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

TL;DR

This paper derives formulas for nonlinear harmonic wave generation, reflection, and transmission using superposition of anharmonic dipoles, emphasizing phase matching and comparing results with coupled-mode theory.

Contribution

It introduces a direct superposition method for analyzing nonlinear harmonic waves, providing explicit expressions and phase matching conditions.

Findings

Transmitted and reflected nonlinear waves propagate only under phase matching.

Results for second-harmonic-generation align with coupled-mode theory.

Explicit formulas for nonlinear wave behavior are derived.

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).