Spontaneous, stimulated, coherent and incoherent nonlinear wave mixing and Hyper-Rayleigh scattering; a unified quantum-field description

By combining a quantum treatment of the radiation field with a superoperator formalism we present compact expressions for a broad variety of coherent and incoherent nonlinear optical signals. Spontaneous signals are classified according to the molecular coherence range: homodyne detected signals result from long range two particle coherence whereas Rayleigh and hyper-Rayleigh scattering are shown to be their short range counterparts. The dependence of the signals on wave vector, number of molecules and the molecular density is discussed for molecular and polymer solutes. Several two-photon induced techniques: second harmonic generation, hyper-Rayleigh scattering, two photon fluorescence and hyper-Raman are described within the same framework.