  The spectral expansion of the Green's tensor for a planar multilayered
structure allows us to semi analytically obtain the angular spectrum
representation of the field scattered by an arbitrary dielectric perturbation
present in the structure. In this paper we present a method to find the
expansion coefficients of the scattered field, given that the electric field
inside the perturbation is available. The method uses a complete set of
orthogonal vector wave functions to solve the structure's vector wave equation.
In the two semi-infinite bottom and top media, those vector wave functions
coincide with the plane-wave basis vectors, including both propagating and
evanescent components. The technique is used to obtain the complete angular
spectrum of the field scattered by a nanohole in a metallic film under Gaussian
illumination. We also show how the obtained formalism can easily be extended to
spherically and cylindrically multilayered media. In those cases, the expansion
coefficients would multiply the spherical and cylindrical vector wave
functions.
