This chapter reviews the main concepts of electromagnetic theory relevant for the understanding of this textbook. Based on Maxwell’s equations, we derive the wave equation and discuss homogeneous solutions, such as plane waves and evanescent waves. We derive the boundary conditions at interfaces between homogeneous media and the Fresnel reflection and transmission coefficients. We discuss energy conservation, causality, and reciprocity of electromagnetic fields. Point response functions are introduced (Green functions) in order to derive the inhomogeneous solution of the wave equation. The chapter concludes with the angular spectrum representation, a framework that allows arbitrary fields to be described as a superposition of plane and evanescent waves.

This introductory chapter sets the stage for the research field of nano-optics. It introduces the fundamental concept of localizing light beyond the diffraction limit through the superposition of propagating and evanescent waves, emphasizing the critical role of evanescent waves. Additionally, it provides a historical overview of the key developments that have shaped nano-optics, and outlines the scope of the book.

The chapter covers subwavelength-localized optical fields and their interaction with matter. Localized fields contain evanescent waves, which decay exponentially away from their source region. To study the interaction of localized fields with matter, we introduce field-confining structures known as optical probes. To interact effectively with the sample, these optical probes are placed within the range of the evanescent waves and raster-scanned across the sample, a technique known as near-field optical microscopy. Given that optical probes inevitably interact with the sample, we start out with a series expansion of these probe–sample interactions, gaining insights into their nature and strength. We then discuss fundamental aspects of light confinement concepts and the corresponding optical probes, such as subwavelength apertures and resonant scatterers. This includes an exploration of how different probe designs influence the probe performance. Finally, we address probe–sample distance control and categorize various realizations of near-field optical microscopes according to the leading terms of the interaction series. This categorization helps to differentiate between different types of microscopes and their specific applications, providing a comprehensive overview of the field.