We investigate the propagation of Γ⌃(X1,X2,ν) the Fourier transform of the mutual coherence function Γ (X1,X2,τ) in nonlinear dielectrics. We assume that the classical phenomenological equations govern the electric field within the dielectric, and we restrict our discussion to the propagation of fields with narrow angular spread. The indeterminate character of the propagation equations is emphasized, and it is shown that a determinate equation results only if the nonlinear term is small. In the quasimonochromatic limit, we investigate for this latter case the dependence of the two-point coherence of the second harmonic on the full fourth-order coherence of the incident beam, a result implied by Ducing and Bloembergen (1964), and Akhmanov et al. (1966). We also show under what circumstances the Hanbury-Brown and Twiss experiment may be performed using a single nonlinear dielectric.
MARK J. BERAN and JOHN B. DEVELIS, "Propagation of the Coherence Function in Nonlinear Dielectrics," J. Opt. Soc. Am. 57, 186-191 (1967)