Generation, reflection and transmission of nonlinear harmonic waves by direct superposition of anharmonic dipoles

Abstract: 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).