  In this paper we describe how to derive the expressions for the higher
nonlinear generation of waves, their transmission and reflection for the case
of a normal incidence plane wave by direct superposition of nonlinear dipoles.
We describe explicitly that the transmitted and reflected nonlinear harmonic
wave can only propagate inside the material if the phase matching condition is
fulfilled and show for the case of second-harmonic-generation that our
calculation yields similar results with coupled-mode-theory (CMT).
