Introduction

This chapter presents the electromagnetic theory that describes the main characteristics of surface electromagnetic modes in general and surface plasmons (SPs) in particular that propagate along single- and double-interface planar guiding structures. We begin with an introduction to electromagnetic theory that discusses Maxwell's equations, the constitutive equations and the boundary conditions. Next, Maxwell's equations in terms of time-harmonic fields, electric and magnetic fields in terms of each other, and the resultant wave equations are presented. Group velocity and phase velocity, surface charge at a metal/dielectric interface and the perfect electric conductor conclude this introduction. Following this introduction are sections that describe the properties of electromagnetic modes that single- and double-interface planar guiding structures can support in terms of the media they are composed of. These media will be presented in terms of their permittivity and permeability whose real part can be either positive or negative. A new formalism will be developed to treat such media in the context of natural materials such as metals and dielectrics and in terms of a collection of subwavelength nanostructures dubbed metamaterials. Finally, the power flow along and across the guiding structures is presented, and the reflectivity from the base of a coupling prism and the accompanied Goos–Hänchen shift are treated. The material covered in this chapter draws heavily from Refs. [1] to [3] for the theory of electromagnetic fields and from Refs. [4] and [5] for the theory of optical waveguides.