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 solutio n in the T-matrix formulation. A systematic derivation of a representation of symmetry operations is presented in the vector space on which the T matr ix operates. From this the set of symmetry relations of the T matrix is obt ained for various point groups. As examples several symmetry groups relevan t to modeling atmospheric particles are treated, such as the K group of sph erical symmetry, the C-infinity v group of axial symmetry, and the D-infini ty h group of dihedral axial symmetry. The D-infinity h symmetry relations for the T matrix in spheroidal coordinates (denoted by script font) are als o derived. Previously known symmetry relations of the T matrix can be verif ied, 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. ( C) 1999 Optical Society of America [S0740-3232(99)01604-X].