Second-harmonic generation in a resonator

A theory of steady-state single-frequency second-harmonic generation in a resonator is developed for the case when an active medium and a nonlinear crystal located inside the pump-laser resonator are separated by a beam splitter which deflects the harmonic out of the resonator. No assumptions are made about the nature of the influence of the harmonic on the the generation of the pump (fundamental-frequency) radiation and the fields in the resonator are defined as superpositions of plane monochromatic waves traveling in opposite directions along the resonator axis. The case of a pump-laser resonator which does not transmit at the fundamental frequency is analyzed in detail. Moreover, a detailed discussion is given of the influence of the absorption in the nonlinear crystal, ratio of the pump and harmonic intensities in the case of their simultaneous generation at the exit from the resonator, influence of feedback at the harmonic frequency (introduced by an additional resonator tuned to the harmonic frequency and coupled optically to the pump-laser resonator), etc. A report is given of an experimental investigation of the dependence of the harmonic intensity on the thickness of the nonlinear crystal and of the influence of a feedback at the harmonic frequency. The experimental results are in good agreement with the theoretical predictions.