The exact equation for Brillouin shifts

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Abstract
The exact equation for the Brillouin shifts is given by [FORMULA] where νi is the frequency of the incident light, θ the scattering angle, n s and ni are the refractive indices for the incident and the stcattered waves ,c tha velocity of light in vacuum, νe the velocity of the acoustic wave responsible for the scattering ; β s = ns υe/c, βi = ni υe/c. The two main additional features are the anisotropic effect for birefringent crystals discussed earlier by the author [3] and the quadratic term. In the case of isotropic crystals or liquids. [FORMULA] The quadratic term leads to unequal displacements of anti-Stokes and Stokes components corresponding to the relativistic Doppler effect but with a small dispersive term. In the case of backward scattering in diamond the quadratic Brillouin effect can be determined experimentally ; the expected shifts for longitudinal components along the [111] direction are for λ 2 537, ΔνAS = + 12.79887 cm-1, Δ νs = - 12.79370 cm-1

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