As outlined in the Introduction of this book, the theoretical description of light was revolutionized in the 1960s through the development of quantum optics
In this chapter we review the description of EM radiation in a wave and quantum picture. The quantum picture has its origin in Dirac’s quantization of the EM field in 1927 [1, 2], which is derived. The two pictures are equivalent in conventional quantum mechanics, which supports a wave-particle ambiguity. In the past, this has led to the widespread use of a “semi-classical” description of light that combines aspects of both descriptions. The fundamentals of the wave and particle concepts reviewed here serve as the basis for later chapters.
In modern x-ray science, the concept of brightness or brilliance plays an important role as a measure of the quality of x-ray sources. We intuitively associate brightness with the intensity that falls into the eye of an observer.
The previous three chapters, forming Part II of this book, described the interaction of x-rays with matter in terms of classical EM waves. The classical wave theory quantitatively yields the Thomson scattering cross section, and scattering and absorption are linked through the Kramers-Kronig formalism.
The Kramers-Heisenberg-Dirac (KHD) formalism has served the x-ray community well for the first 100+ years of x-ray science, and we shall see that it is valid even when the incident x-ray intensity is raised well above the level available at the brightest synchrotron radiation sources. The goal of this chapter is to explore when the KHD perturbation approach ceases to be a good description, and how the basic processes we refer to as x-ray absorption, x-ray scattering and x-ray diffraction change in this largely unchartered x-ray territory that has been opened by the advent of XFELs.
As the first application of the Kramers-Heisenberg-Dirac theory we discuss the quantitative calculation of the x-ray absorption rate and cross section. X-ray absorption spectroscopy (XAS) is so fundamental and important that we devote the next two chapters to its various aspects.
Following our discussion of XAS and its polarization dependence in the last two chapters we here continue with the discussion of two other important first order processes, namely x-ray emission spectroscopy (XES) and Thomson scattering, outlined in Sect. 9.5 and illustrated schematically in Fig. 9.4 b, c. X-ray emission is the inverse of the x-ray absorption process, and both can be described within KHD theory by transitions between two states. The interaction Hamiltonian for the two processes is the same, given by $$ \mathcal{H}_{int}=- e \, \textbf{r} \!\cdot \!\textbf{E}$$ in ( 9.22 ).
In contrast to conventional light, x-rays have allowed us to see the invisible. Invisibility may be caused by the lack of penetration of visible light, preventing us to see below the outermost skin of matter. It also comes in the form of objects that are smaller than the wavelength of visible light, due to the diffraction limit.
InYoung’ double slit, quantum formulation Diffraction, QED description this chapter we discuss an entirely quantum mechanical description of diffraction. We will introduce the remarkably simple new paradigm that diffraction patterns, long associated with wave interference, are instead direct signatures of the quantum states of light. In first order QED (corresponding to conventional quantum mechanics) this link has remained hidden leading to the wave-photon ambiguity. The ambiguity is shown to disappear in second order QED, where only the photon-based description can account for the observed diffraction patterns.
In the previous chapter we discussed the classical description of x-rays with the key building blocks of the electromagnetic (EM) world, electrons, spins, and atoms. Here we extend this treatment to materials. We start by discussing the static response of materials to electric and magnetic fields and then discuss how the static concepts can be extended to include frequency dependent fields.
This chapter is devoted to the quantum formulation of the phenomenon of x-ray dichroism, i.e. the polarization dependence of resonant core to valence transitions. In quantum theory, the four types of polarization dependent absorption effects, XNLD, XMLD, XNCD, and XMCD, whose historical development has been outlined.
