Meromorphic degenerate nonlinear susceptibility: Phase retrieval from the amplitude spectrum

A problem in studying optical nonlinearities is the fact that the important analyzing tools---the dispersion relations for nonlinear susceptibilities---can be applied only in the nondegenerate case (excluding the cases of harmonic generation). We show that a maximum entropy procedure can be utilized in computing the phase of the complex degenerate nonlinear susceptibility [e.g., χ⁽³⁾({ω},{ω},-{ω})] from its amplitude spectrum [{}χ⁽³⁾({ω}){}, ω₁{≤}{ω}{≤}ω₂].