Fundamentals and Applications of Nanophotonics || A dynamical, classical oscillator model for linear and nonlinear optics

摘要： In this chapter we will build and develop a self-consistent, classical oscillator model to describe linear and nonlinear optical interactions like refraction and frequency conversion in both centrosymmetric and noncentrosymmetric materials. In addition to being quite ubiquitous in all of physics, the classical oscillator model of matter is an enormously pedagogical tool that serves as a natural springboard to the description and understanding of quantum systems and leads to a rather detailed portrayal of all the dynamical factors that contribute to most linear and nonlinear optical phenomena. The method is endowed with causality as well as a natural degree of self-consistency that includes linear and nonlinear material dispersions, elements that are usually necessary to understand many of the subtleties of the interaction of light with matter. By way of examples, using this classical approach we will examine harmonic generation in bulk materials and in metal-based nanostructures. In centrosymmetric materials like metals (materials composed of molecules that lack a center of symmetry), second harmonic generation (SHG) arises mostly from nearly free, conduction electrons (nearly free because they are con?ned by the metal walls) and is due to a combination of spatial symmetry breaking (interfaces), the magnetic portion of the Lorentz force, and, to a lesser extent, the interaction of third harmonic (TH) and pump photons. By the same token, the third order nonlinearity (c(3)) gives rise to most of the TH signal, while to a small degree the interaction of pump and SH photons also produces cascaded, TH photons. The classical oscillator model will be pivotal in these systems as well, where a combination of free (Drude) and bound (Lorentz) electrons suf?ces to describe most linear and nonlinear optical phenomena.