Published online by Cambridge University Press: 05 November 2012
At the heart of nano-optics are light-matter interactions on the nanometer scale. For example, optically excited single molecules are used to probe local environments and metal nanostructures are exploited for extreme light localization and enhanced sensing. Furthermore, various nanoscale structures are used in near-field optics as local light sources.
The scope of this chapter is to discuss the interactions of light with nanoscale systems. The light-matter interaction depends on many parameters, such as the atomic composition of the materials, their geometry and size, and the frequency and intensity of the radiation field. Nevertheless, there are many issues that can be discussed from a more or less general point of view.
To rigorously understand light-matter interactions we need to invoke quantum electrodynamics (QED). There are many textbooks that provide a good understanding of optical interactions with atoms or molecules, and we especially recommend the books in Refs. [1–3]. Since nanometer-scale structures are often too complex to be solved rigorously by QED, one often needs to stick to classical theory and invoke the results of QED in a phenomenological way.
The multipole expansion
In this section we consider an arbitrary material system that is small compared with the wavelength of light. We call this material system a particle. Although it is small compared with the wavelength, this particle consists of many atoms or molecules. On a macroscopic scale the charge density ρ and current density j can be treated as continuous functions of position.
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