Quantum theory of light in lossy nonlinear media

We present a canonical quantum theory of radiation in nonlinear media taking into account the effects of linear dispersion and absorption in a consistent way. We apply recently developed concepts of the quantization of radiation in dispersive and absorbing linear media and extend the theory in order to include nonlinear optical processes. In particular, the method enables us to systematically derive the noise sources that arise naturally in the nonlinear terms in the space-time propagation equations of the radiation fields.