When deciding how to organize a book on surface plasmons, it seemed natural to consider the dimensionality of the surfaces on which they exist. On planar surfaces, which include both semi-infinite surfaces as well as multilayer thin films, there is a rich body of phenomena related to propagating surface plasmons. The same is true for surfaces of nanoparticles having a rich variety of phenomena for localized surface plasmons. Surfaces of nanowires and nanogrooves lie in between these two regimes, and these surfaces support both propagating and nonpropagating surface plasmons. In this book, therefore, we have initially categorized the chapters by surface dimensionality, trying to point out both the differences and similarities of the surface plasmon phenomena in these three regimes.

This book does not hesitate to include mathematical derivations of the equations that describe the basic surface-plasmon properties. After all, it was our desire to base the book on Mathematica precisely so that these equations could be explored in detail. Our derivations of the properties of surface plasmons are based on Maxwell's equations in SI units. In Chapter 2, Maxwell's equations are introduced for dense media, i.e., media which can be described by frequency dependent permittivity, permeability and conductivity. Because interfaces are essential to surface plasmons, the electromagnetic boundary conditions are required. Practically all of the results in this book are based on time-harmonic fields that can be most simply represented in complex notation. Unfortunately, in the literature there is no standard definition for the complex functional dependence on time of the electric and magnetic fields.