In this paper, we present an alternative method to Sommerfeld integrals for
the calculation of a point source radiation in a multilayered background,
based on the method of auxiliary sources, also called fictitious sources
method. The method lies upon the decomposition of reflected and transmitted
fields on a basis of secondary sources, which amplitudes are determined by
applying boundary conditions at each multilayer interface, solving an
over-determined system of equations. We present a generalization of the
classical FSM to open stratified domains, with arbitrary number of layers
and arbitrary position of the point source in the multilayer. Two and three
dimensional formalisms are proposed, and compared to exact Sommerfeld
formulation. Computation time reduction factors as high as 100 are obtained
for 2D problems. Moreover, this method enables the study of non-flat
interfaces, which is not possible with Sommerfeld approach. This method can
be used for example in order to determine radiation efficiency of emitting
devices, or it can be integrated in discrete source type electromagnetic
methods for calculation of scattering by a complex target.