A relation is developed between point-group symmetries of light-scattering particles and symmetry relations for the electromagnetic scattering solution in the <i>T</i>-matrix formulation. A systematic derivation of a representation of symmetry operations is presented in the vector space on which the <i>T</i> matrix operates. From this the set of symmetry relations of the <i>T</i> matrix is obtained for various point groups. As examples several symmetry groups relevant to modeling atmospheric particles are treated, such as the <i>K</i> group of spherical symmetry, the <i>C</i><sub>∞<i>v</i></sub> group of axial symmetry, and the <i>D</i><sub>∞<i>h</i></sub> group of dihedral axial symmetry. The <i>D</i><sub>∞<i>h</i></sub> symmetry relations for the <i>T</i> matrix in spheroidal coordinates (denoted by script font) are also derived. Previously known symmetry relations of the <i>T</i> matrix can be verified, and new relations are found for <i>D</i><sub><i>Nh</i></sub> symmetry, i.e., for the important case of particles with dihedral symmetry and an <i>N</i>-fold axis of rotation.
© 1999 Optical Society of America
F. Michael Schulz, Knut Stamnes, and J. J. Stamnes, "Point-group symmetries in electromagnetic scattering," J. Opt. Soc. Am. A 16, 853-865 (1999)