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

Abstract

It is well known that the linear and nonlinear light reflection and transmission formula can be obtained from the standard macroscopic Maxwell equation. In the past, a microscopic approach based on the Ewald–Oseen extinction theorem to derive the reflection and transmission formula by direct dipole summation has been performed by Fearn et al where they successfully derived the Fresnel formula in linear optics. In this work, we extend their work for the first time to derive the nonlinear reflection and transmission formula by direct summation of anharmonically oscillating dipoles for the case of a normal incidence wave, yielding similar results with coupled-mode-theory (CMT). We demonstrate for a decaying incoming field that dipolar radiation is no longer forbidden inside the bulk of a centrosymmetric material. Using the simplified bond hyperpolarizability model (SBHM), we find that these additional bulk dipole contribution must be accounted along with the surface dipoles and bulk quadrupolar contribution to explain recent rotational anisotropy SHG intensity experimental data of Si(111) with high precision.