Point-group symmetries in electromagnetic scattering

A relation is developed between point-group symmetries of light-scattering particles and symmetry relations for the electromagnetic scattering solution in the T-matrix formulation. A systematic derivation of a representation of symmetry operations is presented in the vector space on which the T matrix operates. From this the set of symmetry relations of the T matrix is obtained for various point groups. As examples several symmetry groups relevant to modeling atmospheric particles are treated, such as the K group of spherical symmetry, the C_∞ν group of axial symmetry, and the D_∞h group of dihedral axial symmetry. The D_∞h symmetry relations for the T matrix in spheroidal coordinates (denoted by script font) are also derived. Previously known symmetry relations of the T matrix can be verified, and new relations are found for D_Nh symmetry, i.e., for the important case of particles with dihedral symmetry and an N-fold axis of rotation.