Four-wave mixing using partially coherent fields in systems with spatial correlations.

Abstract

A microscopic correlation function expression for the signal in four-wave mixing is developed. Both stationary and transient (i.e., photon-echo) experiments with coherent or incoherent radiation fields are considered. In general, these observables are described by an eight-point correlation function of the dipole operator involving two particles, and the signal cannot be written as an amplitude squared. Conditions under which the correlation function may be factorized into a product of two four-point, single-particle correlation functions are specified. In this case the conventional approach, based on calculating a nonlinear polarization and substituting it as a source in Maxwell's equations, is justified. However, in the presence of long-range spatial correlations in the sample (e.g., near critical points) the conventional formulation breaks down and the present theory should be used.