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