Damping mechanisms of phonon polaritons, exploited by stimulated Raman gain measurements

Using a two-beam amplifier experiment stimulated Raman gain measurements were performed for the polariton branch of the $256-{\mathrm{cm}}^{\mathrm{-}1}$ $A_1$ (TO) optical phonon mode in ZnO-doped congruent ${\mathrm{LiNbO}}_3$ and undoped nearly stoichiometric ${\mathrm{LiNbO}}_3$ for polariton frequencies from 30 to $230{\mathrm{cm}}^{\mathrm{-}1}.$ The dependence of the peak value and linewidth of the Raman gain curve on the polariton frequency provides detailed information on the frequency-dependent damping of the polariton. Spontaneous Raman spectra of the $256{\mathrm{cm}}^{\mathrm{-}1}$ phonon, with particular emphasis upon the low-frequency wing of the Raman line, complete the results. The experimental results are carefully analyzed by comparison with a theory connecting the stimulated and spontaneous Raman data to the dielectric function of ${\mathrm{LiNbO}}_3,$ which contains the damping of the polaritons. As damping mechanisms the anharmonic decay of the phonon part of the polariton, the scattering at crystal defects and the coupling to low-frequency excitations are discussed. We relate three of the low-frequency excitations to $E$ phonon modes of ${\mathrm{LiNbO}}_3$ and the major part to defect modes.