Gain and Loss Fluctuations in Nonlinear Optical Systems

The interaction of light and matter can be described by a set of coupled nonlinear evolution equations for the material and electromagnetic fields. In order to account for the effects of vacuum fluctuations, noise forces which cause spontaneous transitions have to be included. In these macroscopic systems various sources of noise besides fundamental quantum fluctuations exist which are of macroscopic origin. These cause fluctuations of the cavity dissipation as well as of the external pumping power. In the course of an adiabatic elimination procedure, these fluctuations appear as multiplicative noise in the equations of motion (e.g. for the field intensity, due to the nonlinearity of the interaction). While fluctuations of the cavity damping create noise linear in the field intensity, randomness in the pump strength causes fluctuations that depend nonlinearly on the light intensity. In this respect, the noise terms enter the equations of motion quite differently and have to be distinguished from spontaneous emission noise which is independent of the field strength, and is the basis of all traditional laser models.