Theory of nonlinear light scattering from phonons in crystals

Abstract

Nonlinear light scattering from phonons opens up new possibilities in the study of ionic motion. A theory of nonlinear inelastic light scattering in solids involving two incident photons of frequencies ω₁ and ω₂, a phonon of frequency ω₀, and the scattered photon of frequency ω₃=ω₁+ω₂±ω₀ is developed. When both the incident light waves are the same, it reduces to the intensity-dependent light scattering from phonons in crystals. It is shown that the cross-section for the nonlinear scattering is smaller by a factor |E_L|²/{|E_a|}² as compared to the corresponding linear scattering with only one incident photon, where |E_L| is the amplitude of the electric field of the additional incident wave and E_a is of the order of (10⁶/10⁷) e.s.u. at optical frequencies. A nonlinear polarizability theory for the scattering based on the linear polarizability theory of Born and Bradburn of the first-order linear Raman effect is also considered and shown to be equivalent to the general theory in the limit of zero phonon frequency. Symmetries of the scattering tensor and selection rules for long-wavelength nonpolar optical phonons are derived for all the cubic point groups. These selection rules are different from those for the first-order Raman effect and the intra-red absorption. The rate of photon production in the stimulated nonlinear process is discussed.