Influence of the phase-matching conditions on the spectrum of four-photon light scattering at a one-photon resonance

An analysis is made of the influence of the phase matching conditions on the four-photon scattering spectrum at a one-photon resonance under various focusing conditions. An analytic expression is obtained for the phase matching integral in the limiting cases of hard focusing and strong absorption in a medium with the cubic nonlinearity. A study is made of the influence of one-photon resonances on the form of the spectrum of four-photon scattering by excited and preionisation states of atoms. Calculations are reported of the four-photon scattering spectra in which allowance is made for the interference of the resonant and nonresonant components of the third-order nonlinear susceptibility. A method for the normalisation of the experimental four-photon scattering spectra under one-photon resonance conditions is proposed; this method allows for the distortions associated with the influence of the phase mismatch and of one-photon absorption.