ANTIPHASE DYNAMICS OF MULTIMODE INTRACAVITY 2ND-HARMONIC GENERATION

We study analytically the properties of second-harmonic generation in a laser cavity. We determine the general criterion of stability for stable steady-state multimode operation. When this condition is not verified we construct analytically the emerging periodic solutions and show that they display antiphase dynamics. When the steady state is stable, we prove that there are four internal frequencies irrespective of the mode number. We show that in this case antiphase dynamics occurs in the transient relaxation to the stable steady state and in the response to noise. Transient antiphase dynamics is shown to imply the disappearance of low-frequency features in the total intensity whose power and noise spectra display a single maximum.