Theory of Infrared and Raman Processes in Crystals: Selection Rules in Diamond and Zincblende

To analyze infrared and Raman processes in crystals, the normal-mode spectrum of the crystal can be idealized by a discrete set of oscillators. These belong to the critical points in the lattice vibration spectrum; such points can be determined group theoretically. This approach, plus the relevant space-group selection rules, is used to determine the active one-, two-, three-, and (some) four-phonon combination and overtone processes in diamond and zincblende structures. All two-phonon overtones are infrared dipole forbidden in the diamond structure, verifying a conjecture of Lax and Burstein. Two-phonon overtones of LO and LA modes at $X$ are infrared dipole forbidden in zincblende. Analysis of three-phonon processes will enable unambiguous optical assignments of symmetry species to branches to be made in diamond and zincblende, thus resolving uncertainties at the critical points. Some selection rules for electric quadrupole and magnetic dipole processes are indicated: These may give rise to anisotropic optical absorption in cubic crystals.