Giant subthreshold amplification in synchronously pumped optical parametric oscillators

Synchronously pumped parametric oscillators have been shown to have subthreshold giant amplification of such a magnitude that a macroscopic, entirely noise-driven, signal is present at output even when the device is below threshold. In this paper we quantify the magnitude of the amplification factor in terms of some key device parameters. We use non-normal operator theory to find the noise amplification factor (Kreiss constant) and show that the signal amplitude is proportional to it. We also determine that the noise sensitivity depends in a nontrivial way on the group velocity of the three fields.