Brillouin Scattering in Anisotropic Media: Calcite

We have used comparative Brillouin scattering (reference scatterer: toluene) to measure the nine photoelastic tensor elements of calcite (eight elastically symmetric, one elastically anti-symmetric) in both magnitude and sign. Our measurement of the recently predicted anti-symmetric component agrees in magnitude to 5% with that theoretically predicted. By adopting the theoretical sign for this component, the signs of all other components are determined from the data. The 5% agreement gives a measure of the absolute accuracy of the results. The presence of the antisymmetric component causes p₂₃₂₃ and p₂₃₃₂, previously believed to be equal, to differ by more than a factor of 10. The formulas needed to analyze Brillouin scattering in anisotropic media are derived using a new constitutive relation and a new Green's function for radiation in an anisotropic medium. Inclusion of boundary effects (solid angle expansion, scattering-volume demagnification, etc.) makes the formulas valid outside the scattering medium. The convenience of comparative Brillouin scattering for the numerical determination of the photoelastic tensor components, particularly in low-symmetry crystals, is emphasized.