Symmetry, Unitarity, and Geometry in Electromagnetic Scattering

Upon defining vector spherical partial waves {Ψ_n} 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_nn'=(kπ)dσ.[(∇×ReΨ_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.