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A polarization dependence technique has been developed as a tool to investigate phonon scattering (PS), electronic Raman scattering (ERS), and two-photon absorption (TPA) transition intensities in vanadate and phosphate crystals. A general theory for the polarization dependence (PD) of two-photon transition intensities has been given. Expressions for the polarization dependent behavior of two-photon transition intensities have been tabulated for the 32 crystallographic point groups. When the wavefunctions for the initial and final states of a rare-earth doped in crystals are known, explicit PD expressions with no unknown parameters can be obtained. A spectroscopic method for measuring and interpreting phonon and ERS intensities has been developed to study PrVO{sub 4}, NdVO{sub 4}, ErVO{sub 4}, and TmVO{sub 4} crystals. Relative phonon intensities with the polarization of the incident and scattered light arbitrarily varied were accurately predicted and subsequently used for alignment and calibration in ERS measurements in these systems for the first time. Since ERS and PS intensities generally follow different polarization curves as a function of polar angles, the two can be uniquely identified by comparing their respective polarization behavior. The most crucial application of the technique in ERS spectroscopy is the establishment of a stringent test for the Axe theory. For the first time, the F{sub 1}/F{sub 2} ratio extracted from the experimental fits of the ERS intensities were compared with those predicted by theories which include both the second- and third-order contributions. Relatively good agreement between the fitted values of F{sub 1}/F{sub 2} and the predicted values using the second-order theory has been found.

Polarization dependence of two-photon transition intensities in rare-earth doped crystals