Intensity noise of Kerr oscillators

Absorbing or emitting elements generate noise waves. The main purpose of this paper is to determine from first principles the spectral density of noise waves relating to nonlinear elements. This was done by considering the combination of linear elements (whose noise properties are well understood) and lossless circuits that are nonlinear because of the Kerr effect. Lossless nonlinear circuits transform noise waves but do not generate noise. A semiclassical theory shows that noise waves remain at the shot noise level (for full population inversion) if the optical gain is considered a function of photon rate (rather than optical intensity). This result, in exact agreement with an independent theory of spectral-hole burning, is conjectured to be general. Intensity fluctuations of a Kerr oscillator are squeezed below the shot-noise level for large Kerr constants.