Symmetry, Unitarity, and Geometry in Electromagnetic Scattering

Upon defining vector spherical partial waves {Ψₙ} as a basis, a matrix equation is derived describing scattering for general incidence on objects of arbitrary shape. With no losses present, the scattering matrix is then obtained in the symmetric, unitary form S=-^Q^'*^Q*, where (perfect conductor) ^Q is the Schmidt orthogonalization of ${Q}_{n{n}^{{'}}}=({k}{{π}}){∫}d{{σ}}·{}[({∇}×{}Re{{{Ψ}}}ₙ)×{}{{{Ψ}}}_{{n}^{{'}}}]$, integration extending over the object surface. For quadric (separable) surfaces, $Q$ itself becomes symmetric, effecting considerable simplification. A secular equation is given for constructing eigenfunctions of general objects. Finally, numerical results are presented and compared with experimental measurements.