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Theory of second harmonic generation in a resonator

A theoretical analysis is made of the pulse generation of a second harmonic in a nonlinear crystal placed inside a Q-switched laser resonator. Allowance is made for the saturation of the nonlinear interaction and for the inhomogeneity of the longitudinal distribution of the intensity of the fundamental-frequency radiation in the active element. The following main results of a computer analysis are reported: machine oscillograms of isolated harmonic pulses often have a fine structure; for a given length of the nonlinear crystal there are, under certain conditions, two values of the pump energy which ensure optimal conversion; an increase in the pump energy causes a greater proportion of the total harmonic energy to be generated during the forward pass through the nonlinear crystal; phase-matching curves for the energy of harmonic single pulses are much wider and smoother than in the case of second harmonic generation outside the resonator.