Raman scattering in impurity-induced anharmonic crystals

The theory of first-, second-, and third-order Raman scattering is investigated for isotopically disordered anharmonic crystals. The theory of time-dependent thermodynamic Zubarev Green's functions is adopted to obtain the Raman tensor, intensity of Raman lines, and differential cross sections of various orders of scatterings. It is observed that each class of scattering can be separated into diagonal and nondiagonal parts. The first-order and nondiagonal parts are absent in the case of chemically pure crystals. The diagonal parts are separated into anharmonic and interference terms. The interference terms arise due to the interactions of anharmonic phonons with the local phonons. The temperature and defect dependencies are discussed in detail along with the nature of continuous and line spectra. It is proposed that very high-power laser sources will reveal the third-order spectra, and that the resulting structure can be explained with the help of temperature-dependent one-, two-, and three-phonon density of states.