The properties of optical materials are determined by the fundamental constituents of matter. In this chapter we discuss how to design materials with unusual optical properties by arranging meta-atoms, smaller than the wavelength of light, fabricated using nanotechnology. Meta-atoms arranged in periodic arrays with lattice constants of the order of the wavelength lead to photonic crystals. Photons in photonic crystals behave analogous to electrons in regular crystals, allowing principles from solid-state physics, such as doping, to be carried over. This results in fascinating effects such as photonic bandgaps and localized states of light. Metamaterials arise if meta-atoms are densely packed such that light propagates as if it were in a homogeneous medium. By tuning the properties of the meta-atoms, these materials can be tailored to exhibit exotic optical properties such as negative or near-zero refractive index. Finally, we introduce metasurfaces which directly mold the flow of light – a property that can be used to create ultraflat optical elements.

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.

In contrast to photonic crystals, random media lack spatial symmetry but are characterized by spatial and temporal correlations in the dielectric function. This results in unique effects on light propagation through such media. We begin by deriving the transport equation for light in random media, which, under specific conditions, leads to the diffusive behavior of photons. Following this, we explore phenomena such as Anderson localization and coherent backscattering, which can be attributed to time-reversed scattering pathways and the associated interference effects of photons. Lastly, we examine the application of random media as linear optical elements capable of focusing light to subwavelength spots, introducing the concept of singular-value decomposition in this context.

Based on the angular spectrum representation, we discuss the focusing and localization of electromagnetic fields. In the paraxial limit (weak focusing) we derive the Gaussian beam and discuss its key properties, including its collimation range and divergence. Using the method of stationary phase, we show how the far-field of any known field distribution can be derived and how these far-fields can be embedded in the angular spectrum representation in order to rigorously calculate strongly focused wave fields. Higher-order modes, such as Hermite–Gaussian beams, radially /azimuthally polarized beams, and orbital angular momentum (OAM) beams are introduced and the calculation of focused fields at interfaces is discussed. The chapter concludes with a derivation of the image of a point source, the so-called point-spread function, and a discussion of how it limits the resolution in optical microscopy.

In this chapter we discuss semianalytical methods for calculating optical fields in arbitrary geometries. Semianalytical methods rely on numerical procedures to derive analytical solutions for the problem at hand. Examples are the multiple-multipole method (MMP), the coupled-dipole method (CDM), or the method of moments (MoM). Based on the volume integral equation we show the equivalence of the CDM and the MoM. The comparison allows us to derive the most general form of the polarizability $\alpha$ of a small scatterer. We show that it reproduces the dynamic and quasi-static polarizabilities derived in previous chapters. We derive an equation for calculating the Green function of an arbitrary system, known as the Dyson equation, and discuss how it can be used to iteratively determine the electromagnetic field in an arbitrary geometry.

The chapter provides an overview about superresolution microscopy techniques. We start out discussing the resolution limit and its origin and then review the principles of confocal microscopy in which the multiplication of illumination and detection point-spread function leads to enhanced resolution and contrast. Based on these concepts, resolution improvements due to nonlinear contrast mechanisms are discussed before introducing light-sheet microscopy with its superior axial resolution. The chapter proceeds by introducing structured illumination as a method to enhance the resolution in microscopy by optimizing the detectable bandwidth of spatial frequencies. Superresolution in microscopy is always based on prior information about the sample. In localization microscopy such prior information introduces additional dimensions to the spatial imaging problem, such as time or colour, that are then used to distinguish closely spaced single emitters. Several advanced superresolution microscopy techniques are discussed in that context, such as PALM and STORM as well as MINFLUX and SOFI. At the example of STED microscopy, we discuss how the nonlinearity associated with saturable transitions in conjunction with intensity zeros can in principle lead to unlimited spatial resolution.

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.

In plasmas whose density is underdense the laser pulse can propagate through the plasma, depositing energy and driving plasma waves. The diverse effects seen in plasmas of this density regime are the subject of this chapter. The interplay of field ionization of a gas target, plasma heating and subsequent effects on laser propagation is scrutinized with phenomena such as plasma-induced defocusing and filamentation the subject of chapter sections. The self-consistent response of the plasma subject to a traversing intense pulse is modeled using the quasi-static approximation, illustrating how the ultrafast laser pulse can excite plasma waves. The impact of relativistic self-focusing is assessed and its interplay with those plasma waves discussed, leading to complex propagation effects. A section then addresses instabilities in the laser plasma interaction. The final sections of the chapter discuss how the production of these plasma wave wakefields can be used to accelerate electrons, with a range of regimes described ranging from linear, to nonlinear bubble and beatwave acceleration. A concluding section discusses betatron oscillations of electrons in the bubble acceleration regime.

This chapter opens with a discussion of the definition of the strong field physics, high-intensity regime, arguing that the strong field regime is entered, when considering interactions with atoms and molecules, when the light intensity is high enough that traditional quantum perturbation theory breaks down. If considering interactions in plasmas, the light field can be considered “strong” when the laser field strength is high enough that it dominates the thermal motion of electrons in the plasma. In both cases it is argued that the strong field regime begins at light intensity near 1014 W/cm2. The chapter then goes on to recount a brief history of research in strong field high intensity laser physics, highlighting major achievements in the field since its inception with the initial pioneering publication by Keldysh on strong field atomic ionization. A historical overview of both the atomic-molecular and plasma physics aspects of the field are presented. The chapter concludes with some comments on mathematical notation employed throughout the book.

Utilizing theoretical models from the previous chapter on multiphoton, tunnelling and above-threshold ionization, this chapter presents models for the ionization and fragmentation of small molecules in strong laser fields. Ionization models from the strong field approximation and a molecular tunneling model are presented, augmented with considerations of the additional complications arising from multiatom systems such as vibrational excitation, multielectron effects and molecular alignment. Mechanisms for aligning a linear molecule in a moderate-intensity laser field are discussed, followed by a section scrutinizing the fate of molecular bonds in moderate fields. Aspects of molecular bond evolution such as bond softening and above-threshold dissociation are explored using the Floquet theory of quantum systems in strong fields. The final portion of the chapter describes the dynamics of Coulomb explosions of diatomic molecules subsequent to laser field ionization, and the critical ionization atomic separation distance at which field ionization is enhanced. A concluding section considers fragmentaion of polyatomic molecules.