Nonlinear Optical Coefficients and the Raman Scattering Efficiency of LO and TO Phonons in Acentric Insulating Crystals

Abstract

The relations between nonlinear optical coefficients and Raman scattering efficiencies of LO and TO phonons in crystals of arbitrary (acentric) structure are derived, under the adiabatic, electrostatic, and harmonic approximations usual to lattice dynamical theory. Expressions for the total electro-optic coefficients and the nonlinear optical coefficients are presented in terms of Raman efficiencies and the optic-mode frequencies. The use of the macroscopic field in computing the "electro-optic" contribution to LO scattering efficiencies is shown to be justified. The practical conditions under which these expressions may be solved are examined using scattering data for LiNb${\mathrm{O}}_3$, LiTa${\mathrm{O}}_3$, GaAs, BeO, ZnS, ZnO, and CdS. Theory and experiment are found to be in good agreement. It appears that for many materials nonlinear coefficients and electro-optic coefficients may be determined from Raman data with accuracy comparable to direct measurement in the traditional manner.