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Interaction of Radiation with Matter

Ignacio Pérez-Juste and Olalla Nieto Faza

1.1 Introduction

The interaction of light with matter is at the basis of one of the primary participants in human perception, because a significant part of the cerebral cortex is dedicated to visual processing. This complex mechanism starts with the light-induced isomerization of a retinal molecule that triggers a messenger cascade to produce the transmission of a nerve impulse from the retina. And it is through sight that we gather most of our knowledge of our environment (sizes, colors, shapes, etc.).

However, the chemical properties of the visual pigments in our retinas, together with the structure of the eye, limit our perceptions to light wavelengths between 390 and 750 nm and objects larger than 0.1 mm. Application of our knowledge about the interaction of light with matter and the development of optical instruments allowed us very early to use optical devices to immensely expand the range of objects accessible to our study, from the organelles in cells to faraway galaxies. In parallel, the discovery of electromagnetic radiation outside of the visible range provided incentives and tools for the elaboration of unifying concepts about light and for a myriad of technological applications.

In this chapter, we summarize the main laws that govern the interaction of electromagnetic radiation with matter, and the way in which these laws can be applied to the different phenomena that can arise from this interaction. This information is necessarily limited, and will be developed in more detail as needed in each of the following chapters on specific techniques.

1.2 Spectroscopy: A Definition

Spectroscopy is the study of the interaction of electromagnetic radiation with matter involving either absorption, emission, or scattering of radiation by the system under study. Atomic and molecular spectra can provide detailed information about the structure and chemical properties of the system. Spectroscopic techniques are one of the main sources of molecular geometries, that is, bond lengths, bond angles, and torsion angles, and can also yield, as will be seen, significant information about molecular symmetry, energy level distributions, electron densities, or electric and magnetic properties [1-15].

Spectroscopy has been an essential tool in the development of models for atomic and molecular structure, prompting scientists to refine existing models to accurately reproduce the experimentally observed spacing between energy states. A dramatic example of this is the birth of quantum theory (to explain the discrete nature of electronic transitions in atoms) or the discovery of the element helium in the spectrum of the Sun, well before it was found on Earth [16-19]. Nowadays, spectroscopic tools are routinely used in quantitative and qualitative chemical analysis and in the characterization of new molecules and materials, and play an essential role in such diverse fields as the elaboration and testing of theoretical models, synthetic chemistry, the study of reaction mechanisms, or biochemistry and materials science [20-23].

Atomic and molecular spectroscopies are mainly related to the absorption or emission of electromagnetic radiation and the changes taking place in those systems as a consequence of the energy of the radiation. Diffraction methods, however, involve the wave nature of the radiation, and rely on the interpretation of the interference patterns between waves upon their encounter with obstacles of dimensions roughly close to their wavelength. When these waves correspond to electromagnetic waves in the X-ray region of the spectrum or particles such as electrons or neutrons, their wavelengths are similar to the spacing between atoms in condensed phases such as liquids or crystals and they can be employed to obtain useful information about the atomic positions in these materials. X-ray diffraction produced the key images for unraveling the double-helix structure of DNA, and is routinely used to elucidate the structure of large biomolecules, surfaces, or materials [24-26].

1.3 Electromagnetic Radiation

According to elementary physics, a charge is surrounded by an electric field, and a moving charge, that is, an electrical current, also generates a magnetic field. Besides this, accelerated charges emit electromagnetic radiation, while radiation accelerates charged particles. Maxwell's equations condense all these phenomena describing the dynamics of free charges and currents and providing the foundation of classical electromagnetic theory and the interaction of light and matter. These equations describe macroscopically the behavior of charges in electric and/or magnetic fields, both in vacuum and in materials. Among these, propagation of light in vacuum is easier to describe, since light in matter is constantly absorbed and re-emitted, so that the solution of Maxwell's equations in matter requires detailed knowledge about the structure of the material, a simplified model for the material, or some empirical information about the interaction between light and matter.

Solution of Maxwell's equations without sources (charges or currents) leads to the equation of a propagating electromagnetic wave [27]. Thus, electromagnetic radiation can be described as a wave phenomenon formed by the combination of electric (E) and magnetic (H) fields, which oscillate in phase orthogonal to each other and orthogonal to the direction of propagation as well. For a given direction of propagation, these two orthogonal fields can be oriented in any direction in the plane perpendicular to it. However, if restrictions are imposed on the oscillation planes of the wave, polarized radiation can be obtained. Thus, for a plane-polarized (also known as linearly polarized) wave traveling in the x direction, the electric and magnetic fields of the electromagnetic radiation given by

are always in the same two orthogonal planes. The plane of polarization is conventionally taken to be the plane containing the electric field (the xy plane in Figure 1.1) because, as seen below, radiation and matter usually interact through the electric component. E0 and H0 in the previous equations correspond to the amplitudes, that is, the maximum values of the electric and magnetic fields, respectively.

Figure 1.1 Plane-polarized electromagnetic radiation.

The radiation wavelength, ?, can be defined as the distance between adjacent crests at a given point in time, and the frequency, ?, is the number of oscillations passing by a point in a given time (that is, the inverse of the wave period), usually with units of s-1 or Hz. The relation between frequency and wavelength is given by

where c is the velocity of propagation of the wave. In vacuum, c equals the speed of light (c0), but in general c = c0/n where n is the index of refraction of the propagation medium. For historical reasons, the use of the inverse of the wavelength is also very common in spectroscopy;

It is known as wavenumber and is usually given in units of cm-1.

Ondulatory and corpuscular theories of light coexisted and replaced each other since the seventeenth century, but the wave nature of the electromagnetic radiation was firmly established by Maxwell in the nineteenth century. However, at the beginning of the twentieth century Planck and Einstein showed that radiation also presents the properties of a particle. According to the corpuscular theory, electromagnetic radiation can be described as quantum energy packets named photons that possess an energy given by

where ? is the radiation frequency and h is Planck's constant.

Later, in 1924 de Broglie stated that if electromagnetic waves present properties associated with particles, the particles can also display wavelike properties and proposed that the wavelength of a particle behaving as a wave depends on its linear momentum, p, according to the expression

where m is the particle mass and v is its velocity. Further experiments of diffraction with electron beams confirmed the wavelike properties of particles, and nowadays neutron and electron diffraction techniques, such as X-ray diffraction, are used in laboratories all over the world for the characterization of materials.

According to the previous (1.6), electromagnetic radiation is considered to have a dual nature, as a wave and as a particle, which manifests in different phenomena. As will be seen below, the description of the interaction of light and matter in spectroscopic methods where radiation is absorbed or emitted is based on the corpuscular behavior of the radiation since photons are absorbed or emitted depending on their energy. Diffraction methods, however, are based on the wave behavior of radiation or on the wavelike properties of particles.

1.4 Electromagnetic Spectrum

Depending on its frequency or wavelength, an electromagnetic wave is included in one of the several regions in which the electromagnetic spectrum is divided. As can be seen in Table 1.1, the electromagnetic spectrum covers a large range of...