The tables in this chapter give information on modes and scattering geometries that are in most common use in the study of hypersound in single crystals. Just as in the case of Xrays, Brillouin scattering is not sensitive to the presence or absence of a centre of symmetry (Friedel, 1913). Hence, the results are the same for all crystalline classes belonging to the same centric group, also called Laue class. The correspondence between the point groups and the Laue classes analysed here is shown in Table 2.4.5.1. The monoclinic and triclinic cases, being too cumbersome, will not be treated here.
Crystal system  Laue class  Point groups 
Cubic 




Hexagonal 




Tetragonal 




Trigonal 




Orthorhombic 
O 


For tensor components and , the tables make use of the usual contracted notation for index pairs running from 1 to 6. However, as the tensor is not symmetric upon interchange of , it is necessary to distinguish the order and . This is accomplished with the following correspondence:
Geometries for longitudinal modes (LA) are listed in Tables 2.4.5.2 to 2.4.5.8. The first column gives the direction of the scattering vector that is parallel to the displacement . The second column gives the elastic coefficient according to (2.4.2.6). In piezoelectric materials, effective elastic coefficients defined in (2.4.2.11) must be used in this column. The third column gives the direction of the light polarizations and , and the last column gives the corresponding coupling coefficient [equation (2.5.5.11)]. In general, the strongest scattering intensity is obtained for polarized scattering (), which is the only situation listed in the tables. In this case, the coupling to light () is independent of the scattering angle , and thus the tables apply to any value.
Tables 2.4.5.9 to 2.4.5.15 list the geometries usually used for the observation of TA modes in backscattering (). In this case, is always perpendicular to (pure transverse modes), and is not necessarily parallel to . Cases where pure TA modes with in the plane perpendicular to are degenerate are indicated by the symbol D in the column for . For the Pockels tensor components, the notation is if the rotational term vanishes by symmetry, and it is otherwise.
Tables 2.4.5.16 to 2.4.5.22 list the common geometries used for the observation of TA modes in 90° scattering. In these tables, the polarization vector is always perpendicular to the scattering plane and is always parallel to the incident wavevector of light q. Owing to birefringence, the scattering vector does not exactly bisect and [equation (2.4.4.4)]. The tables are written for strict 90° scattering, , and in the case of birefringence the values of to be used are listed separately in Table 2.4.5.23. The latter assumes that the birefringences are not large, so that the values of are given only to first order in the birefringence.