Two scattering-matrix theories for time-harmonic fields in three dimensions are presented: (ⅰ) a plane-wave theory with a directional spectrum that is obtained through a complex-source point substitution procedure, and (ⅱ) a complex-source beam theory based on a beam expansion of spherical multipole fields. Scattering matrices for plane-wave expansions, which determine the plane-wave spectrum of the scattered field of an object due to an incoming plane wave, are readily available. The analogous scattering matrices based on complex-source beams will be derived from Waterman's T matrices. These scattering matrices determine the beam weights for the scattered field in terms of the output of elementary beam receivers, which sample the incident field at complex points in space. The two scattering-matrix formulations will also be compared with Kerns plane-wave theory.
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