A polarization scheme for four-photon spectrscopy of two - quantum transitions in isotropic media and cubic crystals is presented; a new way of measuring the scattering cross section in two-photon absorption is demonstrated. Irreducible tensor groups are used in averaging the components of the tensor for the molecular resonant hyperpolarizability, and arelationship is established for the invariants of the molecular tensor for two-photon polarizability and the nonzero components of the tensor for the third-order macroscopic susceptibility. Theoretical estimates and experimental results are presented for the polarization dispersion of the signal in various organic liquids. Similar estimates have been made for GaF and ZnSe crystals.
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