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Abstract
The relaxation oscillation in triply resonant optical parametric oscillators (TROs) is studied theoretically. With constant pumping, the intensity noise spectra of the signal wave consist of a zero frequency and a relaxation oscillation frequency. An accurate relation between the relaxation oscillation frequency and the pump power is obtained. The square of the inherent relaxation oscillation frequency in TROs is linear in the square root of the pump power under high-power pumping. Also, the decay rate varies rapidly with low-power pumping and slowly with high-power pumping. Significantly, when there is a relaxation oscillation in the pumping, the undulation of the signal photon density in TROs also contains the relaxation oscillation frequency of the pumping besides its inherent noise. When those two frequencies are close, a resonance will appear, which should be avoided in practice.
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