pump level, and a parameter written as ηSHG, which is related to the ability of the nonlinear crystal to convert the fundamental to the second harmonic. By numerically solving these rate equations, a group of general curves are obtained to express the relations between the solution and the three dimensioniess parameters. In addition, the optimal pump to laser-mode size ratio and the optimal ηSHG are determined. A comparison with the result obtained under the plane-wave approximation is also given.