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Dispersion theory of effective meromorphic nonlinear susceptibilities of nanocomposites

Dispersion theory of the nonlinear effective susceptibilities of layered and Maxwell-Garnett nanocomposites is considered. It is pointed out that in four-wave-mixing processes, where the nonlinear signal has the same angular frequency as the incident light wave, the effective nonlinear susceptibility is a complex meromorphic function. The special feature of such effective nonlinear susceptibilities is that they possess simultaneously poles and zeros in the upper half of the complex-angular-frequency plane. As a solution for the phase-retrieval problem, which cannot be treated by means of Kramers-Kronig relations, an analysis based on the maximum-entropy model is suggested.