Quasi-plane waves and their use in radiation and scattering problems

Abstract

A complete set of solutions to the reduced wave equation which obey Sommerfeld's radiation condition are introduced and shown to play the same role in radiation (source) and scattering problems as do the homogeneous plane waves in problems involving the free field. These wave functions ( quasi-plane waves) are compared and contrasted to the usual plane waves and to spherical wave fields (multipole fields). An expansion for radiated or scattered fields in terms of these wave functions is derived which is analogous to the angular spectrum expansion but which involves only real wavevectors and converges everywhere outside the smallest sphere which completely encloses the source (scatterer).