## Abstract

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 $\mathcal{K}$ group of spherical symmetry, the ${\mathcal{C}}_{\infty v}$ group of axial symmetry, and the ${\mathcal{D}}_{\infty h}$ group of dihedral axial symmetry. The ${\mathcal{D}}_{\infty h}$ symmetry relations for the $\mathcal{T}$ 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 ${\mathcal{D}}_{\mathit{Nh}}$ symmetry, i.e., for the important case of particles with dihedral symmetry and an *N*-fold axis of rotation.

© 1999 Optical Society of America

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