On the angular-spectrum representation of multipole wave fields

The closed-form expression of the angular spectrum of multipole fields, both scalar and vectorial, of any order and degree, evaluated across a plane orthogonal to an arbitrary (fixed) direction, is provided. Such a result has been obtained by starting from the Weyl representation of multipole fields and using suitable transformation rules. Moreover, as far as the vectorial case is concerned, knowledge of the (vectorial) transverse angular spectrum allows one to gain some insight into the polarization structure of the multipole fields evaluated across a typical plane. Such information could be useful, for instance, in those problems dealing with the interaction between planar partially reflecting surfaces and waves.