Quantization of radiation emitted at discontinuities of nonlinearity

Abstract

It is appropriate to base the quantum description of light propagation and down-conversion in a nonlinear medium on a Hamiltonian operator. In pumping with femtosecond pulses, which is not yet treated here, the description is so complicated that the discontinuities of the linear and nonlinear susceptibilities present a specific problem. In contrast, the analogy with a quantum nonlinear beam splitter can be utilized for the quantization of classical input–output relations. On numerical simulation, nonvanishing commutators between output field operators of different modes are revealed and a method of adaptation of these results to quantum input–output relations is also proposed.